Here’s my favorite new fact about N.C.A.A. basketball: teams that are behind by one point at halftime are actually more likely to win than teams that are one point ahead. This striking finding comes courtesy of a terrific new paper by my Wharton colleagues, Jonah Berger and Devin Pope. Their findings are summarized in this graph, which collects info from 6,572 N.C.A.A. basketball games since 2005:
The first dot (on the bottom left) shows that among those teams behind by 10 points at halftime, only 11.8 percent won; the next dot shows that those behind by 9 points won 13.9 percent, and so on. The line of best fit (the solid line) shows that raising your halftime lead by two points tends to be associated with about an 8 percentage-point increase in your chances of winning, and this is a pretty smooth relationship.
But notice what happens when we contrast teams that are one point behind at halftime with teams that are one point ahead: the chances of winning suddenly fall by 2.4 percentage points, instead of rising by 8 percentage points.
Berger and Pope are two of the brightest young behavioral economists around, and they posit a behavioral explanation. Losing can lead to winning because of the strong motivating effects of being close to your goal. You can link some of this to Prospect Theory — loss aversion suggests that you may be willing to work harder to avoid a negative outcome (a loss); the leading teams, by contrast, aren’t focused on the losing domain. And in fact, most of this “catch-up” occurs in the first 10 minutes after halftime.
But how can we tell whether this is the losing team working harder, or the halftime leader easing up?
Here, they move from field evidence to the Wharton behavioral lab, setting up a very simple experiment in which their subjects were challenged to a trivial task — how many times they could type “a” then “b” in half a minute. The subjects were told that if they beat their opponent, they would get a bigger payout. After the first round of competition, some were given feedback, and others weren’t. And here’s the key to the experiment: they randomly told some folks that they were a long way behind their opponent, others were told they were a little bit behind, or exactly tied, a little ahead, or even a long way ahead. Those who were randomly told they were a little bit behind improved their performance dramatically, while the other groups improved by about the same amount as the control condition (that is, the same improvement as those given no feedback at all).
It’s an intriguing finding: being behind by a little yields the greatest possible effort. And while these researchers measure these effects on the basketball court, or on pounding keyboards, their implications for the rest of our lives are even more intriguing. Want your workers to work harder? Tell them that they are running a close second in the race for promotion.
Intrigued? See their write-up in Sunday’s New York Times, or the academic version, here.
and 
. You can also watch it on 
Anyone else think their conclusion (while reasonable) isn’t strongly supported by the data plotted?
Since the data have to be symmetric about the zero axis, drawing a trend from -1 to 0 to 1 is misleading because it appears stronger than a trend from 3 to 4 but is actually just the same in terms of quantity of information. If you plot only 0 to 10 — the independent data points — the data look pretty linear, although there are reversals at 1, 4, and 7 points.
Gooch,
I believe there is plenty of point shaving in the NCAA. In a one point game, it’s not point shaving; It’s throwing a game. I like to think there is not enough of that to explain any part of the trend.
So let me get this straight –
The attempt to win a basketball game is analogous to having typing two keys?
Something seems terribly amiss when trying to “replicate” this experiment in the “lab”.
Freakonomics is running a ‘close second’ as my favorite blog.
Why the focus on the negative slope near the 0 mark but not on negative slopes at -7, -4, +3, +6?
So if a team is second in their division by half a game, and they are underdogs by a one point spread in their next game, how often to they win?
This is clearly a statistical anomaly. Yes, you can make sense of it in a way, but the sample size is just far too small to make any sort of conclusion here. There are less than seven thousand games here, and if I were to venture a guess, I would say about 10 % of these were within a point at half time. That’s 700 games, so if ten games had gone the other way you would not be observing this phenomenon.
Note that teams that are down by 4 are more likely to win than teams that are down by 3 – a phenomenon or an anomaly?
If you remember that all the teams that were ahead by 1 at the half and all the teams that were behind by 1 at the half were all part of the same dataset, then you can see that the relationship between winning percentage and half time score is about as linear as you can expect with these sample sizes.
Half time is psychologically important, as you can carry momentum into the interval and turn things around. However, it’s a fairly random time in the game and it’s unlikely that the same phenomenon observed in the test carried out could be observed in teams that were slightly behind at half time. I would be much more interested in an observation from the last TV timeout, 4 minutes before the end of the game, when you clearly have time to catch up, but you’re either in a position to defend your lead or fight back.
This is nice result. It would be interesting to see when being down a little makes the most difference. Do home teams get a bigger, or visiting teams? Do favorites or underdogs?