Gabriel Desjardins: NHL teams are playing for overtime

In the National Hockey League, the losing team gets zero points in the standings if it loses in regulation time, but one point if it loses in overtime or the shootout. Either way, the winning team gets two points. That means that, if a game is tied after 60 minutes, three points will be split between the teams instead of two. In theory, this should give teams an incentive to "play for the tie" and thus increase the joint reward by 50 percent.

To see how important that third point is, suppose that one average NHL team were to successfully collude with all the other teams to play to a regulation tie. Both teams would ensure that they didn't score in regulation, but, come overtime, both teams would now try hard to win.

What would happen? Well, if it's an average team, it would win 41 games, for two points each, and lose 41 regulation ties, for one point each. That would give it a total of 123 points on the season.

123 points would have led the league last year.

Of course, no team is going to collude to play every game to overtime. But the incentive is still high. On average, getting to overtime gets you 1.5 points. To claim 1.5 points in a regulation game requires a winning percentage of .750. So, for all but the very best teams, it's theoretically better to wait for overtime than to try to win in regulation.

Now, teams aren't actually going to act to maximize their expected points this way, for obvious reasons. First, the fans care about more than just standings points -- they want to be entertained. Paying customers and home viewers will get very upset at having to sit through 60 minutes of ragging the puck before the real action starts. Second, you could argue the idea of teams trying not to win (or even trying not to win "right now") is damaging to the integrity of the game.

Still, the incentive is there, and you should expect that teams will respond to it in whatever ways they can get away with. In a study I did about three years ago, I found that teams are playing to more regulation ties than they used to. After adjusting for the league level of scoring, there was about a 24 percent increase in the frequency of regulation ties in the NHL.

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Is it getting worse? Last week, in a Wall Street Journal column, hockey researcher Gabriel Desjardins found that it is, and also some striking evidence that might suggest why.

Gabriel found that in the past two years, 22.5% of games were tied after 60 minutes, almost exactly the same as in 2005 to 2007. You could conclude that the effect has levelled off. But, this year, there's been a jump. So far this year, Gabriel found, 27.9 percent of games have gone to overtime.

Why is this happening? Well, Gabriel observes, if teams are playing for the regulation tie, you'd expect them to concentrate their efforts in games where the score is tied late. After all, it's hard to play to preserve a tie in the middle of the first period: you'll have to change your style of play for 50 minutes.

So Gabriel looked at what happens in games that are tied with three minutes left in the third period. What did he find?

-- In the past four seasons, scoring in the last three minutes is at about a third less than normal;

-- This season, it's dropped even further: it's more than 60% fewer than normal!

Here are Gabriel's numbers. I've listed the "overall" rates for comparison. Numbers are goals per 60 minutes.

2005-06: 4.27 vs. 6.17 overall
2006-07: 3.04 vs. 5.89
2007-08: 4.64 vs. 5.57
2008-09: 3.43 vs. 5.83
2009-10: 2.05 vs. 5.68 (approx.)

Note the huge drop this season. Is it real?

Well, I counted 157 games that went to overtime this year so far. I'm counting 10 days later than Gabriel was, so let's lower that to 145. If we assume there were also 145 games tied in the last three minutes, that's 435 minutes of hockey, or 7.25 games. If we assume that the distribution of goals per game (in the last three minutes) is Poisson with a mean of 4 (which is roughly the average of the past four years), that means the variance is also 4 (in a Poisson distribution, the mean equals the variance). That means the standard deviation is 2 goals per game. To get the SD of the average over 7.25 games, we divide by the square root of 7.25, which gives 0.74.

So the difference between this year's figure of 2.05, and the expected figure of about 4.00, is a bit less than 3 standard deviations. That's fairly significant. It's probably a combination of something real happening, and a certain amount of luck. But even if some of it is luck, the number does jump out at you.

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Is the NHL happy with this state of affairs, where teams are playing for a tie where they can get away with it? I think, overall, they are. From the standpoint of the league, there are both pros and cons.

On the pro side, more overtime games equals more excitement. More overtimes also means more shootouts, and fans seem to like shootouts.

More subtly, games decided in overtime are less likely to be won by the better team, since there are only five minutes in which the better team must emerge instead of 60. The same is true for shootouts. Indeed, shootouts are so random, or at least so uncorrelated with the other skills of the team, that Gabriel also found evidence that teams might also be playing for the tie in overtime, hoping to get to the shootout. Overtime scoring is also down this year, by the equivalent of about one goal per 60 minutes.

All this means that the winners are more random, which means the standings are more random, which means that more teams are in the hunt for a playoff spot. As I write this, only one team in the East is more than five points out of the playoffs, and only one team in the West is more than ten points out.

And even though the result of any given overtime may be mostly random, it's likely that the better teams are less likely to appear in overtimes, being able to beat their opponents in the first three periods. In that case, the effect is to award the "extra" third points to worse teams more often than better teams, which also has the effect of compressing the standings. I'm not actually sure how large an effect this is, but logic suggests that it must happen to some extent.

On the con side ... I guess the hockey would be a bit less exciting late in the game when both teams are playing for the tie. And, because of the randomness, you might get the most talented teams a bit less likely to move up in the standings. Those seem like pretty small cons.

So I can see why the league likes the new system ... the pros do seem to outweigh the cons, as far as fan interest goes.

But I hate it.

Part of the reason is personal taste; I don't like the idea that you can lose and still gain ground in the standings. And I don't like the idea that mediocre teams are collectively rewarded for not being able to put the other team away. As a statistician, it bugs me that some games are worth three points and some games worth two.

But the more important reason is that I don't like the incentives. When teams go into the game, from the very beginning, hoping it winds up a tie ... well, I think that's just wrong. And when the tie game gets to the third period, between two teams both fighting to make the playoffs, you know that both coaches are seriously thinking about getting to overtime, and securing themselves at least one point. You know that, if they could, they would collude to keep the game tied until the end of regulation. And, for all I know, there might already be some kind of unspoken agreement that certain things won't be done in the last few minutes of a tie game. I'm not expert enough to spot that, but the lower scoring in tie games speaks for itself.

The bottom line is that with the extra point available for the tie, teams aren't playing every instant of every game with the same strategy and desire to win that they would otherwise. And that can't be good for the game.