Possessions and Bonus Possessions

A possession is any identifiable scoring opportunity. A possession begins with the first possession of a half, a rebound, an opponent's score, or an opponent's turnover. A possession also begins with a technical foul on the possessory team.  A possession ends with a shot, a free throw opportunity, or a turnover. Occasionally, a possession may begin but not end. For example, a team may start a possession near the end of a period and hold the ball without a possession-ending event before the period closes.

Should a possession count when it begins or when it ends?

I find two compelling reasons to count a possession only when it ends. First, the team in possession must act to end the possession.  Second, a team with a game ending possession and a lead should hold the ball until time expires if possible. If this final action is counted as a possession, the team's average efficiency for that game falls slightly because the team has an extra possession even though the team does not even attempt to score.

For ease of use, I have developed the following algorithm to compute the number of possessions.

Total Possessions = {Total shots + total turnovers + (total free throws)/2}.

When a team's total free throw attempts is an odd number, I round up to the next higher even number. Obviously, this treatment of free throws is approximate because some free throw opportunities only have one shot, yet others have 3. Rather than precisely track these free throw possessions, there is a relatively small error in the two shot per possession and the round-up protocols.   As I watch games and track possessions live I do count the actually number of free throw opportunities without the simplifying assumption.

All things being equal, each team will enjoy the same number of scoring opportunities [possessions] in a game, whether the pace is slow or fast. FN1  There are some exceptions to this general rule.

When a team opens a half with a possession and enjoys the last possession of that half, the team enjoys one bonus possession. When a team shoots technical free throws, it will enjoy a bonus possession if it retains possession after the free throw attempts. These game anomalies produce a very limited number of bonus possessions in any particular game, if any, and there is no certainty that the same team will always benefit. Over the course of most games, and certainly over the course of a season, the number of bonus possessions from these game anomalies should be compensating and even out. FN2

The most significant source of bonus possessions in basketball is offensive rebounding. Therefore, when the game ends, the difference in the total possessions generally indicates the offensive rebound differential.

Every offensive rebound produces a bonus possession, and the team that secures the most offensive rebounds in a game can use the net bonus possessions to overcome some of the effects of poor shooting or frequent turnovers. Similarly, the team that secures fewer offensive rebounds in a game must perform more efficiently than their opponent to have any opportunity to win the basketball game.

A team that consistently obtains 4 more offensive rebounds than its opponents will enjoy an average of 4 bonus possessions per game. As discussed below, if a team scores 0.9 to 1.1 ppp, four bonus possessions in a game provides a 4 point advantage when every thing else is equal. FN3 FN4

During the 2001-02 season, Kentucky was involved in three basketball games in which the margin of victory or defeat was the offensive rebounding margin. In an exhibition game against Athletes In Action, Kentucky won the game by 5 points, 88-83 even though Athletes In Action out produced Kentucky by 0.976 ppp to 0.936 ppp. However, Kentucky enjoyed nine bonus possessions due to its offensive rebounding margin. Instead of losing the game 83-80, those extra 9 possessions were sufficient to propel Kentucky to the victory. Similarly, Kentucky's exhibition game against Athletes In Action in 2002-03 had a similar result with AIA out producing Kentucky by 1.051 to 0.977 yet Kentucky won the game on the strength of its 7 bonus possession during the game.

A similar result occurred in the first Florida game in Gainesville. Kentucky won 70-68 even though Florida out performed Kentucky 0.872 to 0.805. Kentucky 's nine bonus possessions from offensive rebounding propelled it from a 68-63 loss to the two point victory. The third game determined by offensive rebounding margin occurred when Kentucky played Mississippi State in Starkville . Kentucky lost in overtime even though it posted better offensive efficiency for the game, 0.793 to 0.747. However, the 12 bonus possessions that Mississippi State enjoyed due to its offensive rebounding was sufficient to take the game into overtime and secure the victory.

For the 2002-03 season, Kentucky averaged two bonus possessions per game. There were 12 games in which the offensive rebounding margin was between -1 and +5 [Average +3]. There were 10 games in which Kentucky had 6 or more additional possessions, and 8 games in which Kentucky 's opponent has 2 or more bonus possessions. Among the ACC and SEC teams in 2001-02, the average offensive rebound margin is +1, and 10 teams had a positive margin with Clemson the strongest offensive rebounders at +6. Five teams had negative margins with Arkansas having the poorest margin at -3.

For the 2003-04 season, Kentucky has averaged two bonus possessions per game.  See this data here

Many people do not understand the importance of the offensive rebounding differential. However, overall, the second chance possessions that a team earns through its offensive rebounding may be the most productive type of possession that a team can enjoy.

Field goal attempts either produce 2 or even 3 points on a made regular field goal, or 0 points if missed. If we agree to account for the occasional third point of an old fashioned 3 point play in the free throw analysis, then the efficiency of a possession ending in a field goal attempt is 2 times the shooting percentage for two point attempts. If a team averages 50% on two point attempts, then this type of possession produces 1.00 points per possession. Similarly, for 3 point attempts, the efficiency is 3 times the percentage for three point attempts. If a team averages 40% on three point attempts, it has a 3 point efficiency of 1.2 ppp.

Free thows pose a different situation. When a foul produces free throws, a team may get 1, 2 or 3 shots. As noted above, a free throw attempt following a made basket does not add another possession to the tally. Without tracking each specific possession associated with free throw attempts, it is safe to simplify the analysis by dividing the total free throw attempts after rounding to the nearest even number by 2, Therefore, the efficiency of free throw possessions is 2 times the free throw shooting percentage. If a team makes 70 percent of its free throw attempts, the free throw possession efficiency is 1.4 ppp. If the average free throw shooting percentage is more than 1.5 times the 3 point shooting percentage, then the free throw ending possessions provide a team the highest efficiency.

