## Wednesday, December 12, 2018

### 2007-12 was an era of competitive balance in the NHL

Five years ago, I calculated that in the NHL, it took 73 games until talent was as important as luck in determining the standings. But in a previous study, Tango found that it took only 36 games.

Why the difference?

I think it's because the years for which I ran the study -- 2006-07 to 2011-12 -- were seasons in which the NHL was much more balanced than usual.

For each of those six seasons, I went to hockey-reference to find the SD of team standings points:

SD(observed)
--------------
2006-07  16.14
2007-08  10.43
2008-09  13.82
2009-10  12.95
2010-11  13.27
2011-12  11.73
--------------
average  13.18  (root mean square)

Tango's study was written in August, 2006. The previous season had a higher spread:

SD(observed)
--------------
2005-06  16.52

So, I think that's the answer. It just happened that the seasons I looked at had less competitive balance that the season or seasons Tango looked at.

But what's the right answer for today's NHL? Well, it looks like the standings spread in recent seasons has moved back closer to Tango's numbers:

SD(observed)
--------------
2013-14  14.26
2014-15  15.91
2015-16  12.86
2016-17  15.14
2017-18  15.44
--------------
average  14.76

What does that mean for the "number of games" estimate? I'll do the calculation for last season, 2017-18.

From the chart, SD(observed) is 15.44 points. SD(luck) is roughly the same for all years of the shootout era (although it varies very slightly with the number of overtime losses), so I'll use the old study's number of 8.44 points.

As usual,

SD(talent)^2 = SD(observed)^2 - SD(luck)^2
SD(talent)^2 = 15.44^2 - 8.44^2
SD(talent)   = 12.93

So last year, SD(talent) was 12.93. For the six seasons I looked at, it was 8.95.

SD(talent)
--------------
2016-12   8.95
2017-18  12.93

Now, let's convert to games.*

*Specifically, "luck as important as talent" means SD(luck)=SD(talent). Formula: using the numbers for a full season, divide SD(luck) by SD(talent), square it, and multiply by the number of games (82).

When SD(talent) is 8.95, like the seasons I looked at, it takes 77 games for luck and talent to even out. When SD(talent) = 12.93, like it was last year, it takes only ... 36 games.

Coincidentally, 36 games is exactly what Tango found in his own sample.

talent=luck, after
------------------
2016-12  77 games
2017-18  36 games

Two things we can conclude from this:

1. Actual competitive balance (in terms of talent) does seem to change over time in non-random ways. The NHL from 2006-12 does actually seem to have been a more competitive league than from 2013-18.

2. The "number of games" way of expressing the luck/talent balance is very sensitive to moderate changes in the observed range of the standings.

--------

To expand a bit on #2 ...

There must be significant random fluctuations in observed league balance.  We mention that sometimes in passing, but I think we don't fully appreciate how big those random fluctuations can be.

Here, again, is the SD(observed) for the seasons 2014-17:

SD(observed)
--------------
2014-15  15.91
2015-16  12.86
2016-17  15.14

It seems unlikely that 2015-16 really had that much tighter a talent distribution than the surrounding seasons. What probably happened, in 2015-16, was just a fluke -- the lucky teams happened to be lower-talent, and the unlucky teams happened to be higher-talent.

In other words, the difference was probably mostly luck.

A different kind of luck, though -- luck in how each individual team's "regular" luck correlated, league-wide, with their talent. When the better teams (in talent) are luckier than the worse teams , the standings spread goes up. When the worse teams are luckier, the standings get compressed.

Anyway ... the drop in the chart from from 15.91 to 12.86 doesn't seem that big. But it winds up looking bigger once you subtract out luck to get to talent:

SD(talent)
--------------
2014-15  13.49
2015-16   9.70
2016-17  12.57

The difference is more pronounced now. But, check out what happens when we convert to how many games it takes for luck and talent to even out:

Talent=luck, after
------------------
2014-15  32 games
2015-16  62 games
2016-17  37 games

Now, the differences are too large to ignore. From 2014-15 to 2015-16, SD(observed) went down only 19 percent, but the "number of games" figure nearly doubled.

And that's what I mean by #2 -- the "number of games" estimate is very sensitive to what seem like mild changes in standings variation.

-------

Just for fun, let's compare 2006-07, one of the most unbalanced seasons, to 2007-08, one of the most balanced. Just looking at the standings, there's already a big difference:

SD(observed)
--------------
2006-07  16.14
2007-08  10.43

But it becomes *huge* when when you express it in games:

Talent=luck, after
------------------
2006-07   31 games
2007-08  156 games

In one year, our best estimate of how many games it takes for talent to exceed luck changed by a factor of *five times*. And, I think, almost all that difference is itself just random luck.

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