## Championship Experience Matters! (Super Bowl Edition)

To complete “Championship Week” at Skeptical Sports, I thought I’d post a little fun research I did before this year’s Super Bowl.

Like basketball, teams with championship-winning experience outperform their regular-season records in the playoffs, especially if they make it to the Super Bowl.

So, a bit like my 5-by-5 model, I wanted to come up with a simple metric for picking the Super Bowl winner. Unlike its NBA cousin, however, this method only applies to the championship game, not to the entire playoffs. The main question is, how much better does a team with more Super Bowl winning experience do than it’s opponent?

I feel bad about my text/graphs ratio this week, so I thought I’d tell this story in pictures. Before testing the question, we need to pick the best time period. So, for what number of years does the metric “pick the team with the most super bowl wins” most often pick the ultimate winner:

This was a little surprising to me already: I thought for sure the best n would be a small number, but it turns out to be 6.

Counting 2012, there have been 26 Super Bowls where one team has won more championships in the previous 6 years than the other. Of those games, the team with the greater number has won 20, or 77% of the time—including the Giants. [True story: I was going to publish something on this research before this year’s Super Bowl, but, knowing that it predicted a New York win against the heavily favored Patriots, I chickened out.]

Of course, I’m sure most of you are just itching to pounce right now: Clearly the team with the most recent Super Bowl wins is usually going to be better, right? So clearly this must be confounding this result. So let’s compare it to the predictive accuracy of SRS (Simple Rating System, aka “Margin of Victory adjusted for Strength of Schedule”):

Looking at all 46 Super Bowls, the team with the higher SRS has won 26, or 57%. In Super Bowls where no team had more Super Bowl wins, SRS performs slightly better, correctly picking 12/20 (60%). But the real story is in the games where both had something to say: When SRS and L6 agreed, the team they both picked won 11/14 (79%). But when SRS and L6 disagreed—in other words, where one team had a higher SRS, but the other had more Super Bowl wins in the previous 6 years—the team with the paper qualifications lost to the team with the championship experience 9 of 12 times (75%).

Now, your next thought might be that the years when L6 trumped SRS were probably the years when the teams were very close. But you’d be wrong:

The average SRS difference in 9 years where the L6 team won is actually higher than in the 3 years when it lost!

So how much does L6 add overall? Well, let’s first create a simple method, a bit like 5-by-5:

1. If one team has more Super Bowl wins in the previous 6 years, pick them.
2. Otherwise, pick the team with the best SRS.

Following this method, you would correctly pick 32 of the 46 Super Bowls (70%), for a 10% improvement overall, despite step 1 only even applying in about half of the games (also, note that if you just picked randomly in the 20 Super Bowls where L6 doesn’t apply, you would still be expected to get 30 right overall).

Finally, to try to quantify the difference in predictive value between the two measures, I plugged them both into a logistic regression:

As you can see, L6 is much more predictive, though the 95% confidence intervals do overlap. (Though I should also note, this last chart is based on the regression I ran prior to this year’s game, which ended up being another victory for the championship experience side.)

## Championship Experience Matters! (Un-Sexy Version)

So in Monday’s post, I included my “5-by-5” method (I probably shouldn’t call it a “model”) for picking NBA champions. In case you missed it, here it is again:

1. If there are any teams within 5 games of the best record that have won a title within the past 5 years, pick the most recent winner.
2. Otherwise, pick the team with the best record.

In the 28 seasons since the NBA moved to a 16-team playoff format, this method correctly picked the eventual champion 18 times (64%), comparing favorably to the 10/28 (36%) success rate of the team with the league’s best record.

Henry Abbott blogged about it on ESPN yesterday, raising the obvious follow-up:

The question is, why? Why are teams that have won before so much better at winning again? I’ll kick off the brainstorming:

• Maybe most teams fall short of their potential because of team dynamics of selfishness — and maybe champions are the teams that know how to move past that.
• Maybe there are only a few really special coaches, and these teams have them.
• Maybe there are only a few really special teams, and these teams are them.
• Maybe there are special strategies to the playoffs that only some teams know. Not even sure what I’m talking about here — Sleep schedules? Nutrition? Injury prevention?
• Maybe champions get better treatment from referees.

Anyway, it’s certainly fascinating.

UPDATE: John Hollinger with a good point that fits this and other data: Maybe title-winning team don’t value the regular season much.

Though I think some of these ideas are more on point than others, I won’t try to go parse every possibility. On balance, I’m sympathetic to the idea that “winning in the playoffs” has its own skillset independent of just being good at winning basketball games. Conceptually, it’s not too big a leap from the well-documented idea that winning games has its own skillset independent of scoring and allowing points (though the evidence is a lot more indirect).

That said, I think the biggest factor behind this result may be a bit less sexy: It may simply be a matter of information reliability.

### Winning Championships is Harder than Winning Games

In stark contrast to other team sports, the NBA Playoffs are extremely deterministic. The best team usually wins (and, conversely, the winner is usually the best team). I’ve made this analogy many times before, but I’ll make it again: The NBA playoffs are a lot more like a Major tournament in men’s tennis than any other crowning competition in popular sports.

This is pretty much a function of design: A moderately better team becomes a huge favorite in a 7 game series. So even if the best team is only moderately better than the 2nd best team, they can be in a dominant position.

Combine this with an uneven distribution of talent (which, incidentally, is probably a function of salary structure), and mix in the empirical reality that the best teams normally don’t change very much from year to year, and its unsurprising that “dynasties” are so common.

On the other side of the equation, regular season standings and leaderboards—whether of wins or its most stable proxies—are highly variable. Note that a 95% confidence interval on an 82 game sample (aka, the “margin of error”) is +/- roughly 10 games.

If you think of the NBA regular season as a lengthy 30-team competition for the #1 seed, its structure is much, much less favorable to the best teams than the playoffs: It’s more like a golf tournament than a tennis tournament.

### The Rest is Bayes

Obviously better teams win more often and vice-versa. It’s just that these results have to be interpreted in a context where all results were not equally likely ex ante. For example, the teams who post top records who also have recent championships are far more likely than others to actually be as good as their records indicate. This is pure bayesian inference.

Quick tangent: In my writing, I often reach a point where I say something along the lines of: “From there, it’s all bayesian inference.” I recognize that, for a lot of readers, this is barely a step up from an Underpants Gnomes argument. When I go there, it’s pretty much shorthand for “this is where results inform our beliefs about how likely various causes are to be true” (and all that entails).

There was an interesting comment on Abbott’s ESPN post, pointing out that the 5-by-5 method only picked 5/14 (35.7%) of champions correctly between 1967 and 1980. While there may be unrelated empirical reasons for this, I think this stat may actually confirm the underlying concept. Structurally, having fewer teams in the playoffs, shorter series lengths, a smaller number of teams in the league—basically any of the structural differences between the two eras I can think of—all undermine the combined informational value of [having a championship + having a top record].

To be fair, there may be any number of things in a particular season that undermine our confidence in this inference (I can think of some issues with this season’s inputs, obv). That’s the tricky part of bayesian reasoning: It turns on how plausible you thought things were already.

## Stat Geek Smackdown 2012, Round 1: Odds and Ends

So in case any of you haven’t been following, the 2012 edition of the ESPN True Hoop Stat Geek Smackdown  is underway.  Now, obviously this competition shouldn’t be taken too seriously, as it’s roughly the equivalent of picking a weekend’s worth of NFL games, and last year I won only after picking against my actual opinion in the Finals (with good reason, of course).  That said, it’s still a lot of fun to track, and basketball is a deterministic-enough sport that I do think skill is relevant. At least enough that I will talk shit if I win again.

To that end, the first round is going pretty well for me so far.  Like last year, the experts are mostly in agreement. While there is a fair amount of variation in the series length predictions, there are only two matchups that had any dissent as to the likely winner: the 6 actual stat geeks split 4-2 in favor of the Lakers over the Nuggets, and 3-3 between the Clippers and the Grizzlies.  As it happens, I have both Los Angeles teams (yes, I am from Homer), as does Matthew Stahlhut (though my having the Lakers in 5 instead of 7 gives me a slight edge for the moment).  No one has gained any points on anyone else yet, but here is my rough account of possible scenarios:

On to some odds and ends:

## The Particular Challenges of Predicting 2012

Making picks this year was a bit harder than in years past.  At one point I seriously considered picking Dallas against OKC (in part for strategic purposes), before reason got the better of me.  Abbott only published part of my comment on the series, so here’s the full version I sent him:

Throughout NBA history, defending champions have massively over-performed in the playoffs relative to their regular season records, so I wouldn’t count Dallas out.  In fact, the spot Dallas finds itself in is quite similar to Houston’s in 1995, and this season’s short lead -time and compressed schedule should make us particularly wary of the usual battery of predictive models.

Thus, if I had to pick which of these teams is more likely to win the championship, I might take Dallas (or at least it would be a closer call).  But that’s a far different question from who is most likely to win this particular series: Oklahoma City is simply too solid and Dallas too shaky to justify an upset pick. E.g., my generic model makes OKC a >90% favorite, so even a 50:50 chance that Dallas really is the sleeping giant Mark Cuban dreams about probably wouldn’t put them over the top.

