The Effect of Controlling Tempo

17 February, 1996

What does a team gain by controlling tempo? Usually, when a broadcaster says a team needs to control tempo, they are talking about the team that doesn't like to run. Not always, but usually. This was especially true in the '80's when the slow-down East teams had to "control tempo" when playing the go-go West teams.

Controlling tempo, in my mind, means not forcing a quick shot after you've gotten beaten on a fast break. Basically, it means playing smart basketball. Most teams at the college or pro level can run and can play a half court offense, with only marginally differing ability between the two. Unless they are playing a team coached by Rick Pitino, whose teams have traditionally forced a tempo, they run when the opportunity is there and run a set offense otherwise. The times that teams start to play at their opponents' tempo is when they rush to get a shot off. Can you think of another time that broadcasters criticize a team for not playing at their own tempo?

Well, yes. Teams that like to run, but get stuck in a half court game are described as not playing at their own tempo. But this often (if not always) happens because their defense isn't forcing the turnovers or getting the defensive rebounds it needs to push the ball up the court. It also means the opposition is scoring a lot. Running teams don't force the ball up the court after a made basket very often any more. Some did prior to this decade, like the Lakers in the pros and that Loyola Marymount team of the late '80's. But did that really help them stay at their tempo and win the game?

My general feel on this issue is that teams slow down during the playoffs and in important parts of games. They isolate their best scorer and let that person score at their own pace. I have seen and measured a dramatic slow down in playoff games going back at least as far as 1988 when the Lakers were near the end of their run as Champions. When the Pistons slowed the game down, they seemd to do better against the Lakers. It took a year, but that strategy finally paid off when the Pistons swept the Lakers in '89, a series that was marred by injuries to the two Laker starting guards.

What this has lead to, along with the article, Basketball's Bell Curve, is a theory that slowing down the game can help an underdog win. It's more than a theory, actually, because the method outlined in Basketball's Bell Curve and described in New Measurement Techniques and A Binomial Model of the Game of Basketball, demonstrates how this can be true. The general formula for estimating the probability that a team is going to win is

            __                                        __
            |               (ORtg-DRtg)                |
Win% = NORM |------------------------------------------|
            --                                        --
where SQRT means to take the square root of the quantity in the brackets and NORM means to take the percentile of a mean-zero variance-one normal distribution corresponding to a value given by that in the brackets I faked, Rtg and Opp.RtgG are the points per 100 possessions scored and allowed by the team (their ratings), Var() indicates the variance of the quantity in parentheses, and Cov() indicates the covariance of the quantity in parentheses.

For those who are math-phobic, you should just understand that the larger the term in brackets above, the greater the chance of winning. So if you increase your points per 100 possessions rating while keeping everything else constant, you increase your chance of winning. That's obvious, right? Well, there are some subtle ways to increase the above expression. The one I'm thinking of is when you are an underdog. In this case, you are expected to win less than 50% of the time. This means that the above expression in brackets is less than zero; PPG is less than Opp.PPG. When the top is negative, one way to increase the overall value of the term in brackets is to increase the bottom. This may not be very obvious to people without a statistics course or two (or three or four) in their background, but you can increase the denominator by slowing down the game.

"Huh?" You say. OK, that last statement was a bit of a leap, but it is true. You can trust me and jump to the next paragraph or you can continue reading this one. By slowing down the game, a team reduces the number of possessions on which it can score. The variance of the team's rating and the variance of the opposition's rating both increase with fewer possessions. This is known from the binomial distribution, which is used to describe coin flips. This distribution says that the variance of the probability of success (the probability of scoring on a possession, or the variance of a team's rating) is described by

Var(observed probability) =   p*(1-p)/n
where p is the "true" probability of scoring for each team (which gives us the basis for one team being the underdog, and n is the number of possessions. If you decrease n, you increase the variance of the "observed probability", or the probability seen by a team attempting to score on n possessions. If you can follow the math, you see how slowing the game increases the variance of the "observed probability" of scoring for both the offense and defense (which translates to a higher variance of offensive and defensive ratings), which then makes the term in brackets up above less negative or higher. Hence, an underdog increases its chances of winning to something closer to 50%.

In the extreme, this principal is easy to understand. Look at the Bulls and the 76ers. Over the course of a 95 possession game, it's an easy pick -- you take the Bulls to win. Now, consider a game shortened to one minute. The 76ers have a lot better chance to win, don't they? It's not uncommon for a losing team to go on a four point "run" over the course of a minute. But it is uncommon that a bad team like the Sixers will keep that run going over the course of 95 possessions. So, if the Sixers could just manage to slow the game so that only four possessions are used, they just might beat the Bulls... Of course, this is why basketball instituted a shot clock.

I should follow this scientific explanation up by emphasizing that there are teams that increase their rating by slowing the pace or picking up the pace. I believe this, but have never tried to measure it. This is, of course, important and can offset the principal I demonstrated above. However, what I demonstrated above is not trivial, nor is it a strategy to ignore. It has certainly not been ignored by the Princeton Tigers of the world.

Tracing the Pace and Efficiency of the NBA

The following plot shows the progress of points per game, possessions per game, and ratings (points per possession) from the '73-74 NBA season to last season:

Notice how the pace has gotten dramatically slower, but the efficiency of the offense has mostly improved, though it's been pretty level since the mid 1980's. It's always hard to say exactly why such major changes have occurred in the game. I'm not sure people were conscious of the pace slowing until the past couple years. In 1988 or so, Martin Manley, author of Basketball Heaven, wrote to me suggesting that the pace was going to increase in the future, this despite the trend already evident at the time that the pace was slowing. I'm sure it has slowed even further this season, though I haven't done the calculations. Statistically, the number of turnovers and the number of shots have both decreased, while the number of free throws and offensive rebounds have roughly remained steady. Basically, teams have begun to take better care of the ball and shoot better, which is not entirely surprising.

There is one big glitch in the history of scoring efficiency and that is the big dip in the 1994 season. I cannot recall any big change in the rules to help the defense that year. In fact, I believe that was about the time officials began enforcing brutality in the paint a bit more, increasing their calls again the following year. Someone correct me if I'm wrong, but I can only think of one big change in the league that season -- Michael Jordan didn't play. Sure, he didn't play much in 1995 either, but they moved the three-point line in a couple feet, too, and that brought the league's scoring efficiency back up. But Jordan couldn't affect the league that much...could he?