# 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.

## Michael Peters

Or you could tell your employees that they are running a close second to being fired (which is the equivalent of losing a basketball game). And it's more likely in this current economic climate.

## Garry

A question: the team that gets the first possession in the game does not get the first possession of the second half. Suppose the team that gets the first possession in the game has a higher probability of leading at the end of the first half. Thus the losing team gets the first possession of the second half. Could this account for the fact that that the team losing by one point at half-time has a higher probability of winning the game?

## Ezzie

Interesting, but not altogether unexpected. It's easier to motivate a team that's just trailing than one that is just winning.

On that note, I guess Memphis should be the pick to make the Final Four, since they were moved just behind UConn? :)

## Scott

Garry -

That is not necessarily true as in college basketball there are no jump balls after the start of the game. So if there is a tie up and the official blows his whistle indicating dual possession, the team that has the possession arrow in their favor gets the ball. (The team that loses the tip off at the beginning of the game gets the possession arrow to start).

At the beginning of the second half the ball is awarded to the team with the possession arrow and the possession arrow switches.

## jonathan

I have barely skimmed the paper but what if the better team tends to play worse in the first half because they believe they should win? Or if the weaker team plays harder in the first half because they've convinced themselves they can win?

I didn't see any mention in the paper of the relative strengths of the teams. What if you put in strength of team and find the better team tends highly to be in the group that wins from behind? That would make the analysis to a basketball coach. Without this information, I'm not sure this paper actually says anything about behavior.

## the Gooch

Other than effort, factors that could be at play are biased referees hoping to even things out, and possible point shaving.

## frankenduf

to me, the only possible explanation (other than noisy data) is the halftime adjustments- so, if this data depicts a process, the moral would be: halftime adjustments are more important than a one-point spot (assuming less adjustments are done when leading by 1)

## Brad

This is widely known in election strategy--claim you are just behind before the election to get more voters out to the polls.

If a candidate says he's winning by a long shot, nobody shows up to vote for him.

## Kyle

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.

## DrS

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.

## Caliphilosopher

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".

## David

Freakonomics is running a 'close second' as my favorite blog.

## Boris

Why the focus on the negative slope near the 0 mark but not on negative slopes at -7, -4, +3, +6?

## Zach

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?

## Rik Waero

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.

## blink

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?

## Tim

@ Kyle -- I agree.

This seems like a stretch. The data is plotted in a way that looks as though there are twice as many data points as there really are. Also the trend does look pretty linear if going from 0-10.

## Kyle

I guess zero isn't an independent data point either, since half the teams are going to win either way. That may be why the polynomial trend line doesn't include it and makes the conclusion stronger.

## Jim

Kyle is right and a look at the academic paper is even more revealing. As Kyle correctly points out, only one half of the chart is independent data. The other half is just its mirror image and therefore tends to magnify whatever slight variations there may be near 0. Note that the trend lines presented conveniently exclude tied games and are projected to what would be a one half point difference Why exclude a real data point and why project a trend to a point in between two real data points? The only reason that comes to mind for me is to emphasize a "trend" that wouldn't be there if the actual data from tied games had been included in the trend. In the academic paper they also present a chart that runs from -3 to +3, which is an unrepresentative range that exaggerates the appearance of an anomaly for -1 and +1. The fact of the matter is that a one point difference in a basketball game is less than a single field goal and for practical purposes is a tie. With teams trading baskets it is essentially random which team is ahead at any particular moment, such as half time. I am not a statistician, but the charts in the academic paper seem to support the proposition that the team's prior record is by far the best predictor of who wins a close game. To my eye the authors cherry picked their presentation to emphasize a point that is at best marginally supported. It is a sad commentary that this passes for scholarly work from a leading school of economics sufficiently important to warrant publication in a leading national newspaper.

## Marty

Judging from the "fit", the best strategy might be for a team to figure out how to be losing by a half a point going into halftime. Or extrapolating the curve, maybe a 0.01 point deficit would be better yet.

Seriously, though, I'm with Kyle and Rik--I'd like to see some error bars on the data.