That last little bit is important: The “paper gap” between Dallas and OKC is so great that even if Dallas were considerably better than they appeared during the regular season, that would only make them competitive, while if they were about as good as they appeared, they would be a huge dog (this kind of situation should be very familiar to any serious poker players out there).

But why on earth would I think Dallas might be any good in the first place? Well, I’ll discuss more below why champions should never be ignored, but the “paper difference” this year should be particularly inscrutable.  The normal methods for predicting playoff performance (both my own and others) are particularly ill-suited for the peculiar circumstances of this season:

1. Perhaps most obviously, fewer regular season games means smaller sample sizes.  In turn, this means that sample-sensitive indicators (like regular season statistics) should have less persuasive value relative to non-sensitive ones (like championship pedigree).  It also affects things like head to head record, which is probably more valuable than a lot of stats people think, though less valuable than a lot of non-stats people think.  I’ve been working on some research about this, but for an example, look at this post about how I thought there seemed to be a market error w/r/t Dallas vs. Miami in game 6, partly b/c of the bayesian value of Dallas’s head to head advantage.
2. Injuries are a bigger factor. This is not just that there are more of them (which is debatable), but there is less flexibility to effectively manage them: e.g., there’s obv less time to rehab players, but also less time to develop new line-ups and workarounds or make other necessary adjustments. In other words, a very good team might be hurt more by a role-player being injured than usual.
3. What is the most reliable data? Two things I discussed last year were that (contra unconventional wisdom) Win% is more reliable for post-season predictions than MOV-type stats, and that (contra conventional wisdom) early season performance is typically more predictive than late season performance.  But both of these are undermined by the short season.  The fundamental value of MOV is as a proxy for W% that is more accurate for smaller sample sizes. And the predictive power of early-season performance most likely stems from its being more representative of playoff basketball: e.g., players are more rested and everyone tries their hardest.  However, not only are these playoffs not your normal playoffs, but this season was thrown together so quickly that a lot of teams had barely figured out their lineups by the quarter-pole. While late-season records have the same problems as usual, they may be more predictive just from being more similar to years past.
4. Finally, it’s not just the nature of the data, but the nature of the underlying game as well. For example, in a lockout year, teams concerned with injury may be quicker to pull starting players in less lopsided scenarios than usual, making MOV less useful, etc. I won’t go into every possible difference, but here’s a related Twitter exchange:

Which brings us to the next topic:

## The Simplest Playoff Model You’ll Never Beat

The thing that Henry Abbott most highlighted from my Smackdown picks (which he quoted at least 3 times in 3 different places) was my little piece of dicta about the Spurs:

I have a ‘big pot’ playoff model (no matchups, no simulations, just stats and history for each playoff team as input) that produces some quirky results that have historically out-predicted my more conventional models. It currently puts San Antonio above 50 percent. Not just against Utah, but against the field. Not saying I believe it, but there you go.

I really didn’t mean for this to be taken so seriously: it’s just one model.  And no, I’m not going to post it. It’s experimental, and it’s old and needs updating (e.g., I haven’t adjusted it to account for last season yet).

But I can explain why it loves the Spurs so much: it weights championship pedigree very strongly, and the Spurs this year are the only team near the top that has any.

Now some stats-loving people argue that the “has won a championship” variable is unreliable, but I think they are precisely wrong.  Perhaps this will change going forward, but, historically, there are no two ways to cut it: No matter how awesomely designed and complicated your models/simulations are, if you don’t account for championship experience, you will lose to even the most rudimentary model that does.

So case in point, I came up with this 2-step method for picking NBA Champions:

1. If there are any teams within 5 games of the best record that have won a title within the past 5 years, pick the most recent.
2. Otherwise, pick the team with the best record.

Following this method, you would correctly pick the eventual NBA Champion in 64.3% of years since the league moved to a 16-team playoff in 1984 (with due respect to the slayer, I call this my “5-by-5” model ).

Of course, thinking back, it seems like picking the winner is sometimes easy, as the league often has an obvious “best team” that is extremely unlikely to ever lose a 7 game series.  So perhaps the better question to ask is: How much do you gain by including the championship test in step 1?

The answer is: a lot. Over the same period, the team with the league’s best record has won only 10/28 championships, or ~35%. So the 5-by-5 model almost doubles your hit rate.

And in case you’re wondering, using Margin of Victory, SRS, or any other advanced stat instead of W-L record doesn’t help: other methods vary from doing slightly worse to slightly better. While there may still be room to beef up the complexity of your predictive model (such as advanced stats, situational simulations, etc), your gains will be (comparatively) marginal at best. Moreover, there is also room for improvement on the other side: by setting up a more formal and balanced tradeoff between regular season performance and championship history, the macro-model can get up to 70+% without danger of significant over-fitting.

In fairness, I should note that the 5-by-5 model has had a bit of a rough patch recently—but, in its defense, so has every other model. The NBA has had some wacky results recently, but there is no indication that stats have supplanted history. Indeed, if you break the historical record into groups of more-predictable and less-predictable seasons, the 5-by-5 model trumps pure statistical models in all of them.

## Uncertainty and Series Lengths

Finally, I’d like to quickly address the complete botching of series-length analysis that I put forward last year. Not only did I make a really elementary mistake in my explanation (that an emailer thankfully pointed out), but I’ve come to reject my ultimate conclusion as well.

Aside from strategic considerations, I’m now fairly certain that picking the home team in 5 or the away team in 6 is always right, no matter how close you think the series is. I first found this result when running playoff simulations that included margin for error (in other words, accounting for the fact that teams may be better or worse than their stats would indicate, or that they may match up more or less favorably than the underlying records would suggest), but I had some difficulty getting this result to comport with the empirical data, which still showed “home team in 6” as the most common outcome.  But now I think I’ve figured this problem out, and it has to do with the fact that a lot of those outcomes came in spots where you should have picked the other team, etc. But despite the extremely simple-sounding outcome,  it’s a rich and interesting topic, so I’ll save the bulk of it for another day.

## Sports Geek Mecca: Recap and Thoughts, Part 1

So, over the weekend, I attended my second MIT Sloan Sports Analytics Conference. My experience was much different than in 2011: Last year, I went into this thing barely knowing that other people were into the same things I was. An anecdote: In late 2010, I was telling my dad how I was about to have a 6th or 7th round interview for a pretty sweet job in sports analysis, when he speculated, “How many people can there even be in that business? 10? 20?” A couple of months later, of course, I would learn.

A lot has happened in my life since then: I finished my Rodman series, won the ESPN Stat Geek Smackdown (which, though I am obviously happy to have won, is not really that big a deal—all told, the scope of the competition is about the same as picking a week’s worth of NFL games), my wife and I had a baby, and, oh yeah, I learned a ton about the breadth, depth, and nature of the sports analytics community.

For the most part, I used Twitter as sort of my de facto notebook for the conference.  Thus, I’m sorry if I’m missing a bunch of lengthier quotes and/or if I repeat a bunch of things you already saw in my live coverage, but I will try to explain a few things in a bit more detail.

For the most part, I’ll keep the recap chronological.  I’ve split this into two parts: Part 1 covers Friday, up to but not including the Bill Simmons/Bill James interview.  Part 2 covers that interview and all of Saturday.

## Opening Remarks:

From the pregame tweets, John Hollinger observed that 28 NBA teams sent representatives (that we know of) this year.  I also noticed that the New England Revolution sent 2 people, while the New England Patriots sent none, so I’m not sure that number of official representatives reliably indicates much.

The conference started with some bland opening remarks by Dean David Schmittlein.  Tangent: I feel like political-speak (thank everybody and say nothing) seems to get more and more widespread every year. I blame it on fear of the internet. E.g., in this intro segment, somebody made yet another boring joke about how there were no women present (personally, I thought there were significantly more than last year), and was followed shortly thereafter by a female speaker, understandably creating a tiny bit of awkwardness. If that person had been more important (like, if I could remember his name to slam him), I doubt he would have made that joke, or any other joke. He would have just thanked everyone and said nothing.

## The Evolution of Sports Leagues

Featuring Gary Bettman (NHL), Rob Manfred (MLB), Adam Silver (NBA), Steve Tisch (NYG) and Michael Wilbon moderating.

This panel really didn’t have much of a theme, it was mostly Wilbon creatively folding a bunch of predictable questions into arbitrary league issues.  E.g.: ” “What do you think about Jeremy Lin?!? And, you know, overseas expansion blah blah.”

I don’t get the massive cultural significance of Jeremy Lin, personally.  I mean, he’s not the first ethnically Chinese player to have NBA success (though he is perhaps the first short one).  The discussion of China, however, was interesting for other reasons. Adam Silver claimed that Basketball is already more popular in China than soccer, with over 300 million Chinese people playing it.  Those numbers, if true, are pretty mind-boggling.

Finally, there was a whole part about labor negotiations that was pretty well summed up by this tweet:

## Hockey Analytics

Featuring Brian Burke, Peter Chiarelli, Mike Milbury and others.

