Parity in hockey: a simulation

I wrote a bit of R code to explore the ‘parity question’ in the NHL; specifically, if all teams were more or less equal, what would we expect to see in terms of regular season point totals? You can find the code for generating a hockey schedule here and the simulation code here.

The scheduler is just a dirty optimizing algorithm that I came up with that is probably inferior to what the NHL uses, but it seems to work. You can set the schedule parameters and it seems to work fairly well provided the inputs result in a feasible solution; for example, don’t lower the max games too much or it won’t be able to solve. I had to create the scheduler to generate a realistic play schedule that the hockey simulator could use.

For a given schedule, the hockey simulator plays a season of hockey and sums up point totals. For the purpose of this experiment, I assume that all teams have an equal chance of winning. If a team loses, they have a x% chance at getting a loser point (by default, this is set at 11%).

I then run the simulation many times. One way to investigate the results is to plot out the distribution of top regular season team (the team with the most points). Here is a histogram of the maximum point totals over 1000 simulations:

How does this compare to real data? Well, it depends on the season, but generally speaking, the best teams in the real world do better than the best teams in the simulation. This suggests that the NHL has not yet reached the point of real parity. The far left values on the figure below tell us the mean, range (95%) and maximum (of the maximum points) over 1000 simulations. Tampa Bay outperformed the parity simulation even after 1000 simulations–suggesting that their regular season performance in 2018/2019 was far from a matter of luck.

Nevertheless, imagine if 2018/2019 Tampa Bay was an anomaly, and the trend of real NHL point maximums continues downward–where the best regular season team gets point totals that approach 107 or so in a few years. At that point, it might suggest that the NHL has reached some level of true parity, where the vagaries of year-to-year luck (like injuries) will play an increasingly large role in determining the success of a team, rather than true superiority of skill and tactics on the ice.