The Case for Dennis Rodman: Guide

Post

Rodman-Specific

Broader Analytical

Part 1(a): Rodman vs. Jordan

• Dennis Rodman has dominated Rebounding Percentage more than anyone has dominated any major stat.
• Before Rodman, we should have expected a rebounder of that quality to appear about once every 400 years.

• Use standard deviations to measure relative greatness
• Outliers can skew their own data against them

Part 1(b): Defying the Laws of Nature

• Rodman had an almost unnatural ability to dominate rebounding on both ends of the court simultaneously
• Rodman showed no trade-off between offensive and defensive rebounding rates

• The trade-off between offensive and defensive rebounding exists, and is generally a completely separate phenomenon from rebounding ability.

Part 1(c): Rodman vs. Ancient History

• Contrary to popular opinion, Rodman was a much better rebounder than Wilt Chamberlain or Bill Russell, and it’s not close

• Total Rebound Percentages for players prior to 1970 can be estimated with extreme accuracy

Part 2(a)(i): Player Valuation and Conventional Wisdom

• On induction, Rodman will be the worst scorer and the best rebounder in the Hall of Fame
• Rodman scored even less than we would expect the lowest scoring Hall of Famer to have
• Rodman was an even better rebounder than we would expect the best rebounder in the Hall of Fame to be
• The Hall of Fame likes point-scorers better

• Everyone uses statistics, yet no one listens to statisticians—in part because statisticians build overreaching models, then believe and defend them
• Rebounding percentage correlates more strongly with winning than points per game.
• Added: Individual rebounding percentage has a more causative effect on team rebounding percentage than individual PPG does on team PPG.

Part 2(a)(ii): Player Valuation and Unconventional Wisdom

• Player Efficiency Rating ranks Dennis Rodman as the 7^th best player on the 1995-96 Bulls championship team
• Player Efficiency Rating is terrible
• Extreme rebounding ability like Rodman’s may have exponential value

• Player Efficiency Rating fails completely as a predictor of true player value
• PER rewards Usage rate (shooting), despite no correlation between Usage and shot efficiency
• PER’s many layers of complications and adjustments are demonstrably counterproductive

Part 2(b): With or Without Worm

• Rodman has the highest Margin of Victory differential of any player since 1986 with a remotely similar sample size
• Rodman’s value comes mostly from extra possessions from extra rebounds
• Despite claims that he was exclusively a defensive player, Rodman’s teams played significantly better on offense with him in the lineup, even after accounting for his offense rebounding

• Introduce my brand of game-by-game “With or Without You” stats
• Two main areas of player impact: Reciprocal Opportunities, and Reciprocal Efficiency
• Impact on one aspect of a game can easily be reflected in other areas statistically
• Completely independent confirmation of the results of previous analysis is powerful evidence

Part 3(a): Just Win Baby (in Histograms)

• Rodman’s Win Percentage differential is even better than his Margin of Victory differential
• Specifically, his Win% differential is #1 of the 470 players who qualified for the study—by a wide margin
• Adjusting for the quality of teams Rodman played for makes his differential even better

• Introduce win percentage differential, which is incredibly useful for research and hypothesis-testing in many contexts
• It is harder to have a big impact on better teams
• In a game of small margins, exceptional performance in limited areas can be more valuable

Part 3(b): Rodman’s X-Factor

• Not only is Rodman’s Win% differential greater than his (already great) MOV differential, it is greater by one of the largest margins of any player
• After adjusting for sample size, Rodman’s X-Factor is by far the largest of any qualifying player
• The most plausible explanations for this disparity suggest that, in Rodman’s case, his Win% differential may be the more trustworthy metric

• “X-Factor” is the difference between MOV-predicted and actual Win% differentials
• Higher MOV’s and larger sample sizes should correspond to smaller X-Factors
• 3-D plots are a visually appealing way of identifying less-obvious outliers
• There are several plausible causes for real team and/or player X-factors

Part 3(c): Beyond Margin of Victory

• Using a standardized model for combining MOV and Win% differentials (which weights MOV more heavily), Rodman still places #1 in the set of 462 qualifying players (many of whom have MUCH smaller samples)
• Depending on which metric you favor, Rodman’s differentials place between the 98^th percentile and the 99.98^th percentile among full-time players (approximately 5% make the Hall of Fame)

• The statistical community over-values Margin of Victory and under-values raw winning percentages
• Winning is a provably existent skill, separate from scoring and allowing points.
• Predicting regular season win expectations is best done with a combination of Margin of Victory AND Win percentage
• The larger the sample size, the more heavily Win % should be weighted

Part 3(d): Endgame: Statistical Significance

• Rodman’s win differentials alone are statistically significant well beyond the 99% level of confidence.
• Looking at the overall statistical significance for player win differentials over the broadest possible pool of 1539 players, Rodman ranks between 2st and 8^th, depending on your preferred metric.
• Rodman’s average ranking across metrics is second only to Shaquille O’Neal (who’s sample includes over twice as many qualifying games).

• Introduce “Black Box” as a term for when variance gets eaten up by events that have binary outcomes.
• Standard deviations for win differentials can be found by sampling
• These can be adjusted to different sample sizes mathematically
• Using this process, we can measure the statistical significance of individual win differentials for many players who didn’t have sufficient samples to qualify for earlier comparisons

Part 4(a): All-Hall?

• There are indirect reasons to believe Rodman’s Win Differential is more reliable than his Margin of Victory Differential

• Occam’s Razor and Bayes Theorem reasoning can make unlikely or only mildly supported independent hypotheses much more likely

Part 4(b): Rodman v. Jordan 2

• Rodman’s unusual consistency and otherworldly impact per possession used suggest that he may have had even more value than his Win Differentials indicate

• Introduce “Invisible Value” and “I-Factor”