The panel started with Peter Chiarelli being asked how the world champion Boston Bruins use analytics, and in an ominous sign, he rambled on for a while about how, when it comes to scouting, they’ve learned that weight is probably more important than height.

Overall, it was a bit like any scene from the Moneyball war room, with Michael Schuckers (the only pro-stats guy) playing the part of Jonah Hill, but without Brad Pitt to protect him.

When I think of Brian Burke, I usually think of Advanced NFL Stats, but apparently there’s one in Hockey as well.  Burke is GM/President of the Toronto Maple Leafs. At one point he was railing about how teams that use analytics have never won anything, which confused me since I haven’t seen Toronto hoisting any Stanley Cups recently, but apparently he did win a championship with the Mighty Ducks in 2007, so he clearly speaks with absolute authority.

This guy was a walking talking quote machine for the old school. I didn’t take note of all the hilarious and/or non-sensical things he said, but for some examples, try searching Twitter for “#SSAC Brian Burke.” To give an extent of how extreme, someone tweeted this quote at me, and I have no idea if he actually said it or if this guy was kidding.

In other words, Burke was literally too over the top to effectively parody.

On the other hand, in the discussion of concussions, I thought Burke had sort of a folksy realism that seemed pretty accurate to me.  I think his general point is right, if a bit insensitive: If we really changed hockey so much as to eliminate concussions entirely, it would be a whole different sport (which he also claimed no one would watch, an assertion which is more debatable imo).  At the end of the day, I think professional sports mess people up, including in the head.  But, of course, we can’t ignore the problem, so we have to keep proceeding toward some nebulous goal.

Mike Milbury, presently a card-carrying member of the media, seemed to mostly embrace the alarmist media narrative, though he did raise at least one decent point about how the increase in concussions—which most people are attributing to an increase in diagnoses—may relate to recent rules changes that have sped up the game.

But for all that, the part that frustrated me the most was when Michael Schuckers, the legitimate hockey statistician at the table, was finally given the opportunity to talk.  90% of the things that came out of his mouth were various snarky ways of asserting that face-offs don’t matter.  I mean, I assume he’s 100% right, but just had no clue how to talk to these guys.  Find common ground: you both care about scoring goals, defending goals, and winning.  Good face-off skill get you the puck more often in the right situations. The question is how many extra possessions you get and how valuable those possessions are? And finally, what’s the actual decision in question?

## Baseball Analytics

Featuring Scott Boras, Scott Boras, Scott Boras, some other guys, Scott Boras, and, oh yeah, Bill James.

In stark constrast to the Hockey panel, the Baseball guys pretty much bent over backwards to embrace analytics as much as possible.  As I tweeted at the time:

Scott Boras seems to like hearing Scott Boras talk.  Which is not so bad, because Scott Boras actually did seem pretty smart and well informed: Among other things, Scott Boras apparently has a secret internal analytics team. To what end, I’m not entirely sure, since Scott Boras also seemed to say that most GM’s overvalue players relative to what Scott Boras’s people tell Scott Boras.

At this point, my mind wandered:

How awesome would that be, right?

Anyway, in between Scott Boras’s insights, someone asked this Bill James guy about his vision for the future of baseball analytics, and he gave two answers:

1. Evaluating players from a variety of contexts other than the minor leagues (like college ball, overseas, Cubans, etc).
2. Analytics will expand to look at the needs of the entire enterprise, not just individual players or teams.

Meh, I’m a bit underwhelmed.  He talked a bit about #1 in his one-on-one with Bill Simmons, so I’ll look at that a bit more in my review of that discussion. As for #2, I think he’s just way way off: The business side of sports is already doing tons of sophisticated analytics—almost certainly way more than the competition side—because, you know, it’s business.

E.g., in the first panel, there was a fair amount of discussion of how the NBA used “sophisticated modeling” for many different lockout-related analyses (I didn’t catch the Ticketing Analytics panel, but from its reputation, and from related discussions on other panels, it sounds like that discipline has some of the nerdiest analysis of all).

Scott Boras let Bill James talk about a few other things as well:  E.g., James is not a fan of new draft regulations, analogizing them to government regulations that “any economist would agree” inevitably lead to market distortions and bursting bubbles.  While I can’t say I entirely disagree, I’m going to go out on a limb and guess that his political leanings are probably a bit Libertarian?

Featuring Jeff Van Gundy, Mike Zarren, John Hollinger, and Mark Cuban Dean Oliver.

If every one of these panels was Mark Cuban + foil, it would be just about the most awesome weekend ever (though you might not learn the most about analytics). So I was excited about this one, which, unfortunately, Cuban missed. Filling in on zero/short notice was Dean Oliver.  Overall, here’s Nathan Walker’s take:

This panel actually had some pretty interesting discussions, but they flew by pretty fast and often followed predictable patterns, something like this:

1. Hollinger says something pro-stats, though likely way out of his depth.
2. Zarren brags about how they’re already doing that and more on the Celtics.
3. Oliver says something smart and nuanced that attempts to get at the underlying issues and difficulties.
4. Jeff Van Gundy uses forceful pronouncements and “common sense” to dismiss his strawman version of what the others have been saying.

E.g.:

Zarren talked about how there is practically more data these days than they know what to do with.  This seems true and I think it has interesting implications. I’ll discuss it a little more in Part 2 re: the “Rebooting the Box Score” talk.

There was also an interesting discussion of trades, and whether they’re more a result of information asymmetry (in other words, teams trying to fleece each other), or more a result of efficient trade opportunities (in other words, teams trying to help each other).  Though it really shouldn’t matter—you trade when you think it will help you, whether it helps your trade partner is mostly irrelevant—Oliver endorsed the latter.  He makes the point that, with such a broad universe of trade possibilities, looking for mutually beneficial situations is the easiest way to find actionable deals.  Fair enough.

## Coaching Analytics

Featuring coaching superstars Jeff Van Gundy, Eric Mangini, and Bill Simmons.  Moderated by Daryl Morey.

OK, can I make the obvious point that Simmons and Morey apparently accidentally switched role cards?  As a result, this talk featured a lot of Simmons attacking coaches and Van Gundy defending them.  I honestly didn’t remember Mangini was on this panel until looking back at the book (which is saying something, b/c Mangini usually makes my blood boil).

There was almost nothing on, say, how to evaluate coaches, say, by analyzing how well their various decisions comported with the tenets of win maximization.  There was a lengthy (and almost entirely non-analytical) discussion of that all-important question of whether an NBA coach should foul or not up by 3 with little time left.  Fouling probably has a tiny edge, but I think it’s too close and too infrequent to be very interesting (though obviously not as rare, it reminds me a bit of the impassioned debates you used to see on Poker forums about whether you should fast-play or slow-play flopped quads in limit hold’em).

There was what I thought was a funny moment when Bill Simmons was complaining about how teams seem to recycle mediocre older coaches rather than try out young, fresh talent. But when challenged by Van Gundy, Simmons drew a blank and couldn’t think of anyone.  So, Bill, this is for you.  Here’s a table of NBA coaches who have coached at least 1000 games for at least 3 different teams, while winning fewer than 60% of their games and without winning any championships:

Note that I’m not necessarily agreeing with Simmons: Winning championships in the NBA is hard, especially if your team lacks uber-stars (you know, Michael Jordan, Magic Johnson, Dennis Rodman, et al).

## Part 2 coming soon!

Honestly, I got a little carried away with my detailed analysis/screed on Bill James, and I may have to do a little revising. So due to some other pressing writing commitments, you can probably expect Part 2 to come out this Saturday (Friday at the earliest).

## Graph of the Day: Quarterbacks v. Coaches, Draft Edition

[Note: With the recent amazing addition to my office, I’ve considered just turning this site into a full-on baby photo-blog (much like my Twitter feed).  While that would probably mean a more steady stream of content, it would also probably require a new name, a re-design, and massive structural changes.  Which, in turn, would raise a whole bevy of ontological issues that I’m too tired to deal with at the moment. So I guess back to sports analysis!]

In “A History of Hall of Fame QB-Coach Entanglement,” I talked a bit about the difficulty of “detangling” QB and coach accomplishments.  For a slightly more amusing historical take, here’s a graph illustrating how first round draft picks have gotten a much better return on investment (a full order of magnitude better vs. non-#1 overalls) when traded for head coaches than when used to draft quarterbacks:

Note: Since 1950. List of #1 Overall QB’s is here.  Other 1st Round QB’s here.  Other drafted QB’s here.  Super Bowl starters here.  QB’s that were immediately traded count for the team that got them.

Note*: . . that I know of. I googled around looking for coaches that cost their teams at least one first round draft pick to acquire, and I could only find 3: Bill Parcells (Patriots -> Jets), Bill Belichick (Jets -> Patriots), and Jon Gruden (Raiders -> Bucs).  If I’m missing anyone, please let me know.

Sample, schmample.

But seriously, the other 3 bars are interesting too.

## Thoughts on the Packers Yardage Anomaly

In their win over Detroit on Sunday, Green Bay once again managed to emerge victorious despite giving up more yards than they gained. This is practically old hat for them, as it’s the 10th time that they’ve done it this year. Over the course of the season, the 15-1 Packers gave up a stunning 6585 yards, while gaining “just” 6482—thus losing the yardage battle despite being the league’s most dominant team.

