# When Losing Leads to Winning

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.

## Jason11

Teams that are down by 4 points are also more likely win than teams down by 3 points. Is it easier to motivate a team down by 4 than a team down by 3?

The conclusions drawn in the article dont really mesh with the actual data very well.

## Donald Simon

Without knowing the number of games making up each point you don't know how wide a band can be put around the fitted curves. For all I know a straight line will fit the data.

## asmart

agree with kyle and tim. from the plot, it is impossible to tell if this is a trend or just noise. A drop of 2.4% (really 1.2%) is probably well within a standard deviation.

## Brian

Kyle, Tim--Dead on.

The graph is very misleading with the curves drawn the way they are. Take away the curves and you've got a fairly linear scatterplot. You'd never look at the zero point and think there's any anomaly there.

## M Kossar

Looks to me like residual error can explain it.

if you like at the dots, I can't four times (besides the one near zero) where the dot to the right is lower than the dot to the left.

Are there behavorial theories for those instances. I would hope that the published paper shows the difference at -1 and 0 is statistically different than the others.

## Bill

Avis built a memorable advertising campaign around this concept. Remember, "We Try Harder" . . . because we're #2 behind Avis?

## Bob Steinberg

Very nice but you still have to play the game and win on the court not in the newspaper or in a survey. You cheapen the all the hard work and effort that goes into competing.

## mparkinson

There is an old saying in chess: the hardest thing to do is win a won game. You do tend to ease up when you think you are sufficiently ahead. And chess is a complicated enough game that if you aren't way way ahead, the person who is behind just might find a way to catch up, and at least force a draw. Chess is not the same as basketball, of course, but the psychology is definitely the same. What is fascinating is the now observable fact that being only a little bit behind is a strong motivating force to try a lot harder, and that being just a little bit ahead, while it may not make you ease up, doesn't give any motivation to try hard to extend the size of your lead. Neat piece of analysis.

## Jeff M.

This is a poor statistical analysis, as presented here. A straightline fit to all the data is necessary, and the R^2 needs to be reported. From there, the chances of a deviation being statistically signficant needs to be worked out. Only then could you decide, to what confidence level, the statistical anomaly is valid.

It's a shame such poor mathematical work even gets published.

## asmart

just looked at the paper and I have to say again that the statistical analysis is dubious. The trend line represents the best fit of a quintic regression. This seems like an unnecessarily high order regression, which would artificially exaggerate the "near zero" trend. A linear regression would probably give just as good a fit. Also, I'm not very familiar with regression discontinuity methods, but in this case, such an approach seems suspect considering that the data on either side of the discontinuity are mirror images.

## Mark Messier

This look like pretty lazy statistics to me. First off, this plot shows the same data twice (read the points from left to right and compare a reading from right to left -- its obvious the points are mirror images of each other) so one can't really compare one point ahead to one point behind -- its the same data! You can only compare, say, 1 point behind to 50/50 probability of winning. When you do this, you realize that to measure a 2.4% deviation from 50% winning probability you would need a sample with roughly 10000 "down by 1" games in it. I'm sure the sample has no way near that number of games based on the scatter in the other points. This is an over-interpreted random fluctuation. Who edits this journal?

## Rick Groves

While I agree with the general suggestion that the framing of the data suggests an effect that may not really be present (though I assume the paper includes significance tests), the -1,0,1 data series is unique in that it is the only 3 consecutive data points in which the slope is negative.

All other cases in which the 2nd number has a lower % than the preceding number is followed by a 3rd % greater than the first.

## Brady

This study blindly misses the most important part of any basketball halftime -- coaching. The coaches get to digest the entire first half and make changes, and I hazard that has a lot more to do with success or failure in the second half than anything you'll find in the Wharton behavioral lab.

## Doug Hill

Heart can't be quantified. That's what wins basketball games.

## Scott

Garry (second comment) has an excellent point. Also, seems like in general the level of noise (probably just due to sampling) would explain the fluctuation about zero. From the data there is just as much evidence that being 3 up is better than being 4 up.

## tom

I wonder why they decided they should fit some cubic or exponential curve for the plot. That is so misleading, especially when you notice that either one of the 2 fitted curves totally bombs at predicting the "tied at halftime" datapoint.

## jf

I agreee Kyle et al.

It's noise! Put the error bars on that graph and there's NOTHING to see.

## Scott

A couple of responses to other people's comments:

Marty - if you look at the paper (linked in this article), the error bars are shown in Figure 1B (in the appendix). As suggested might be the case by you and others, the error bars range from about 46% to 52% for a team 1 point ahead, so we certainly couldn't reject the possibility that teams winning at halftime might be favourites. The graph doesn't show margins greater than 3 so we can't say if this is the case for the other "anomaly points. I have only skim read the paper though.

Rick - Of course points -1, 0, 1 have a constant slope. The winning percentage of point 0 must be 50% as it applies to both teams in the game, while if -1 is >50% then 1 must be <50% and vice versa. There is actually only one informative point in these three...

## Scott #2

Sorry just noticed I'm not the only Scott posting here. Comment 38 is mine, the others belong to at least one other Scott.

One more comment upon reading the paper further. It does state that they have controlled for things like team quality, home team, second half possession arrow etc and the result still holds (although statistical significance remains unclear). We are just presented with the basic graph on this blog.

## Jack S.

Remember the tortoise and the hare... maybe being ahead at half makes the team a little more tired and by the end of the game out of energy.

More importantly, the half way point is a completely meaningless demarcation. Unlike the end of the game where these is much strategy in picking the right person to foul, taking time outs, setting up the last shot, there is no incentive for anything special at the half and there is a risk that getting the last shot involves a foul (bad news when fouls are limited) or risks injury, or burns up too much energy that will be needed later.