The final minutes of a pro basketball game are often the most critical.
Professional basketball fans are obsessed with how their favorite superstars perform in the clutch. LeBron James in particular has been criticized for not taking over in the fourth quarter and refraining from taking the "big shots" when the game is on the line. Some observers, however, take a contrarian view by pointing out that points do not become more valuable by being scored later in the game. In a recent article at The Atlantic, Derek Thompson scoffed atthe idea that LeBron scoring 20 points in the second quarter is any less valuable than him scoring an equivalent amount in the fourth. This is similar to the criticism of coaches' behavior when a player gets in "foul trouble." Coaches tend to take their players out when they pick up two or three fouls early in the game so they can make sure that their stars don't foul out and are available later on. Fans point out that this makes no sense; a player is taken out of the game now to eliminate the possibility of him being taken out of the game later—at best, he still ends up missing the same amount of playing time.
While the logic here is seductive, it has a major flaw. Anybody who regularly watches the NBA knows that games have a way of tightening up as they go along. Call this "the tightening theory." When a team gets down big early, at some point they are expected to make a run. Their defense becomes more ferocious and the team with the lead gets complacent, setting up a fourth-quarter showdown. If this is true, then playing extremely well early can affect the game later on by causing you and your teammates to slack off and your opponents to play harder. On the other hand, by playing well in the fourth quarter, a star ensures that his team finishes strong and does so without costing them any points later on in the game. Under this theory, it makes sense to care about clutch performance or take a player out when he gets in foul trouble, because the game is going to end up tight anyway.
But is there any evidence that games actually do have a tendency to tighten up, more than chance would predict? In fact, there is. If the tightening theory is true, then teams that get out to an early lead will tend to get outscored later on. This is in fact what happens. I looked at the first 79 games of the 2012 NBA playoffs, through the conference finals:
In 75 of those games, one team had a lead at half-time, while in four others the score was tied. If what happens early in the game has no effect on what happens later, then we would expect teams that outscore their opponents in the first half to also do so in the second. In fact, we find the opposite. In the first three rounds of the playoffs, teams that were ahead at half-time lost the second half 61 percent of the time. In 84 percent of the 75 games with a half-time leader, the team ahead did not maintain its pace; the team losing at half-time either won or tied the second half or did not get outscored as badly as it did in the first two quarters.
The numbers also show that the tightening theory becomes more applicable as the playoffs move along. This is probably because there is more likely to be a larger talent disparity between teams playing one another in the first few rounds. The first place Spurs, for example, won seven out of eight halves against the eighth-seeded Jazz.
Later on in the playoffs, however, the Spurs would have a much harder time holding on to their leads. In game 6 of the Western Conference Finals, although they were up 15 at the half, the Spurs' season ended with them getting crushed by the Thunder in the third and fourth quarters. Earlier in the playoffs, the first game of the Clippers-Grizzlies series saw one of the greatest comebacks in sports history, with LA stealing a one-point win after being down by 24 with eight minutes left. Empirical data confirms our instinct that these kinds of games are much more common than one would expect if players always gave their best and were not mentally affected by the scoreboard. The best time to be a great player is the fourth quarter, because that's when most games are decided.