This anomaly certainly captures the imagination, and I’ve received multiple requests for comment.  E.g., a friend from my old poker game emails:

Just heard that the Packers have given up more yards than they’ve gained and was wondering how to explain this.  Obviously the Packers’ defense is going to be underrated by Yards Per Game metrics since they get big leads and score quickly yada yada, but I don’t see how this has anything to do with the fact they’re being outgained.  I assume they get better starting field position by a significant amount relative to their opponents so they can have more scoring drives than their opponents while still giving up more yards than they gain, but is that backed up by the stats?

Last week Advanced NFL Stats posted a link to this article from Smart Football looking into the issue in a bit more depth. That author does a good job examining what this stat means, and whether or not it implies that Green Bay isn’t as good as they seem (he more or less concludes that it doesn’t).

But that doesn’t really answer the question of how the anomaly is even possible, much less how or why it came to be.  With that in mind, I set out to solve the problem.  Unfortunately, after having looked at the issue from a number of angles, and having let it marinate in my head for a week, I simply haven’t found an answer that I find satisfying.  But, what the hell, one of my resolutions is to pull the trigger on this sort of thing, so I figure I should post what I’ve got.

# How Anomalous?

The first thing to do when you come across something that seems “crazy on its face” is to investigate how crazy it actually is (frequently the best explanation for something unusual is that it needs no explanation).  In this case, however, I think the Packers’ yardage anomaly is, indeed, “pretty crazy.”  Not otherworldly crazy, but, say, on a scale of 1 to “Kurt Warner being the 2000 MVP,” it’s at least a 6.

First, I was surprised to discover that just last year, the New England Patriots also had the league’s best record (14-2), and also managed to lose the yardage battle.  But despite such a recent example of a similar anomaly, it is still statistically pretty extreme.  Here’s a plot of more or less every NFL team season from 1936 through the present, excluding seasons where the relevant stats weren’t available or were too incomplete to be useful (N=1647):

The green diamond is the Packers net yardage vs. Win%, and the yellow triangle is their net yardage vs. Margin of Victory (net points).  While not exactly Rodman-esque outliers, these do turn out to be very historically unusual:

## Win %

Using the trendline equation on the graph above (plus basic algebra), we can use a team’s season Win percentage to calculate their expected yardage differential.  With that prediction in hand, we can compare how much each team over or under-performed its “expectation”:

Both the 2011 Packers and the 2010 Patriots are in the top 5 all-time, and I should note that the 1939 New York Giants disparity is slightly overstated, because I excluded tie games entirely (ties cause problems elsewhere b/c of perfect correlation with MOV).

## Margin of Victory

Toward the conclusion of that Smart Football article, the author notes that Green Bay’s Margin of Victory isn’t as strong as their overall record, noting that the Packers “Pythagorian Record” (expectation computed from points scored and points allowed) is more like 11-5 or 12-4 than 15-1 (note that getting from extremely high Win % to very high MOV is incidental: 15-win teams are usually 11 or 12 win teams that have experienced good fortune).  Green Bay’s MOV of 12.5 is a bit lower than the historical average for 15-1 teams (13.8) but don’t let this mislead you: the disparity between the yardage differential that we would expect based on Green Bay’s MOV and their actual result (using a linear projection, as above) is every bit as extreme as what we saw from Win %:

And here, in histogram form:

So, while not the most unusual thing to ever happen in sports, this anomaly is certainly unusual enough to look into.

For the record, the Packers’ MOV -> yard diff error is 3.23 standard deviations above the mean, while the Win% -> yard diff is 3.28.  But since MOV correlates more strongly with the target stat (note an average error of only 125 yards instead of 170), a similar degree of abnormality leaves it as the more stable and useful metric to look at.

Thus, the problem can be framed as follows: The 2011 Packers fell around 2000 yards (the 125.7 above * 16 games) short of their expected yardage differential.  Where did that 2000 yard gap come from?

# Possible Factors and/or Explanations

Before getting started, I should note that, out of necessity, some of these “explanations” are more descriptive than actually explanatory, and even the ones that seem plausible and significant are hopelessly mixed up with one another.  At the end of the day, I think the question of “What happened?” is addressable, though still somewhat unclear.  The question of “Why did it happen?” remains largely a mystery: The most substantial claim that I’m willing to make with any confidence is that none of the obvious possibilities are sufficient explanations by themselves.

While I’m somewhat disappointed with this outcome, it makes sense in a kind of Fermi Paradox, “Why Aren’t They Here Yet?” kind of way.  I.e., if any of the straightforward explanations (e.g., that their stats were skewed by turnovers or “garbage time” distortions) could actually create an anomaly of this magnitude, we’d expect it to have happened more often.

And indeed, the data is actually consistent with a number of different factors (granted, with significant overlap) being present at once.

## Line of Scrimmage, and Friends

As suggested in the email above, one theoretical explanation for the anomaly could be the Packers’ presumably superior field position advantage.  I.e., with their offense facing comparatively shorter fields than their opponents, they could have literally had fewer yards available to gain.  This is an interesting idea, but it turns out to be kind of a bust.

The Packers did enjoy a reciprocal field position advantage of about 5 yards.  But, unfortunately, there doesn’t seem to be a noticeable relationship between average starting field position and average yards gained per drive (which would have to be true ex ante for this “explanation” to have any meaning):

Note: Data is from the Football Outsiders drive stats.

This graph plots both offenses and defenses from 2011.  I didn’t look at more historical data, but it’s not really necessary: Even if a larger dataset revealed a statistically significant relationship, the large error rate (which converges quickly) means that it couldn’t alter expectation in an individual case by more than a fraction of a yard or so per possession.  Since Green Bay only traded 175ish possessions this season, it couldn’t even make a dent in our 2000 missing yards (again, that’s if it existed at all).

On the other hand, one thing in the F.O. drive stats that almost certainly IS a factor, is that the Packers had a net of 10 fewer possessions this season than their opponents.  As Green Bay averaged 39.5 yards per possession, this difference alone could account for around 400 yards, or about 20% of what we’re looking for.

Moreover, 5 of those 10 possessions come from a disparity in “zero yard touchdowns,” or net touchdowns scored by their defense and special teams: The Packers scored 7 of these (5 from turnovers, 2 from returns) while only allowing 2 (one fumble recovery and one punt return).  Such scores widen a team’s MOV without affecting their total yardage gap.

[Warning: this next point is a bit abstract, so feel free to skip to the end.] Logically, however, this doesn’t quite get us where we want to go.  The relevant question is “What would the yardage differential have been if the Packers had the same number of possessions as their opponents?”  Some percentage of our 10 counterfactual drives would result in touchdowns regardless.  Now, the Packers scored touchdowns on 37% of their actual drives, but scored touchdowns on at least 50% of their counterfactual drives (the ones that we can actually account for via the “zero yard touchdown” differential).  Since touchdown drives are, on average, longer than non-touchdown drives, this means that the ~400 yards that can be attributed to the possession gap is at least somewhat understated.

## Garbage Time

When considering this issue, probably the first thing that springs to minds is that the Packers have won a lot of games easily.  It seems highly plausible that, having rushed out to so many big leads, the Packers must have played a huge amount of “garbage time,” in which their defense could have given up a lot of “meaningless” yards that had no real consequence other than to confound statisticians.

The proportion of yards on each side of the ball that came after Packers games got out of hand should be empirically checkable—but, unfortunately, I haven’t added 2011 Play-by-Play data to my database yet.  That’s okay, though, because there are other ways—perhaps even more interesting ways—to attack the problem.

In fact, it’s pretty much right up my alley: Essentially, what we are looking for here is yet another permutation of “Reverse Clutch” (first discussed in my Rodman series, elaborated in “Tim Tebow and the Taxonomy of Clutch”). Playing soft in garbage time is a great way for a team to “underperform” in statistical proxies for true strength.  In football, there are even a number of sound tactical and strategic reasons why you should explicitly sacrifice yards in order to maximize your chances of winning.  For example, if you have a late lead, you should be more willing to soften up your defense of non-sideline runs and short passes—even if it means giving up more yards on average than a conventional defense would—since those types of plays hasten the end of the game.  And the converse is true on offense:  With a late lead, you want to run plays that avoid turnovers and keep the clock moving, even if it means you’ll be more predictable and easier to defend.

So how might we expect this scenario to play out statistically?  Recall, by definition, “clutch” and “reverse clutch” look the same in a stat sheet.  So what kind of stats—or relationships between stats—normally indicate “clutchness”?  As it turns out, Brian Burke at Advanced NFL Stats has two metrics pretty much at the core of everything he does: Expected Points Added, and Win Percentage Added.  The first of these (EPA) takes the down and distance before and after each play and uses historical empirical data to model how much that result normally affects a team’s point differential.  WPA adds time and score to the equation, and attempts to model the impact each play has on the team’s chances of winning.

A team with “clutch” results—whether by design or by chance—might be expected to perform better in WPA (which ultimately just adds up to their number of wins) than in EPA (which basically measures generic efficiency).

