After a basketball game ends there are two critical questions. Who won the game? Why did they win the game? The first question is easy, but the second question -- the "why" question -- is harder. The standard game recap written by a beat writer sometimes touches on this question, and sometimes it does not. This is not meant to be a critique of beat writers,who usually do a good job of taking a handful of post game quotes, a few quickly skimmed statistics, and a bit of game narrative and stringing it all together into a story. Much of the time, these stories are well-written and informative. But they often don't answer the "why" question.

Answering the "why" question is the main focus of my weekly Inside the Numbers articles that appear here at Burnt Orange Nation during the college basketball season. I work from the top down, starting from the final score of the game and then unwinding the box score from there. I thought it would be helpful to explain the process I go through to do this each week. I do this for two reasons. First, you might want to try to use some of these methods yourself to understand box scores from other games. Second, should I get hit by a bus, Peter will have this post to use as a guide when he gives my gig to someone else. And getting hit by a bus is a real possibility, as I play in traffic a lot.

#### Step 1: Start from the final score, and work backwards.

The basic premise of this approach is that the only statistics that matter are the final score, and the numbers that impact that final score. To that end, the two most important statistics for each team are the number of shots attempted, and the points scored per shot. Basketball is a really simple game. You win by some combination of taking more shots than your opponent and being more efficient with your shots then your opponent. Counting shots is a little bit tricky, as you have to account for both free throw attempts and field goal attempts in a way that makes sense. For reasons that I have described previously, the best way to do this is to calculate "shots" as FGA + 0.475 x FTA. With a way to count shots, calculating the points scored per shot is easy. For historical reasons, rather than reporting points per shot, statgeeks commonly use true shooting percentage, which is just

TS% = 0.5 x points/(FGA + 0.475 x FTA)

With true shooting percentages for each team, and the number of shots attempted by each team, we have taken the first step required in understanding the outcome of a basketball game. A team with the advantage in both true shooting percentage and the number of shots attempted wins 100 percent of the time. If one team has an advantage in true shooting percentage while the other team took more shots, we can use the rule of thumb that a 0.01 differential in TS% is worth approximately 1.3 extra shots to weigh the relative importance of these two numbers. This rule of thumb almost always works for NCAA basketball games, although it is not quite right if a game is played at an exceptionally slow or exceptionally fast pace.

With step 1 complete, we now understand how differences in shooting efficiency and the number of shots between the teams affected the game outcome. The four remaining steps will provide more detail to help understand these two factors.

#### Step 2: Two margins that matter.

Total rebounding margin, a commonly cited statistic, is not all that helpful when it comes to understanding wins and losses in basketball. But offensive rebounding margin can be very helpful. Offensive rebounding margin factors directly into understanding why one team took more shots than the other team.

For a similar reason, turnover margin is important. To a good approximation the differential in the number of shots each team attempted is simply

{shot differential} = {offensive rebounding margin} - {turnover margin}

where "shot differential" refers to the difference in FGA + 0.475 x FTA between the two teams. Taking more shots than your opponent is one of the ways that you can win, and more shots generally come from an advantage in offensive rebounding margin and turnover margin.

With step 2 complete, we know understand the role that offensive rebounding and turnovers played in creating a shot number advantage for one of the two teams. Step 3 will help us to better interpret these margins.

#### Step 3: Rebounding and turnover percentages provide more detail about shot differential.

Offensive and defensive rebounding percentages can be calculated for teams, and can be estimated for individual players. Studying rebounding percentages generally helps with understanding the offensive rebounding margin. The team offensive rebounding percentage is the percentage of possible rebounds that a team's offense collected. For NCAA division one basketball, offensive rebounding percentages typically fall between 30 and 35 percent. Anything that falls outside this range indicates that a team was unusually strong or weak on the glass.

Individual offensive rebounding percentages are estimates of the available offensive rebounds that a player grabbed while on the floor. Individual defensive rebounding percentages can also be estimated. When I am trying to understand a game that had a large rebounding margin, I usually start off by studying the offensive and defensive rebounding percentages of the big guys. For an individual player, a number of around 10 percent or greater for offensive rebounding percentage generally indicates a strong offensive rebounding performance. For defensive rebounding percentage, if a team's big men don't average around 20 to 25 percent, it usually leads to trouble. Of course, it is also important to look at the rebounding percentages of guards, as many guards make important contributions on the glass. Guards with a defensive rebounding percentage greater than about 10 percent are a big help to their team's rebounding efforts.

Team and individual turnover percentages are also helpful. Team turnover percentage is straightforward; it is simply an estimate of the percentage of team possessions that end in a turnover. In general for college basketball, anything lower than 20 percent is good for the offense, and anything greater than 20 percent is bad.

