Last spring I read “Thinking, Fast and Slow,” a phenomenal book from Nobel Prize-Winning Psychologist and Expert in Behavioral Economics Daniel Kahneman. In one particular chapter he discusses a concept known as “loss aversion,” one that affects us every day but to which we pay very little attention. This is an article about a way in which loss aversion may have a serious impact on the NHL playoffs, one that nobody has investigated to my knowledge until now, and one about which I spoke at last weekend’s DC Hockey Analytics Conference.
Let’s begin with score effects, or specifically the idea that teams trailing in games tend to get the majority of the shots. It is a concept to which hockey fans have loosely subscribed for decades, but one that wasn’t really fleshed out or proven until the late Tore Purdy (aka JLikens) took on the task in 2009. From that point on, the concept was expanded, leading to this chart from a Cam Charron article in the winter of 2013.
The conclusion is obvious. Beyond a shred of a doubt, teams trailing in games, on average, control the play. But why is this the case? For the conference, I came up with a list of five reasons I believed score effects to be so commonplace.
Following a disappointing loss to Edmonton back in January, Washington Capitals Head Coach Barry Trotz had the following to say about his team’s attempt to protect a late lead. “When you’re up 4-2, you’re not thinking, ‘Let’s make it 5-2.’ You should say, ‘Let’s make sure we secure the hockey game.’” His view that teams should essentially bunker with a lead isn’t an uncommon one. Coaches tend to preach the safe play consistently to players, not wanting one glaring mistake to cost the team a victory. I’m not going to debate the merits of such an attitude here, but the fact is it exists. Coaches coach more conservatively with a lead, playing the guys they trust to make the safe plays, to play strong positional defense and not necessarily those who would push the play forward. Those players are going to play the way their coach advises, so as not to get benched because of a glaring mistake. Trailing coaches, meanwhile, will ice the players who are most likely to be aggressive, to pinch, to take shots and to score goals. It’s a two-way tactical effect that is apparent both to the eye and the stat sheet.
The question, though, is whether there is an effect at play that might be just as important, but that isn’t tactical at all. Kahneman describes loss aversion by using the following example. Imagine a man approaches you on the street offering the following wager: You will flip a coin. If the coin lands on heads, he will pay you $150. If it lands on tails, you must pay him $100. The expected value of such a wager is positive, however the majority of people will turn down the offer.
“The reason you like the idea of gaining [$150] and dislike the idea of losing $100 is not that these amounts change your wealth,” Kahneman writes. “You just like winning and dislike losing — and you almost certainly dislike losing more than you like winning.”
“This asymmetry between the power of positive and negative expectations or experiences has an evolutionary history. Organisms that treat threats as more credible than opportunities have a better chance to survive and reproduce.”
Kahneman discovered that one would have to be offered the coin flip deal at significantly higher than even odds (gaining $250 to risk losing $100) before the majority of people would accept it.
So how does this apply to score effects and playoff hockey? We know that the score of a game impacts the shot share, but could the same be said for the score of a playoff series? Could there be score effects present in a 0-0 game in the playoffs?
In order to investigate this hypothesis, I grabbed all of the shot attempt data from WAR-On-Ice going back to 2002-03 and split it by series score heading into the game. That provided me with the following chart.
While there is a strange effect present that is making teams down by two games control just under 50% of attempts, by and large the trend is clear. Trailing teams get a boost going into important games. To confirm that this wasn’t simply the result of variance, I conducted a 95% confidence interval for the true mean Corsi For Percentage when trailing. The interval was from 50.01 to 51.51. Since we know that the true mean CF% when tied is 50.00%, the result indicates that there is a slight, but statistically significant association between the score of the series and the shot differential.
I wanted to make one adjustment, however. We know that the best teams generally have the best shot attempt differentials, and the best teams also win games, so wouldn’t good teams, leading in series, putting up positive shot attempt totals, skew these results? To solve this problem, I used each team’s regular season shot attempt differential to create an expected possession result for each series and then adjust the observed result for what would have been expected.
That gave me a new shot attempt differential for each game, and with that I recalculated the mean results for each series score differential, and the results were as follows.
Once adjusting for strength of opposition, the results were especially clear-cut. The means for teams trailing were all above 50 percent, and the confidence interval these new means provided me for the true CF% when trailing was between 50.52 and 51.94, indicating a moderately strong effect.
Loss aversion is having a clear impact, as teams trailing in the series have a sense of desperation that is not embodied by the leading squad. But are there tactical factors at play as well? Would a coach change his team’s strategy when trailing in a series?
At least anecdotally, the answer would appear to be yes. So while it’s a weaker effect, playoff series score effects appear to more closely resemble individual game score effects than one might have anticipated. So keep that in mind if a team facing elimination appears to outperform what one would expect from them in terms of controlling the play this playoff season. While there are still potential confounding variables like the home/away split and the potential skewing provided by regular score effects in these games, it does appear as though this new kind of score effects is present and impactful.