For most aspects of the game, the relationship between these two is strong enough to make such comparisons possible.  Here are plots of this comparison for each of the 4 major categories (2011 NFL, Green Bay in green), starting with passing offense (note that the comparison is technically between wins added overall and expected points per play):

And here’s passing defense:

Rushing offense:

And rushing defense:

Obviously there’s nothing strikingly abnormal about Green Bay’s results in these graphs, but there are small deviations that are perfectly consistent with the garbage time/reverse clutch theory.  For the passing game (offense and defense), Green Bay seems to hew pretty close to expectation.  But in the rushing game they do have small but noticeable disparities on both sides of the ball.  Note that in the scenario I described where a team intentionally trades efficiency for win potential, we would expect the difference to be most acute in the running game (which would be under-defended on defense and overused on offense).

Specifically: Green Bay’s offensive running game has a WPA of 1.1, despite having an EPA per play of zero (which corresponds to a WPA of .25).  On defense, the Packers’ EPA/p is .07, which should correspond to an expected WPA of 1.0, while their actual result is .59.

Clearly, both of these effects are small, considering there isn’t a perfect correlation.  But before dismissing them entirely, I should note that we don’t immediately know how much of the variation in the graphs above is due to variance for a given team and how much is due to variation between teams.  Moreover, without knowing the balance, the fact that both variance and variation contribute to the “entropy” of the observed relationship between EPA/p and WPA, the actual relationship between the two is likely to be stronger than these graphs would make it seem.

The other potential problem is that this comparison is between wins and points, while the broader question is comparing points to yards.  But there’s one other statistical angle that helps bridge the two, while supporting the speculated scenario to boot: Green Bay gained 3.9 yards per attempt on offense, and allowed 4.7 yards per attempt on defense—while the league average is 4.3 yards per attempt.  So, at least in terms of raw yardage, Green Bay performed “below average” in the running game by about .4 yards/attempt on each side of the ball.  Yet, the combined WPA for the Packers running game is positive! Their net rushing WPA is +.5, despite having an expected combined WPA (actually based on their EPA) of -.75.

So, if we thought this wasn’t a statistical artifact, there would be two obvious possible explanations: 1) That Green Bay has a sub-par running game that has happened to be very effective in important spots, or 2) that Green Bay actually has an average (or better) running game that has appeared ineffective (especially as measured by yards gained/allowed) in less important spots. Q.E.D.

For the sake of this analysis, let’s assume that the observed difference for Green Bay here really is a product of strategic adjustments stemming from (or at least related to) their winning ways, how much of our 2000 yard disparity could it account for?

So let’s try a crazy, wildly speculative, back-of-the-envelope calculation: Give Green Bay and its opponents the same number of rushing attempts that they had this season, but with both sides gaining an average number of yards per attempt.  The Packers had 395 attempts and their opponents had 383, so at .4 yards each, the yardage differential would swing by 311 yards.  So again, interesting and plausibly significant, but doesn’t even come close to explaining our anomaly on its own.

## Turnover Effect?

One of the more notable features of the Packers season is their incredible +22 turnover margin.  How they managed that and whether it was simply variance or something more meaningful could be its own issue.  But in this context, give them the +22, how helpful is that as an explanation for the yardage disparity?  Turnovers affect scores and outcomes a ton, but are relatively neutral w/r/t yards, so surely this margin is relevant.  But exactly how much does it neutralize the problem?

Here, again, we can look at the historical data.  To predict yardage differential based on MOV and turnover differential, we can set up an extremely basic linear regression:

The R-Square value of .725 means that this model is pretty accurate (MOV alone achieved around .66).  Both variables are extremely significant (from p value, or absolute value of t-stat).  Based on these coefficients, the resulting predictive equation is

YardsDiff = 7.84*MOV – 23.3*TOdiff/gm

Running the dataset through the same process as above (comparing predictions with actual results and calculating the total error), here’s how the new rankings turns out:

In other words, if we account for turnovers in our predictions, the expected/actual yardage discrepancy drops from ~125 to ~70 yards per game.  This obv makes the results somewhat less extreme, though still pretty significant: 11th of 1647.  Or, in histogram form:

So what’s the bottom line?  At 69.5 yards per game, the total “missing” yardage drops to around 1100.  Therefore, inasmuch as we accept it as an “explanation,” Green Bay’s turnover differential seems to account for about 900 yards.

It’s probably obvious, but important enough to say anyway, that there is extensive overlap between this “explanation” and our others above: E.g., the interception differential contributes to the possession differential, and is exacerbated by garbage time strategy, which causes the EPA/WPA differential, etc.

## “Bend But Don’t Break”

Finally, I have to address a potential cause of this anomaly that I would almost rather not: The elusive “Bend But Don’t Break” defense.  It’s a bit like the Dark Matter of this scenario: I can prove it exists, and estimate about how much is there, but that doesn’t mean I have any idea what it is or where it comes from, and it’s almost certainly not as sexy as people think it is.

Typically, “Bend But Don’t Break” is the description that NFL analysts use for bad defenses that get lucky.  As a logical and empirical matter, they mostly don’t make sense: Pretty much every team in history (save, possibly, the 2007 New England Patriots) has a steeply inclined expected points by field position curve.  See, e.g., the “Drive Results” chart in this post.  Any time you “bend” enough to give up first downs, you’re giving up expected points. In other words, barring special circumstances, there is simply no way to trade significant yards for a decreased chance of scoring.

Of course, you can have defenses that are stronger at defending various parts of the field, or certain down/distance combinations, which could have the net effect of allowing fewer points than you would expect based on yards allowed, but that’s not some magical defensive rope-a-dope strategy, it’s just being better at some things than others.

But for whatever reason, on a drive-by-drive basis, did the Green Bay defense “bend” more than it “broke”? In other words, did they give up fewer points than expected?

And the answer is “yes.”  Which should be unsurprising, since it’s basically a minor variant of the original problem.  In other words, it begs the question.

In fact, with everything that we’ve looked at so far, this is pretty much all that is left: if there weren’t a significant “Bend But Don’t Break” effect observable, the yardage anomaly would be literally impossible.

And, in fact, this observation “accounts” for about 650 yards, which, combined with everything else we’ve looked at (and assuming a modest amount of overlap), puts us in the ballpark of our initial 2000 yard discrepancy.

# Extremely Speculative Conclusions

Some of the things that seem speculative above must be true, because there has to be an accounting: even if it’s completely random, dumb luck with no special properties and no elements of design, there still has to be an avenue for the anomaly to manifest.

So, given that some speculation is necessary, the best I can do is offer a sort of “death by a thousand cuts” explanation.  If we take the yardage explained by turnovers, the “dark matter” yards of “bend but don’t break”, and then roughly half of our speculated consequences of the fewer drives/zero yard TD’s and the “Garbage Time” reverse-clutch effect (to account for overlap), you actually end up with around 2100 yards, with a breakdown like so:

So why cut drives and reverse clutch in half instead of the others?  Mostly just to be conservative. We have to account for overlap somewhere, and I’d rather leave more in the unknown than in the known.

At the end of the day, the stars definitely had to align for this anomaly to happen: Any one of the contributing factors may have been slightly unusual, but combine them and you get something rare.

## Tim Tebow and the Taxonomy of Clutch

There’s nothing people love more in sports than the appearance of “clutch”ness, probably because the ability to play “up” to a situation implies a sort of super-humanity, and we love our super-heroes. Prior to this last weekend, Tim Tebow had a remarkable streak of games in which he (and his team) played significantly better in crucial 4th-quarter situations than he (or they) did throughout the rest of those contests. Combined with Tebow’s high profile, his extremely public religious conviction, and a “divine intervention” narrative that practically wrote itself, this led to a perfect storm of hype. With the din of that hype dying down a bit (thank you, Bill Belichick), I thought I’d take the chance to explore a few of my thoughts on “clutchness” in general.

This may be a bit of a surprise coming from a statistically-oriented self-professed skeptic, but I’m a complete believer in “clutch.”  In this case, my skepticism is aimed more at those who deny clutch out of hand: The principle that “Clutch does not exist” is treated as something of a sacred tenet by many adherents of the Unconventional Wisdom.

On the other hand, my belief in Clutch doesn’t necessarily mean I believe in mystical athletic superpowers. Rather, I think the “clutch” effect—that is, scenarios where the performance of some teams/players genuinely improves when game outcomes are in the balance—is perfectly rational and empirically supported.  Indeed, the simple fact that winning is a statistically significant predictive variable on top of points scored and points allowed—demonstrably true for each of the 3 major American sports—is very nearly proof enough.

The differences between my views and those of clutch-deniers are sometimes more semantic and sometimes more empirical.  In its broadest sense, I would describe “clutch” as a property inherent in players/teams/coaches who systematically perform better than normal in more important situations. From there, I see two major factors that divide clutch into a number of different types: 1) Whether or not the difference is a product of the individual or team’s own skill, and 2) whether their performance in these important spots is abnormally good relative to their performance (in less important spots), whether it is good relative to the typical performance in those spots, or both.  In the following chart, I’ve listed the most common types of Clutch that I can think of, a couple of examples of each, and how I think they break down w/r/t those factors (click to enlarge):

Here are a few thoughts on each:

### 1. Reverse Clutch

I first discussed the concept of “reverse clutch” in this post in my Dennis Rodman series.  Put simply, it’s a situation where someone has clutch-like performance by virtue of playing badly in less important situations.

