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ANALYSIS OF THE GAME OF BASKETBALL
Change in Position on Definition of Possessions
When I began my work regarding offensive and defensive efficiencies, measured in points scored or allowed per possession, I had to define a possession. Two alternatives existed. First, some people, principally Ken Pomeroy, defined a possession as a trip into offensive court for a scoring opportunity, known as a Pomeroy Possession [PP]. Second, others defined a possession as any identifiable scoring opportunity, which is the definition I adopted, known as Multiple Possession [MP].
The difference between the two is how each treats an offensive rebounding. In the MP system, an offensive rebound begins a new scoring opportunity, thus a new possession, while in the PP system, an offensive rebound represents nothing but a continuation of the same possession that started when the offensive team began the possession. In both systems, the possession does not “count” until a possession ending event occurs. For the PP system, a possession ending event is a turnover, a made basket, a made free throw opportunity, or a missed shot resulting in a transfer of possession through a defensive rebound. For the MP system, a possession ending event is a shot attempt, a free throw opportunity or a turnover.
The argument over which definition best represents the flow of the game has raged for several years. I have advanced multiple arguments in defense of the MP system. However, the strongest argument in favor of the PP system has been that teams that score via offensive rebounding should not be penalized with a lower efficiency because the MP system included more than one possession for the basket rather than one possession. For example, on such a trip into offensive court, a team could score a basket on its first attempt to score, and its single trip efficiency would be 2.0 points for the possession. That would be the case even if the team had to take 2 or more shot attempts, with 1 or more offensive rebounds, to get their score. However, under the MP system, that trip would have a single possession efficiency of 2.0, 1.0, 0.5, 0.4 points per possession if the score required 1, 2, 3, 4 or even 5 shots before the team scored their basket.
My counter argument to this powerful argument in favor of the PP system has been that since the margin of offensive rebounding in games, over seasons, and between opponents is relatively small, and that the impact of this accounting factor is merely procedural and not substantive. Yes, the MP efficiencies would be lower than the corresponding PP efficiencies, but that shift in the absolute value of the efficiencies was relatively uniform, and that the comparative efficiencies game to game, team to team, and season to season are so similar as to not represent a substantive difference.
About 4 seasons ago, I began to track rebounding rates by measuring and tracking all rebounding in terms of a percentage of missed shots resulting in offensive rebounds by each team. In the process, I have learned that the NCAA D1 average rebounding rate is about 33%, e.g. the shooting team gets an offensive rebound following about 1/3 of its own missed shots. During the first 4 years of this tracking, the range of offensive rebounding rates for UK and its collective opponents have all fallen within the range of 31% to 35%. Rebounding rates within this range were completely consistent with my argument that the impact of offensive rebounding rates upon the comparative efficiencies was procedural, not substantive.
The 2009-10 UK team has forced me to reevaluate my position. Through 10 games, this UK team has an offensive rebounding rate of about 45% while the collective UK opponents remain at about 31%. This difference [14% instead of 4%] has become substantive, and the comparative efficiencies between games, teams, etc. differ in a significant way for the PP and MP systems. The UK offensive efficiency is significantly lower in relation to the defensive efficiency under the MP system than it is under the PP system.
I have demonstrated that the key parameter in any efficiency based system is the algebraic difference between the offensive and defensive efficiencies for a team, a parameter I have called the Net Game Efficiency, NGE. A higher NGE translates into a more powerful team. In addition, the algebraic difference between NGE values for two teams is a strong indicator of which team is the better team. For the 2009-10 UK team, the PP system produces a significantly higher NGE value for UK than the MP system, and the predicted game to game margins using the MP system have consistently under predicted the game margins by about 3 points per game, which has not occurred in prior seasons. I recast the predicted game margins for the first 10 games using the PP system, and it is clear that not only does the recasting provide a much smaller average margin difference, e.g. about 1 point per game, but a smaller standard deviation for the 10 games in the aggregate.
For these reasons, my opinion is shifting. I now agree that the PP system does provide a stronger basis for game to game, team to team, and season to season comparisons. I am in the process of changing my data reporting, game forecasting, and other presentations from the MP to the PP system. This transformation cannot be complete because the vast majority of the historical data does not include offensive rebounding data. Therefore, efficiency values will continue to appear based on each of these systems.
To illustrate the differences, the NCAA D1 average efficiency in recent years has been 0.86 points per possession under the MP system. The NCAA D1 average at present in the 2009-10 season is about 1.00 points per possession. Team to team offensive and defensive efficiencies will generally be higher for the PP system than the MP system by a similar shift, but not an exact shift of that mean difference. Second, the range of pace, team to team, from the slowest to the fastest, will be much smaller under the PP system than the MP system.
Now for some specific comparisons for this UK team through 10 games.
As you can see, this shift from MP to PP results in an increase in average margin from 11.7 ppg to 13.9 ppg.
Your comments are always welcome.
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