An Inconsistent Consistency Story

Posted on March 22, 2007 by


A few days ago I made a comment about the consistency of the Minnesota Timberwolves. The point I was trying to make was that given the past productivity of the players employed by Minnesota, one should expect this team to be hovering around the average mark. This means this team will win some and lose some.

When Kevin Garnett and Kevin McHale see this team win, though, they seem to think (judging by their quotes) that if the team could always play as well as it did when it won, it would win more frequently. In other words, from their perspective, the team loses because it is inconsistent.

I argued the opposite. The team loses fairly often because its players perform in a fashion consistent with past performance. Many of the players on the Timberwolves are below average, and consequently, we should expect this team to lose with some regularity. Not all the time. But more frequently than either Garnett or McHale want.

The Wisdom of Brian Goff

Okay, I restated the argument (badly again, I think). Here is a similar argument from Brian Goff, a fellow contributor to the Sports Economist.

ESPN replayed a little bit of Billy Donovan’s post-game press conference Sunday night. In response to an off-camera question that seemed to be about the Gators’ struggling to beat Purdue, Donovan offered remarks to the effect:

“The difference between teams like Purdue and us is not big. We’re a good basketball team, but so is Purdue. The margin for error in games like this on neutral courts is very small.”

His remarks were longer and more extensive but expressed, at least implicitly, two basic points that often escape the talking heads in the media. First, the average average performance level for the better teams in the tournament and those below them is not large. With all of the movement of young players to the NBA in recent years, very few teams have several juniors or seniors likely to play in the NBA. Most of the NBA-bound or NBA-impact players are freshmen or sophomores. With home court (or near home court) advantage removed in most NCAA games, this average performance difference moves even closer.

Second, team performance varies around this average level. That’s second nature to people in economics or statistics. Yet, sports media analysts frequently talk as if performance levels are fixed, or, at least, should be if coaches/players were really “focused” or some similar statements. Instead, variations in performance are going to occur for lots of reasons other than lack of preparation. Team-specific match-ups, player health, random bounces of the ball, officiating and other factors create variable performance.

Maybe nowhere do I see this lack of understanding more than when golf analysts talk about Tiger Woods. During some of Tiger’s winning streaks, some of these guys have seriously wondered whether anyone will ever beat him again. After his devastating performance in the 2000 U.S. Open, this kind of talk exploded as it again recently. In effect, the observers treated the upper end of his performance distribution as his average (seems to be a common occurrence among amateur golfers, also — I’m sure it has a cognitive science name).

For those of us who are in economic education, we should be careful not to undersell the value of fundamental ideas like this one or assume that the general point is widely grasped and easily applied to specific contexts.

An Attempt to Connect Two Stories

Both my story, and the argument Professor Goff offers, centers on the issue of sample size. Garnett and McHale observe their team win a game, or a small collection of games, and conclude that their team is really good (if it could play that well all the time). The larger data set – based on the player’s career performances – suggests something different. The larger data set gives us a better picture of what a player’s average, or expected performance, will be. And when we understand that picture, we see quite clearly why the Timberwolves will win a few games here and there, but are not likely to be consistent winners.

As we watch the NCAA Tournament it is the same story. The teams in the Sweet 16 tend to be among the best in college basketball. Tonight eight teams will offer us a performance, which may be better, the same, or worse than their average performance. If a better team performance worse than their long-run average, and a worse team performs better than their own long-run average, an upset will occur. This upset will tell us nothing about the nature of either team. Members of the media, though, will tell us stories about this upset as if something about the true nature of the players and teams could be inferred from one data point.

And Now I Will Be Inconsistent

All that being said, I am not sure life would be better if the media reported these events as Goff and I suggest. Do we really want to live in a world where the media tells us after each game “well, you can’t really draw an inference from this game. After all it is only a sample of one. Either team could have won this game and we do not know any more about the quality of these teams and players now then we did before the game was played. Basically, there is nothing to be learned here so let’s just get on with our lives.”

See, that wouldn’t make for interesting commentary at all. Yes, if you have some understanding of statistics it is a problem when people draw inferences where none can be drawn. But I am not sure I have a suggestion for what else the people in the media should say when the game is over. They have to say something, and the pure statistical answer is probably not going to appeal to very many people.

– DJ

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