While I don’t think this is a particularly common phenomenon, it may be relevant to the Tebow discussion.  During Sunday’s Broncos/Pats game, I tweeted that at least one commentator seemed to be flirting with the idea that maybe Tebow would be better off throwing more interceptions. Noting that, for all of Tebow’s statistical shortcomings, his interception rate is ridiculously low, and then noting that Tebow’s “ugly” passes generally err on the ultra-cautious side, the commentator seemed poised to put the two together—if just for a moment—before his partner steered him back to the mass media-approved narrative.

If you’re not willing to take the risks that sometimes lead to interceptions, you may also have a harder time completing passes, throwing touchdowns, and doing all those things that quarterbacks normally do to win games.  And, for the most part, we know that Tebow is almost religiously (pun intended) committed to avoiding turnovers.  However, in situations where your team is trailing in the 4th quarter, you may have no choice but to let loose and take those risks.  Thus, it is possible that a Tim Tebow who takes risks more optimally is actually a significantly better quarterback than the Q1-Q3 version we’ve seen so far this season, and the 4th quarter pressure situations he has faced have simply brought that out of him.

That may sound farfetched, and I certainly wouldn’t bet my life on it, but it also wouldn’t be unprecedented.  Though perhaps a less extreme example, early in his career Ben Roethlisburger played on a Pittsburgh team that relied mostly on its defense, and was almost painfully conservative in the passing game.  He won a ton, but with superficially unimpressive stats, a fairly low interception rate, and loads of “clutch” performances. His rookie season he passed for only 187 yards a game, yet had SIX 4th quarter comebacks.  Obviously, he eventually became regarded as an elite QB, with statistics to match.

### 2. Not Choking

A lot of professional athletes are *not* clutch, or, more specifically, are anti-clutch. See, e.g., professional kickers.  They succumb under pressure, just as any non-professionals might. While most professionals probably have a much greater capacity for handling pressure situations than amateurs, there are still significant relative imbalances between them.  The athletes who do NOT choke under pressure are thus, by comparison, clutch.

Some athletes may be more “mentally tough” than others.  I love Roger Federer, and think he is among the top two tennis player of all time (Bjorn Borg being the other), and in many ways I even think he is under-appreciated despite all of his accolades.  Yet, he has a pretty crap record in the closest matches, especially late in majors: lifetime, he is 4-7 in 5 set matches in the Quarterfinals or later, including a 2-4 record in his last 6.  For comparison, Nadal is 4-1 in similar situations (2-1 against Federer), and Borg won 5-setters at an 86% clip.

Extremely small sample, sure. But compared to Federer’s normal expectation on a set by set basis over the time-frame (even against tougher competition), the binomial probability of him losing that much without significantly diminished 5th set performance is extremely low:

Thus, as a Bayesian matter, it’s likely that a portion of Rafael Nadal’s apparent “clutchness” can be attributed to Roger Federer.

### 3. Reputational Clutch.

In the finale to my Rodman series, I discussed a fictional player named “Bjordson,” who is my amalgamation of Michael Jordan, Larry Bird, and Magic Johnson, and I noted that this player has a slightly higher Win % differential than Rodman.

Now, I could do a whole separate post (if not a whole separate series) on the issue, but it’s interesting that Bjordson also has an extremely high X-Factor: that is, the average difference between their actual Win % differential and the Win % differential that would be predicted by their Margin of Victory differential is, like Rodman’s, around 10% (around 22.5% vs. 12.5%).  [Note: Though the X-Factors are similar, this is subjectively a bit less surprising than Rodman having such a high W% diff., mostly because I started with W% diff. this time, so some regression to the mean was expected, while in Rodman’s case I started with MOV, so a massively higher W% was a shocker.  But regardless, both results are abnormally high.]

Now, I’m sure that the vast majority of sports fans presented with this fact would probably just shrug and accept that Jordan, Bird and Johnson must have all been uber-clutch, but I doubt it.  Systematically performing super-humanly better than you are normally capable of is extremely difficult, but systematically performing worse than you are normally capable of is pretty easy.  Rodman’s high X-Factor was relatively easy to understand (as Reverse Clutch), but these are a little trickier.

Call it speculation, but I suspect that a major reason for this apparent clutchiness is that being a super-duper-star has its privileges. E.g.:

In other words, ref bias may help super-stars win even more than their super-skills would dictate.

I put Tim Tebow in the chart above as perhaps having a bit of “reputational clutch” as well, though not because of officiating.  Mostly it just seemed that, over the last few weeks, the Tebow media frenzy led to an environment where practically everyone on the field was going out of their minds—one way or the other—any time a game got close late.

### 4. Skills Relevant to Endgame

Numbers 4 and 5 in the chart above are pretty closely related.  The main distinction is that #4 can be role-based and doesn’t necessarily imply any particular advantage.  In fact, you could have a relatively poor player overall who, by virtue of their specific skillset, becomes significantly more valuable in endgame situations.  E.g., closing pitchers in baseball: someone with a comparatively high ERA might still be a good “closing” option if they throw a high percentage of strikeouts (it doesn’t matter how many home runs you normally give up if a single or even a pop-up will lose the game).

Straddling 4 and 5 is one of the most notorious “clutch” athletes of all time: Reggie Miller.  Many years ago, I read an article that examined Reggie’s career and determined that he wasn’t clutch because he hit an relatively normal percentage of 3 point shots in clutch situations. I didn’t even think about it at the time, but I wish I could find the article now, because, if true, it almost certainly proves exactly the opposite of what the authors intended.

The amazing thing about Miller is that his jump shot was so ugly. My theory is that the sheer bizarreness of his shooting motion made his shot extremely hard to defend (think Hideo Nomo in his rookie year).  While this didn’t necessarily make him a great shooter under normal circumstances, he could suddenly become extremely valuable in any situations where there is no time to set up a shot and heavy perimeter defense is a given. Being able to hit ANY shots under those conditions is a “clutch” skill.

### 5. Tactical Superiority (and other endgame skills)

Though other types of skills can fit into this branch of the tree, I think endgame tactics is the area where teams, coaches, and players are most likely to have disparate impacts, thus leading to significant advantages w/r/t winning.  The simple fact is that endgames are very different from the rest of games, and require a whole different mindset. Meanwhile, leagues select for people with a wide variety of skills, leaving some much better at end-game tactics than others.

Win expectation supplants point expectation.  If you’re behind, you have to take more risks, and if you’re ahead, you have to avoid risks—even at the cost of expected value.  If you’re a QB, you need to consider the whole range of outcomes of a play more than just the average outcome or the typical outcome.  If you’re a QB who is losing, you need to throw pride out the window and throw interceptions! There is clock management, knowing when to stay in bounds and when to go down.  As a baseball manager, you may face your most difficult pitching decisions, and as a pitcher, you may have to make unusual pitch decisions.  A batter may have to adjust his style to the situation, and a pitcher needs to anticipate those adjustments.  Etc., etc., ad infinitum.  They may not be as flashy as Reggie Miller 3-ball, but these little things add up, and are probably the most significant source of Clutchness in sports.

### 6. Conditioning

I listed this separately (rather than as an example of 4 or 5) just because I think it’s not as simple and neat as it seems.

While conditioning and fitness are important in every sport, and they tend to be more important later in games, they’re almost too pervasive to be “clutch” as I described it above.  The fact that most major team sports have more or less uniform game lengths means that conditioning issue should manifest similarly basically every night, and should therefore be reflected in most conventional statistics (like minutes played, margin of victory, etc), not just in those directly related to winning.

Ultimately, I think conditioning has the greatest impact on “clutchness” in Tennis, where it is often the deciding factor in close matches

### 7. True Clutch.

And finally, we get to the Holy Grail of Clutch.  This is probably what most “skeptics” are thinking of when they deny the existence of Clutch, though I think that such denials—even with this more limited scope—are generally overstated.  If such a quality exists, it is obviously going to be extremely rare, so the various statistical studies that fail to find it prove very little.

The most likely example in mainstream sports would seem to be pre-scandal Tiger Woods.  In his prime, he had an advantage over the field in nearly every aspect of the game, but golf is a fairly high variance sport, and his scoring average was still only a point or two lower than the competition.  Yet his Sunday prowess is well documented: He has gone 48-4 in PGA tournaments when entering the final round with at least a share of the lead, including an 11-1 record with only a share of the lead.  Also, to go a bit more esoteric, Woods has successfully defended a title 22 times.  So, considering he has 71 career wins, and at least 22 of them had to be first timers, that means his title defense record is closer to 40-45%, depending on how often he won titles many times in a row.  Compare this to his overall win-rate of 27%, and the idea that he was able to elevate his game when it mattered to him the most is even more plausible.

Of course, I still contend that the most clutch thing I have ever seen is Packattack’s final jump onto the .1 wire in his legendary A11 run.  Tim Tebow, eat your heart out!

