The prisoner’s dilemma of spring hockey

The following a post is from Hockey Night in Headingley, a blog created by University of Manitoba economics professors and hockey parents, Ryan and Janice Compton.

In this, their latest entry from April 3, the hockey parents discuss the growing prevalence of spring hockey in Manitoba and how the trend can be reversed.

The prisoner’s dilemma of spring hockey

For many kids across Canada, hockey is winding down and summer sports are on the horizon. For some though, the real hockey season is only just beginning – spring hockey season.

Last year the Winnipeg Free Press gained a lot of attention from Winnipeg hockey parents with their article on spring hockey in Winnipeg, and earlier this week CBC ran a similar segment on the existence of these leagues.

For our family, this is our 4th season of spring hockey. Our oldest son has played for 3 different spring hockey organizations over the years and is excited for his spring season to begin next week (our middle son also plays hockey, however, he has only played one year and so isn’t spring hockey material yet, much to the delight of Janice). Participation in spring hockey isn’t rare among 10 year olds. On our son’s winter 9A1 team (the highest level in Winnipeg Minor Hockey for that age group but still a level with a lot of variation in hockey ability) 11 of the 14 kids are playing spring hockey this year. There are close to 15 teams in Manitoba at the 2004 age group. It is not just the superstars looking for an NHL career who are playing spring hockey.

Deep down, we know this is risky. In the WFP article linked above, Peter Woods, executive director of Hockey Manitoba, argues that “a one-dimensional, full-time approach can ultimately lead to overuse injuries, burnout and a lack of exposure to other social groups and coaching styles.” We weigh this against our son’s desire to play at a high level.

Although we have our reservations about the amount of hockey our son plays, we are not going to discuss here whether spring hockey is good or bad. What we are interested in here is how we can use economic theory to explain why there such a strong demand to continue hockey until almost Canada Day. Some of the reasons for spring hockey demand that you might hear (these are not mutually exclusive) are (i) overly zealous parents with NHL aspirations for their kids, (ii) improved player development opportunities in spring hockey relative to winter hockey, and (iii) the possibility that kids really just enjoy playing and want to extend their hockey season rather than play soccer or baseball. The explanation that we are more interested in though, and one you hear less about, is what we’ll call the prisoner’s dilemma of spring hockey.

We believe one of the key reasons for joining spring hockey is not to make the NHL, but simply to help the kids to keep up with their peer group. If a player is trying to move to a higher level next year or not fall to a lower one, he or she needs to be competitive at tryouts in the fall. At tryouts, they need to be not just good, but as good (or better) than the other kids. It used to be that a one week camp before tryouts would be enough (that was certainly the case in the 1980s when Ryan was a kid), but now much of the competition has been playing hockey for 3 or 4 (or perhaps even 6) straight months over the spring and summer. In order to compete you need to do what the other kids are doing, and that’s where the prisoner’s dilemma and a little basic game theory comes in. (If game theory isn’t your cup of tea, jump ahead to our discussion of the implications of the model and you should still be able to follow easily).

The game theory set up is as follows:

The players: “Our son” and “Everyone Else.”
The strategies: Play only 6 months a year (think the regular winter season) or play all year (think the regular winter season plus spring hockey).
The game: Each year there are two hockey seasons – the regular season and the extended (spring) season. Normalize the cost of the regular season to zero. The cost of the extended season is some positive amount which captures the monetary cost, the added risk of injury and the opportunity cost of not playing other sports. At the end of the extended season, the players compete for spots on the upcoming year’s regular winter season competitive team. The probability of making the competitive team depends on your relative amount of training.
The payoffs: Let C be the cost of playing the extended season, and X be the value that players (and parents) place on making the competitive regular season team. Assume players have a 50% chance of making the competitive team if they train as much as everyone else. If they train more, they have a 75% chance of making the team, if they train less they have a 25% chance of making the team.

The payoffs are shown in the following diagram.

As long as C < 0.25X (as long as the cost of playing is less than the expected benefit) the dominant strategy is to play the extended season. No matter what the “others” do, our son is better off playing the extended season in this model. Assuming everyone has similar payoffs, the efficient outcome (where we, together, would like to be) is where all play only the regular season. But the equilibrium outcome (where we end up, because we are all doing what is best for ourselves) is where all play the extended season. Economists use similar models to explain why firms advertise too much, why political candidates spend too much on campaigns, why co-workers vying for a promotion work too many hours, etc.

With this structure as a backdrop, we can then discuss a number of facets.

(1) Why are there more spring teams at the older ages? There are approximately 15 spring teams in Manitoba for 10 year olds, and 4 for seven year olds. It is not hard to see that X – the value of being on a competitive winter team – increases as the kids get older.

(2) Why has spring hockey grown in the past decades? We’ve assumed the benefit of the spring team is the additional probability of making the higher level winter team. This gap in probabilities grows the more kids are playing spring hockey. The more popular spring hockey becomes, the more beneficial it is for keeping up. In this respect, it is not dissimilar to the decision to attend university for some students. With more and more students earning a BA, the obvious benefit of the BA is sometimes unclear. Jobs that once required a HS diploma now require a degree. But the gap between the earnings of college graduates and high school graduates has increased so that while a university degree is not a ticket to a great job, not getting a university degree when so many others are will certainly hurt. Similarly, while playing spring hockey might not be a clear ticket to a competitive winter team, not playing spring hockey when so many others are will hurt your chances.

(3) It seems to us that spring hockey is more popular here than in some other provinces, why? We would argue that the costs of not playing other sports may be lower in Manitoba. An indoor rink in April is often preferable to being outside playing soccer in a parka, toque and mitts. Additionally, the seasons for baseball and soccer are quite short in Manitoba relative to other provinces.

(4) Finally, if we are in an inefficient outcome, and we (hockey parents) want to cut back on the amount of hockey that the kids play, what can we do to reverse the trend? Cooperation (agreeing to play less hockey year round) is unlikely to work because there are too many players involved and an incentive to cheat. So we need to change the payoffs of the game. One way to do this is to move tryouts for the Hockey Manitoba winter season. Currently kids try out at the start of the season in the fall. We’d suggest having the kids try out in the spring (following the end of winter hockey) for that upcoming year’s winter hockey team. This is done in London, Ontario (and other areas of Ontario), and spring hockey appears to be less popular there (granted, they also don’t have snow in April, so there are other differences). While this too has some problems, it does change some of the benefits of continuing hockey year round and it may reduce the demand for some.

In the meantime, we will be at the rinks well into June. Perhaps we will see you there.

Professors Ryan and Janice Compton