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Pace Yourself, Virginia: A Brief Guide to Tempo-Free Statistics

Many conventional basketball statistics offer skewed comparisons by not removing the effects of pace. This post explains the importance of keeping statistics tempo-free.


It has come to my attention1 that my statistics posts thus far may have glossed over some of the important and foundational points of advanced basketball statistics. In my eagerness to evaluate the Hoos from various statistical perspectives, I neglected to bring the less-nerdy of us up to speed.

The Finals scheduling break seemed like the perfect time to remedy this issue. This post2 attempts to explain perhaps the most basic and critical of these points: pace and corresponding tempo-free statistics. An explanation of the concept of pace is followed by a comparison of some tempo-free statistics to their conventional counterparts.

[The Importance of Pace]

Let's start with a common statement that perfectly represents the problems with pace-dependent conventional statistics:

Team A scores 65 points per game. Team B scores 70 points per game. Therefore, Team B's offense is better than Team A's offense.

Seems reasonable, doesn't it? To prove that it's not, we'll analogize to the well known statistic of points per game for individual players.

Take fictitious players A and B, who have won over the Virginia faithful with imaginary heart, hustle, grit and determination, and who can hold a sufficiently solid imaginary Pack-Line to start for the Hoos. It's the first game of the season. For the sake of argument, these players love to kick it old-school3 and refuse to take any three pointers.

Suppose Player A took 15 two-point shots, making 5. Player B made 5 of his 10 two-pointers. We can see that Player A required 5 more shots to make the same number of baskets as Player B. Now raise your hand if you think these players performed equally well offensively.4 Preposterous, right? Notice that both players are scoring 10 points per game at the conclusion of game one.

When we're talking about individual players, we can all appreciate that offensive performance depends not just on the number of shots that are made, but also on the number of opportunities that each player had to shoot. Points per game doesn't tell us everything. Player B had the better game because he made the same point contribution with fewer opportunities. This intuitive sense of skill evaluation is somehow often lost in the translation to team points per game.

If shots taken are the best measure of offensive opportunities for an individual player, possessions are the best offensive opportunity measure for a team as a whole. An offensive possession generally ends with a made basket, a turnover, or a missed shot rebounded by the opposing team. A possession represents one chance to score for a given team. The problem is, not every college basketball team averages the same number of possessions per game, more commonly referred to as pace.5 So, to belabor the point, teams average a different number of opportunities to score per game, meaning that points per game as a team statistic runs into the same problems that we outlined for individual players.

[Points Per Possession and Examples]

The solution to this problem is to determine how many points each team would score given a standard number of possessions. This is easily accomplished by dividing a team's points per game by their pace, or possessions per game, giving team points per possession. Let's look at an example comparing one of the slowest teams in the country, the Hoos, to one of the fastest, previous opponent Seattle University.

The Hoos score 63.2 points per game, good for 257th in the country. Seattle scores 64 points per game. Does Seattle, one of the worst teams in college basketball, have a better offense than the Hoos? Of course not. They just play faster. Seattle averages 77.2 possessions per game6 while the Hoos average 60.7 possessions per game.7 So the Hoos offense scores 1.04 points per possession (119th) to Seattle's 0.83 points per possession (339th).8 After removing the effects of pace, rendering the statistics "tempo-free," we can see that the Hoos offense is decidedly better at converting scoring opportunities.

The same analysis applies to the defensive side of the ball. Here though, by limiting points due to the slow pace, points against per game artificially improves the Hoos defensive rank. The Hoos allow 50 points per game, 3rd in the country, but at 60.7 possessions per game allow 0.82 points per possession, 9th in the country. The tempo-free stat still proves that Bennett's Pack-Line forms one of the best early-season defenses.9

[Other Key Tempo-Free Statistics vs. Conventional Counterparts]

We've outlined how points per possession better measures offensive ability than points per game, but team points is not the only statistic that is best compared tempo-free. Below are two other statistics that are best discussed without the influence of pace.10

Rebounding Percentage vs. Rebounding Margin: Rebounding margin measures the difference between the number of rebounds that a team averages per game and the number of rebounds their opponents average per game. A high rebounding margin would indicate that a team is full of superior rebounders; if pace were not a factor.11 A fast pace means more possessions and more shots. More shots means more opportunities to rebound. A rebound margin in a given game will increase as the pace increases, even as two teams rebound the same relative to each other. Rebounding percentage, a team's rebounds divided by the total number of rebounds in the game, is a better tempo-free measure.12

Turnover Percentage vs. Turnovers: The turnover statistic encounters the same problems. Turnovers end possessions. A faster pace means more possessions, and more opportunities to cough up a turnover. So just because one team or player has more turnovers than another doesn't necessarily mean that the former is worse at maintaining possession. Turnover percentage better measures the propensity to do so by obtaining the turnovers per possession, which when multiplied by 100, gives the percentage of possessions that end in a turnover. I'll stop. You get it.

So please, when referencing basketball statistics, end pacism; keep your stats tempo-free.


1 via the recent use of some pace-laden statistics on Twitter

2 which is both chart-free and tempo-free

3 like, 1980 old school

4 No hands, just as I thought!

5 Tony Bennett notoriously prefers to use most of the shot clock on offense, while other teams rely more on a fast-break offense.

6 4th in the country

7 342nd in the country. Out of 347. Yep, not a typo.

8 sometimes "points per 100 possessions" is used to make the number look more like a regular score, for those who consider decimals their mortal enemies. Here, 104 for the Hoos offense, 83 for Seattle's offense.

9 although note that this is not adjusted for strength of opponent, which is a much more complicated process. Since the Hoos have played relatively bad offenses so far, their points against per game should increase as they enter ACC play.

10 this is by no means an exhaustive list. I think (or hope) after this post, though, you'll be able to figure out which other statistics are tainted by the varying speeds of teams.

11 well, pace is just one of the myriad issues with rebound margin. Anything that lessens the opportunity to rebound hurts a team's rebound margin. Defenses that create turnovers prevent shots, meaning they can't grab defensive rebounds. Teams who strategically avoid the offensive glass to get back on defense also pass up rebounding opportunities. It doesn't mean they're bad at rebounding, it just means that they'd rather play defense.

12 although it's best split into offense and defense for reasons that are only somewhat relevant to our pace discussion.