## A Defense of Sudden Death Playoffs in Baseball

So despite my general antipathy toward America’s pastime, I’ve been looking into baseball a lot lately.  I’m working on a three part series that will “take on” Pythagorean Expectation.  But considering the sanctity of that metric, I’m taking my time to get it right.

For now, the big news is that Major League Baseball is finally going to have realignment, which will most likely lead to an extra playoff team, and a one game Wild Card series between the non–division winners.  I’m not normally one who tries to comment on current events in sports (though, out of pure frustration, I almost fired up WordPress today just to take shots at Tim Tebow—even with nothing original to say), but this issue has sort of a counter-intuitive angle to it that motivated me to dig a bit deeper.

Conventional wisdom on the one game playoff is pretty much that it’s, well, super crazy.  E.g., here’s Jayson Stark’s take at ESPN:

But now that the alternative to finishing first is a ONE-GAME playoff? Heck, you’d rather have an appendectomy than walk that tightrope. Wouldn’t you?

Though I think he actually likes the idea, precisely because of the loco factor:

So a one-game, October Madness survivor game is what we’re going to get. You should set your DVRs for that insanity right now.

In the meantime, we all know what the potential downside is to this format. Having your entire season come down to one game isn’t fair. Period.

I wouldn’t be too sure about that.  What is fair?  As I’ve noted, MLB playoffs are basically a crapshoot anyway.  In my view, any move that MLB can make toward having the more accomplished team win more often is a positive step.  And, as crazy as it sounds, that is likely exactly what a one game playoff will do.

The reason is simple: home field advantage.  While smaller than in other sports, the home team in baseball still wins around 55% of the time, and more games means a smaller percentage of your series games played at home.  While longer series’ eventually lead to better teams winning more often, the margins in baseball are so small that it takes a significant edge for a team to prefer to play ANY road games:

Note: I calculated these probabilities using my favorite binom.dist function in Excel. Specifically, where the number of games needed to win a series is k, this is the sum from x=0 to x=k of the p(winning x home games) times p(winning at least k-x road games).

So assuming each team is about as good as their records (which, regardless of the accuracy of the assumption, is how they deserve to be treated), a team needs about a 5.75% generic advantage (around 9-10 games) to prefer even a seven game series to a single home game.

But what about the incredible injustice that could occur when a really good team is forced to play some scrub?  E.g., Stark continues:

It’s a lock that one of these years, a 98-win wild-card team is going to lose to an 86-win wild-card team. And that will really, really seem like a miscarriage of baseball justice. You’ll need a Richter Scale handy to listen to talk radio if that happens.

But you know what the answer to those complaints will be?

“You should have finished first. Then you wouldn’t have gotten yourself into that mess.”

Stark posits a 12 game edge between two wild card teams, and indeed, this could lead to a slightly worse spot for the better team than a longer series.  12 games corresponds to a 7.4% generic advantage, which means a 7-game series would improve the team’s chances by about 1% (oh, the humanity!).  But the alternative almost certainly wouldn’t be seven games anyway, considering the first round of the playoffs is already only five.  At that length, the “miscarriage of baseball justice” would be about 0.1% (and vs. 3 games, sudden death is still preferable).

If anything, consider the implications of the massive gap on the left side of the graph above: If anyone is getting screwed by the new setup, it’s not the team with the better record, it’s a better team with a worse record, who won’t get as good a chance to demonstrate their actual superiority (though that team’s chances are still around 50% better than they would have been under the current system).  And those are the teams that really did “[get themselves] into that mess.”

Also, the scenario Stark posits is extremely unlikely: basically, the difference between 4th and 5th place is never 12 games.  For comparison, this season the difference between the best record in the NL and the Wild Card Loser was only 13 games, and in the AL it was only seven.  Over the past ten seasons, each Wild Card team and their 5th place finisher were separated by an average of 3.5 games (about 2.2%):

Note that no cases over this span even rise above the seven game “injustice line” of 5.75%, much less to the nightmare scenario of 7.5% that Stark invokes.  The standard deviation is about 1.5%, and that’s with the present imbalance of teams (note that the AL is pretty consistently higher than the NL, as should be expected)—after realignment, this plot should tighten even further.

Indeed, considering the typically small margins between contenders in baseball, on average, this “insane” sudden death series may end up being the fairest round of the playoffs.

## Hyperbole of the Day: Coach Ryan On Coach Belichick

And no, I don’t mean Rex:

“You can have Bill Parcells as a head coach and Vince Lombardi as a D-coordinator and Bill Walsh as the offensive coordinator and I think Belichick would beat them by two touchdowns if it came down to coaching,” Ryan said. “It’s going to come down to players and coaches and everything.”

From this ESPN article, which of course focuses on Rob Ryan’s opinion of Tom Brady.

Crazy hyperbole, though I’m not sure exactly what he means by “if it came down to coaching.”  Surely he doesn’t think that Belichick is better at all three skills: He is suggesting that Belichick has some super-quality that trumps mere offensive, defensive, and motivational strategies.

What strikes me as really funny, though, is the selection of Vince Lombardi as the “dream” defensive coordinator.  A much more natural choice would have been Buddy Ryan, but I guess Rob can’t very well go saying that Belichick would run laps around his own father.

## 10/9 NFL Sunday Live Blog

Alright, I made it. You know the drill, and if you don’t, details here.  Please leave comments and/or questions, etc.

1:40: Made it home just in time for the crazy ending of the Houston/Oakland game.  Interesting play within 2 minutes: Houston takes a sack, but is called for a personal foul/facemask.  Meanwhile, they go under the hood to check if Oakland had 12 men on the field, and they did.  By rule, the 12 men was declined, then the personal foul was accepted, with the end result being 1st and 25.  So the Oakland penalty is declined but still wipes out the sack?  Normally I pride myself on knowing all the obscure NFL rules, but this one was new to me.  Or maybe I missed something.

1:52: I got some questions this week about the purpose of the PUPTO metric, and how good it is as far as predicting future performance.  I’d say it’s more of a “story of the game(s)” stat than a “quality of the team” stat.  It does hold its own for predicting future outcomes, but there are a lot less crude methods in that area that are more effective (in general, turnovers should be handled more delicately).

1:55: Watching Jets and Patriots now, of course.

One other interesting question I was reminded of during that game–are timeouts over-used to avoid a delay of game penalty? Seems like they have to be, since 5 yards is almost inconsequential relative to your ability to run 3-4 extra plays late in the game. Of course it depends on what the probability is you’ll be coming back late in the game, but seems hard to believe it’s so low to justify burning a timeout just to avoid a 5-yard penalty.

I agree it would be interesting to quantify the actual value of a Time Out at various points in the game, but intuitively I’d guess that they’re not as valuable as you think.  They’re a bit like insurance, in that you’re super-glad that you had them when you need them, but I think the situations where a timeout makes much of a difference are more rare than you think.

For example, I’ve linked this before:

This table assumes you have the ball with 2 minutes left on the yardline indicated, and the four columns correspond to the number of timeouts you have.  Even on your own 10, the difference between 0 timeouts and 3 timeouts is less than 3%—and this is one of the more leveraged situations, you’d think (note: I can’t speak for the complete accuracy of the method FC used, but this is one of the few win % analyses out there I’ve seen that accounts for timeouts.  As I’ve noted before, ANFL Stats WPA Calculator does not include them).

2:18: So, from the earlier games, let’s see: Colts and Eagles lose again.  So maybe Peyton Manning is more valuable than a few wins, and maybe spending a lot of money on free agents isn’t a good way to get and NFL Championship.  I’m feeling like it’s about time for another one of my big “I Told You So” round-ups.

2:28: So here’s something I drew up on my iPad while I was without internet over the weekend.  It’s a generic visualization of a Punt/Go For It decision:

I have a longer post in the works that explains better and uses some actual data, but despite looking complicated, I think it’s actually a pretty simple way of analyzing these situations quickly.  In particular, it lets you adjust for relative team strength and/or type of offense without having to resort to complicated math (you can just “shock” the curves like you would in an econ class).

2:40: “Bills force late INT to finish off fading Eagles” is one of ESPN’s headlines for the Bills/Eagles game.  Not saying Vick didn’t screw the pooch in this one, but as I’ve been harping on the past couple of weeks, if there’s a time to risk throwing an interception, it’s when you’re down by 5 with under 2 minutes left.  If I were the coach and that drive ended with anything other than a touchdown or an interception, I’d be pissed.

2:46: I should make this a TMQ-like running item: “Interception of the Week,” celebrating the game-losing turnovers that happened at the most appropriate time to gamble.  It’s a bit like back when I played a lot of live poker: I used to record my “worst” river calls (where I called with some ridiculously weak hand and ended up being up against a monster), and then I’d brag about them to my friends.

2:51: Man, when did Wes Welker become New England’s “greatest asset”?  I remember when he was on the Dolphins, I thought he was underrated as a situational player, and I was unsurprised to see the Patriots pick him up.  Then his numbers went way up with Randy Moss, which I would have expected, and I kind of thought he got a bit overrated.  But now with Moss in the wind, he’s putting up even bigger numbers.  Crazy.

