On Friday the NHL released the 2013-2014 regular season
schedule. This season will be the first played under the new conference and
division alignment which sent Winnipeg west and Columbus and Detroit east. A
key aspect of the new alignment is that there is an imbalance in the number of
teams in the East (16) and in the West (14). In this post I'll discuss a paper
I wrote a couple months back (How the West will be Won: Using Monte Carlo Simulations to Estimate the Effects of NHL Realignment). In the paper, I show
that because 8 teams make the playoffs from each conference, the new alignment
and playoff qualification rules unfairly disadvantage Eastern Conference teams.

**Specifically, I'll show that the 8**

^{th}seed in the East will (on average) be 2 or 3 points better in the standings than the 8^{th}seed in the West. And I'll show that about 40% of the time, the 9^{th}seed in the East would have made the playoffs if they were in the West (compared to just 20% of the time when the inverse is true).
This research was my first foray into hockey analytics. Back
in March the NHL announced it had settled on a plan to realign the conference
and division structure. Starting this upcoming season, the NHL will have two
conferences, and each conference will feature two divisions. The Eastern
Conference will have 16 teams, and the Western Conference will have 14 teams.
Each conference will continue to feature an 8 team playoff, with the conference
winners meeting in the Stanley Cup Final.

It was this final feature of the realignment that caught my
attention. How is it that the NHL owners (especially in the East) agreed to a
plan in which Eastern teams have a 50% chance of making the playoffs, compared
57% among Western teams? Almost automatically, it has become harder to qualify
in the East than in the West. So this got me thinking about how this new
alignment will actually play out and whether or not it will actually be unfair.
I was specifically interested in what I call in the paper the "conference
gap," which is the number of end-of-season points by the 8

^{th}seed in the East minus the points by the 8^{th}seed in the West.
The obvious problem with learning about the conference gap
is that the NHL hasn't yet played a single game under these new rules, let
alone a whole season. So, being a good statistician who knows how to write
fancy R code, I decided to simulate full NHL seasons and then calculate the
conference gap. And not just 5 or 10 simulated seasons. I simulated 10,000 of
them.

The intuition behind my simulation was pretty
straightforward. To simulate one season, I randomly draw 30 numeric
values from a normal (bell-shaped) distribution. These 30 values correspond to
the underlying quality or ability of the 30 teams. Then I go through and
simulate all 1,230 games in the NHL schedule (adjusted appropriately to take
into account the new scheduling matrix). For each game, I draw a number from
two normal distributions (each centered at the value of two teams' underlying
ability). These two numbers can be thought of the amount of effort or skill the
two teams put forth during this game. The game is "won" by whichever
team drew the higher number for their game performance value. I also account for games going into overtime, which I
discuss this more thoroughly on page 12 of the paper.

After I've simulated all 1,230 games, I calculate the final
standings as well as the conference gap. Then as a point of comparison, I use the
same 30 underlying ability values to rerun the season, only this time I apply
the old schedule matrix, old alignment, and old playoff qualification rules. I
repeat all these steps 10,000 times (essentially simulating 10,000 seasons) to get a nice understanding of how big the
conference gap will be. In the paper, I go into more detail about how I tweaked
my algorithm, so that I don't end up with the best team having 150 points and the worst having 15. That discussion starts on page 16
of the paper. It suffices to say though that you'd have a pretty tough time telling the difference between results from my simulations and the results from a real NHL season.

The graph below plots the conference gap for the 10,000
seasons simulated under the old and new alignment structures. The blue parts of
the graph correspond with the new rules, and the red parts correspond with the
old.

What you can see is that under the old rules the average
conference gap was 0.143 points in favor of the Western Conference, although
this value is not statistically significantly different from zero. Under the
new rules, however, the average conference gap is 2.76 points.

*This means that, on average, the 8*^{th}seed in the East had 2.76 more points than the 8^{th}seed in the West.
The graphs also contain the information of how often the
conference gap favored the East versus the West.

**. This means that starting next year, we're about twice as likely to see a better Eastern 8***In the old alignment, 47% of seasons had the better 8*^{th}seed in the West, and 46% of seasons had an better Eastern 8^{th}. In the new alignment, this difference gets huge. 62% of the time, the East's 8 had a better record than the West's 8, compared to just 32% of the time the inverse was true^{th}. Under a fair set of rules in which your geographic location shouldn't affect your chances of making the playoffs, these numbers should be 50/50.**. The opposite, in which the 9**

*My simulations also show that 38% of the time, the 9*^{th}seed in the East would have qualified for the playoffs if they had only been located in the West^{th}Western team would have made the playoffs in the East, occurs only 21% of the time

*. Even more striking, my simulations suggest that 21% of the time the 10*^{th}(!) seed in the East would make the playoffs if they were in the Western Conference.
I might do another post in the next couple days, detailing a
couple other interesting things that are in the paper. But until then, here's
the takeaway... Expect that in about 62% of seasons, the 8

^{th}seed in the East will have a better record than the 8^{th}seed in the West. And in 38% of seasons, the 9^{th}seed in the East will have a better record than the 8^{th}seed in the West. And
Your Monte Carlo estimation assumes the distribution of talent is identical across conferences. But lately the West has been better than the East, as indicated by the fact that each of the last few pre-strike years one or more western conference teams have missed the playoffs with point totals higher than those of Eastern conference teams that got in. If you buy this, then the unfairness is baked in to the current system based on conferences, the question is just how it will be manifest (in unbalanced conferences) or in allocating playoff spots by conference.

ReplyDeleteActually, it didn't happen in 11-12 (when the Kings won as the 8 seed in the West) but it did in the two preceding years.

ReplyDeleteThis doesn't take away from your nice statistical analysis, just from the fairness argument. I think the best way to address this is to have the top 16 point total teams make the playoffs. Of course then the unbalanced schedule would come in to play, but it would probably be better.

Thanks for the feedback. I definitely agree that this might serve to balance out the fact that the West is better. In an ideal world though we'd have great balance between the two conferences, but if this were the case the West would benefit from this structural advantage. I think you're onto something with the suggestion that the top 16 teams should make the playoffs. That would be a pretty radical change for the NHL to make, but they seem to like to make changes that bring attention to the league. Maybe some day we'll see that happen.

ReplyDeleteMake two more teams then it be even out.

ReplyDelete