The entire above analysis is based on all possessions that end in an actual scoring opportunity. However, turnovers end a possession with no points, and the overall “efficiency” is clearly 0 ppp. The rate of turnovers, e.g the ratio of total turnovers to total possessions is much more important to the game than total turnovers. If a game is played in the 70 possession range, then 14 turnovers is one turnover for every 5 possessions, or a 20% turnover rate. Similarly, a team with 16 turnovers in a 90 possession game would have a turnover rate of 17%. Ten turnovers in a 90 possession game equals an 11% turnover rate.

The turnover rate must be factored in with the efficiencies presented in the preceding paragraphs to determine the actual game efficiencies. My analysis of game efficiencies are all based on overall efficiency, which includes the turnover rates. Prior to the 1972 season, Kentucky's official statistics do not include turnovers.  Therefore, I am limited in my approach to seasons since 1972, Rupp's last as coach.

Another way to divide possessions is to look at the efficiency of the team in its first shot attempts and its second [or third or fourth, or …] chance points. This can be done with the game tracking system I have developed by tracking the total second chance points and offensive rebounds. Starting with the Kentucky @ Georgia game in February 14, 2004 , this data will be added to the game tracking spreadsheet.

For this inaugural game of this analysis, Kentucky grabbed 7 offensive rebounds and scored 9 second chance points while Georgia grabbed 18 offensive rebounded and scored 22 second chance point. When these numbers are removed for the overall scoring efficiencies the first chance and second chance efficiencies are:

Kentucky Georgia

 First Chance ppp 0.843 0.732 Second Chance ppp 1.286 1.222

This game suggests that the point production may be significantly higher for second chance possessions than first chance possessions. I will continue to track this relationship through the 2004-04 season.  The actual game data through Morehead State on December 8, 2004 indicates that this early suggestion is the rule, but there are exceptions already appearing.  First, it is now clear that no team will ALWAYS have higher efficiency on its second chance opportunities than its first chances.  Kentucky has had two games that offend the rule.

Second, it seems clear that some teams defend against second chance possessions better than others.  The 2005 Kentucky has consistently held opponents' second chance efficiencies at low levels, often lower than the opponents' first chance efficiency.  Therefore, the second chance efficiency is an important factor required to assess the value of the offensive rebounding bonus possessions.

When a team shoots a high percentage from the floor, the number of second chance opportunities will clearly be fewer, but there is no data to suggest that the efficiency of the second chance possession is a function of the number of second chance opportunities in a game.

Therefore, if teams have higher efficiency during second chances than first chances, a team's overall game efficiency is nearly always increased due solely to offensive rebounding. However, since that relationship appears reciprocal, the important tracking interest is in the bonus possessions produced by the net offensive rebounding differential.

Why would a team be more efficient on second chance points than on first chance points? First, on most first chance possessions, the defense is established and the offensive team must attack the set defense to find their scoring opportunities. However, with possessions that begin with an offensive rebound, the defense is often disorganized at the instant of the rebound, and these possessions often end with either a foul [the most efficient method of scoring] or a tap-in or other relatively easy shot. Only when the team decides to pull the ball back out following an offensive rebound and run its half court offense would the defense have an opportunity to reset itself.

In short, teams get more easy scores in second chance possessions than in first chance possessions.

On first impression, one may argue that there is very little difference between tracking shooting percentage or overall efficiency. Certainly, a team that makes 50% of its two point field goal attempts has an efficiency of 1 ppp for those specific possessions. However, that analysis alone does not account for the effect of turnovers or the distribution a two point and three point baskets on the calculation. To understand the relative strengths of the two teams and their game performance, a fan must not only track shooting percentage but also turnovers, offensive rebounding, and free throw percentage. Tracking efficiency as I described above only requires a fan to track one set of values that blend all of these relevant factors into their team's average offensive and defensive efficiencies.  This system permits a fan to track the game's progress through the 10 TV Commercial segments, and a team's progress during the season with just one set of values .

Footnotes

1. When a team engages in a slow-paced game, it by definition limits the number of possessions that its opponent will have. An opponent's possession cannot begin until the team's own possession is ended with either a shot, free throw opportunity, or turnover. When a team chooses to shoot the basketball as quickly as possible, then it inevitably provides its opponent with a greater number of scoring opportunities. This is precisely why the total number of points allowed by a team is a poor indicator by itself of that team's defensive prowess.

2. This supposition that over the course of a season, the net tally of these bonus possessions will even out is similar to the concept of random sampling errors in scientific measurements. The accumulation of small random error will not affect the overall measurements to a statistically significant degree. This is similar to the concept of compensating errors in a level survey.

3. While I have never isolated the actual number of points that a team scores for each bonus possession, it is intuitively clear that a bonus possession from a technical foul provides 2 times the free throw shooting percentage of the player awarded the shots, usually the shooting teams best free throw shooter. This means an efficiency for that possession of between 1.6 and 1.8 points. In the case of bonus possessions created by offensive rebounds, the rebounding team so frequently takes advantage of its second chance to score that its efficiency on these bonus possessions is probably higher than the overall average team efficiency. The value and importance of offensive rebounding can not be overstated. Four extra offensive rebounds per game often translate into 4 to 8 bonus points.

4.  If one prefers to define a possession ending event, a missed shot that results in the beginning of an opponent's possession, then an offensive rebound would not provide a bonus possession, but simply a continuation of a possession.  This treatment would reduce the number of total possessions for the game, and increase the offensive and defensive efficiencies.  However, I prefer the definiions presented in this essay because it recognizes the importance of offensive rebounding by factoring the bonus possessions into the analysis.