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

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 98th percentile and the 99.98th 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.

, 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