Individual turnover percentages take us further, although they have to be interpreted carefully. Each possession ends with one player either taking a shot or turning the ball over(*). For each player, the turnover percentage is calculated by determining the percentage of possessions that end with the ball in a player's hands that results in a turnover. Individual turnover percentage is a helpful statistic, but it has to be interpreted carefully. What a player is asked to do on offense has a big effect on turnover percentage. A catch-and-shoot three point shooter will likely have a low turnover percentage, while a ball handling point guard typically has a higher turnover percentage. Players who handle the ball a lot but seldom shoot generally have artificially high turnover percentages. For this reason, it is very important to consider individual turnover percentages in the context of what a player is asked to do. If a pass oriented point guard has 20 percent turnover percentage, he is probably helping his team, whereas a big man who turns the ball over in 20 percent of his possessions probably is hurting.

(* Note: this is not completely true. There are usually one or two turnovers per game that are charged to a team, rather than an individual player.)

With step 3 complete, we now understand how well each team did at rebounding and turnovers, and can determine how individual players impacted these results.

#### Step 4: Put the team true shooting percentages into context.

This step is short. Generally, a team true shooting percentage much greater than about 0.550 indicates some combination of a good shooting and bad defense. A team true shooting percentage of 0.500 or less indicates some combination of poor shooting and good defense.

With step 4 complete, we now know if each team generally shot well, or shot poorly. The final step will provide some insight into how individual performances affect true shooting percentage.

#### Step 5: Determine the impact of individual players on team true shooting percentages.

Team true shooting percentage is a complex aggregate of the performance of individual players. To help unwind this, I use a tool called Points Above Median (PAM).

I do a little calculation after every game to help quickly identify which players are doing the most damage with their scoring. It helps me to identify which players are giving their team both efficiency (as measured by true shooting percentage) and volume (as measured by the number of shots they take). The theory behind this calculation is simple. Let's say a player takes a ton of shots, but misses a bunch of them. Players like this will often rack up a decent point total, but will use a lot of shots to do it. These players provide scoring volume (something a team needs), but not much efficiency. There are other players that will take very few shots, but do so with great efficiency. These players help a team, but the impact of their low volume scoring can only be so great. In a good scoring game, a player will combine both volume and efficiency.

To measure how much each individual player affects team true shooting percentage on offense, I calculate how many points above a baseline value that each player scores, given the number of shots attempted. For the baseline, I use the median level of points a team in the NCAA scores on shots from the floor, 0.96 points per shot. This was more or less an arbitrary choice. The * PAM* calculation I do for each player after each game is

PAM = points - 0.96 x (FGA + 0.475 x FTA)

A PAM of two or greater is pretty good, while anything negative is not. Individual games where a player has a PAM as high as 10 are rare, but will occasionally happen. When you are quickly eyeballing the box score of a game, it is perfectly reasonable to estimate PAM as

PAMest = points - (FGA + FTA/2)

Understanding the impact of individual defense on opponent true shooting percentage from box score statistics is difficult. But one easy measure to look at is something called shot block percentage. To calculate shot block percentage, you first assume that all blocked shots come on two point attempts. This isn't quite right, but is close enough to provide a reasonable estimate. Team shot block percentage is an estimate of the fraction of opposing two point attempts that were blocked. The NCAA median team shot block percentage is about nine percent. The University of Kentucky led the nation in shot block percentage last season, blocking an estimated 20 percent of opponent two point attempts(*). It is also possible to estimate individual shot block percentages. A number greater than five percent is pretty good. Jeff Withey of Kansas led the nation in shot block percentage last season, turning away an estimated of 15 percent of opponent attempts.

(* It turns out in the case of Kentucky, the estimate is off by a few percentage points; based on play-by-play data Kentucky blocked about 18 percent of opponent two point attempts. The estimate is off because the Wildcats blocked 4 percent of opponent three point shots, which is a very high percentage. For comparison, the third best shot blocking team was Connecticut, and the Huskies blocked 1 percent of opponent three point attempts, which is a typical value.)

With step 5 complete, we now know how individual players affected team shooting efficiency, and understand the role that team shot blocking as well as individual shot blockers played in determining shooting efficiency.

#### Now you can become a statgeek

Beyond these two measures, there is a lot of information to help explain true shooting percentage that is not in the box score. I make heavy use of play-by-play data, but compiling individual game play-by-play data can be tedious without the computer programs I have built to speed the process. So that sort of work will take more effort to recreate if I am hit by a bus.

Even without play-by-play data, there is a tremendous amount of information available in a box score. Only basic arithmetic is needed to extract this information. All you need is a pocket calculator or a spreadsheet.

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