2:55: So my Quantum Randy Moss post—though the most popular non-Dennis Rodman post I’ve ever written—is one of my least brag-worthy in terms of results: Since I posted it (at the start of last season), Moss had his first 0 catch game, was dumped by two teams, was a non-factor on another, retired in a huff, and reportedly New England wouldn’t even take him back for less money.  I mean, I stand by my analysis, but what an unexpected disaster.

3:15: David Myers: I’ll look into that in a bit.  You could be right that I missed something, but it seemed to work out when I did it on paper.

3:20: So the “Reward” in that graph is the value of your drive times the odds of making the first down, and the “Risk” is the value of the opponent’s drive on the current LoS vs. where they would be expected to get the ball after a punt (times the chances of your failing to convert).  So you’re saying the green arrow on the left should extend to the opp’s drive value curve, but I’m not getting why.

Wouldn’t that be double-counting?

3:30: Nevermind, I get what you’re saying, misread your comment.  You’re saying you should also count denying the opponent a possession at all.  But outside of time-pressure scenarios, I don’t think that has any additional value (aside from what’s already covered in my proportions).

4:07: Argh, I’m getting bogged down in some database mechanics for an idea I was just having.  Note to self: don’t do massive original research projects during the live blog.

4:10: Myers expanded on his comment:

If you punt on play N, then the transition of scoring potential from play N to play N + 1 is from the green solid point to the red solid point, or A + C. The value of the _possession_ in turn has to be the additive inverse of that (plus whatever value is gained by the additional yardage made to get the first). Note this is logically equivalent to the argument about turnover value from The Hidden Game of Football (pp 102-103, 1988 edition). This valuation scheme is not original to me.

I’ll have to postpone looking into this until I have more time (love the academic citation btw).

4:52: Ugh, a little less than timely.  I was trying to find a more elegant way of doing this, but here’s a graph of the 2007 Patriots offense:

5:07: And here’s the comparison pic:

5:15: FWIW, the linear trendline equations for those two graphs are

$y = .014x + 2.58$

and

$y=.036x + .49$

respectively.

5:20: I just built those graphs from play-by-play data, which I started during the New England game (see, I was trying to reminisce about the crazy 2007 New England offense that you should never ever punt to).  Not only is that game over, but the night game is starting.  Sometimes I definitely overestimate my own speed.

5:23: Short break and I’ll be back with some crazy Aaron Rodgers stats.

5:40: Ok, quick side-product of what I was doing above: here’s a graph of expected points resulting from a 1st down on each yard line in the red zone:

6:02: Also, I don’t think the variations in that graph are all noise.  First, the sample is pretty huge (n=15,088),  and it’s consistent with other research I’ve done about the bizarre things that happen with a “compressed field.”  Here are some of the features that I can see and the theoretical justifications:

1. There’s a decline right before the 10 yard line, with the 10 yard line itself being a pretty serious local minimum.  I think this happens because of the shortened field and the increasing difficulty of getting a first down without getting a touchdown (e.g., from the 11 yard line, you can only get a first down inside the 1, but from the 13 yard line you have 3 yards to work with).  This is relevant b/c the odds of a touchdown on any given play from the 10, 11, 12 aren’t that different.
2. There’s a flattening that occurs between the 20 and the 15: I think this is where you first experience “compressed field” issues (less room for receivers to run).  But then around the 15, I think the effect is “complete” (at least for a while), and the natural advantage of being closer takes over again.
3. There’s a “statistically significant” outlier on the 3 yard line, where 1st and goal on the 3 is actually less valuable than 1st and goal on the 4.  I’m fairly certain that this at least in part due to configuration issues (as you have limited offensive options on the 3), though I think it may also be caused by poor play selection.  Specifically, teams call a much higher percentage of running plays from the 3 than from the 4, while defenses are pretty much always stacked against the run.
4. The slope at the 10 going down to the 8 is somewhat greater than in other areas of the graph where the expectation is increasing linearly (incidentally, as I mentioned 2 weeks ago, this is one of the things that makes EPA and WPA models difficult: you have some pretty dramatic shifts over a small number of yards, and you can’t really model it with a continuous equation).  This effect I also think might have something to do with play selection, or even 2nd-order play selection: that is, teams pass a fair amount, which is good, running is also fairly effective (b/c defenses are more focused on pass), and successful runs often leave them at a yardline (like the 4+) where they are still willing to pass.

Really, it may seem crazy, but I’ve looked into most of these effects and have found support for them.

6:36: Ok, as I’ve noted before, Rodgers’ consistently low interception % is pretty unusual, though of course his sample size is tiny:

Now let’s compare to the rest of the league (starting at least 8 games):

Obviously he is way on the left side of this blob, and his “slope” (if you can call it that with only 3 points so far) is much higher.

6:40: Let’s compare to Peyton Manning:

Rodgers’ Int% with a 40% win rate is almost half that of Peyton Manning’s (and, it goes without saying, Manning is a pretty consistent QB).

6:45: And, of course, what Rodgers analysis could be complete without comparison to Brett Favre:

6:52: I should note, of course, that I have no problem with Favre or Manning’s numbers here.  I cite Rodger’s consistency not b/c I think it’s necessarily better, but just b/c it’s interesting.  I would expect a QB to have a higher Int% when playing for a losing team, whether he is consistent or not.  Generally, I think a relatively high “shot group” on this graph, with a relatively low slope, can be a good thing: It may simply reflect that the QB is taking necessary risks when required to (though, clearly, isolating the causes and effects is incredibly difficult).

7:00: I see Tiger Woods bounced back with three 68’s in a row in the Frys.com tournament.  He finished tied for 30th.  In what is basically a “Quest for the Card” tournament.  In a field that contained 9 of the world’s top 100 players.

Comeback?

7:15: Atlanta is such a sneaky franchise. They seem to be competitive every couple of years, putting together good-to-great regular seasons, but haven’t won more than one playoff game since 1998.  I think you can win with great passing and great running, great defense and great running, but you can’t win with great running alone.  Their performance, to me, seems like a classic run good/run bad situation, where they probably haven’t changed all that much year to year, but being a little better than average keeps them occasionally in contention (while still being at a disadvantage against the actually better teams that they have to face in the playoffs).

7:42: Rodgers has a sick Adjusted Net Yards Per Attempt (generally considered the best non–play-by-play single QB metric) this season, leading the league with 9.7 going into this weekend.

So, out of curiosity, I was kind of curious just how much better ANY/A is than the pariah of QB stats: the NFL Passer Rating.  So here are a couple of simple scatter-plots, ANY/A first:

And here’s PER:

ANY/A obv does better, though maybe not as much as I would have guessed.

7:47: Of course, both stats are subject to causation/entanglement issues, ANY/A possibly even moreso (as it includes sacks and weights interceptions more heavily).

7:54: That style of touchdown where a receiver has one defender, breaks for the sideline, then turns, leaps and stretches out for the touchdown, is always hailed as a great play, despite being completely textbook and despite being executed pretty much exactly the same way by every receiver in the NFL—normally differing only by whether they are close enough and have a good enough angle to get inside the pylon.

7:58: Man, I’m excited for Detroit/Chicago tomorrow.  Can’t remember the last time I thought that.

8:14: Ok, I can’t help but return to this David Myers point from earlier:

If you punt on play N, then the transition of scoring potential from play N to play N + 1 is from the green solid point to the red solid point, or A + C. The value of the _possession_ in turn has to be the additive inverse of that (plus whatever value is gained by the additional yardage made to get the first).

I don’t think the possession has value in addition to its scoring potential, or at least not as much as you’re suggesting.  This method you’re describing counts the value of not giving the opponent the ball in addition to the value of keeping the ball for yourself.  But I really think you shouldn’t do that, since you haven’t decreased the expected possessions for the game of your opponent—or, at least, you certainly haven’t decreased it by 1.  They are still going to get the ball when your possession is over.  By holding the ball now, you make it slightly more likely that the last drive of the game will be yours (depending on how much time is left, etc), but you’re still going to be trading possessions 1 for 1.

For an analogy, think of rebounding in basketball: Occasionally I’ve heard casual fans suggest that offensive rebounds must be more important than defensive rebounds because you not only get a possession but you take one away from your opponent.  But this is strictly false: A rebound is worth one possession regardless (note, of course, offensive rebounds probably are more valuable than defensive rebounds, but only because you are less likely to get them).  What you gain by getting an offensive rebound is exactly your expectation for your new possession, b/c the other team is still going to get the ball back when it’s over.  I can’t see any distinction between this and converting a 4th down.

8:24: Also, it’s true that, depending on where you are on the field, your opponent may be expected to get the ball back in a worse position.  But this effect should be included in whatever you use for value on the Y-axis.  At least, a perfect metric for the Y-axis would include it (though I think a proxy like expected points is good enough for most approximations, which is what that graphing method is all about).

8:29: Wow, can’t wait for that Packers/Chargers game.

8:32: Game, set, match.  Respect to Aaron Rodgers for breaking a Kurt Warner record (PER over first 1500 attempts).  Was there anything more incredible in the history of football than the 1999 Rams?