May 01, 2011

## Stat Nerd Sunday: ‘Better rest’ means more success in playoffs?

(Ed. Note: Welcome to Stat Nerd Sunday, where we occasionally obsess over hockey numbers like a Dungeon Master obsessing over the level of his warrior elf. Here's Matt Barr, formerly of LCS: Guide To Hockey and Trolleytracks and now blogging hockey at Kertwang.me.)

To celebrate the start of the second round, I wanted to look at the proposition that a better-rested team has an advantage in the next round over a team that took the full seven games to advance.

It makes intuitive sense: A team that's had days off, without travel, with a chance to nurse nagging injuries, should be fresher, healthier and more energetic than a team that's been through a longer series that ended more recently.

Evidence of this advantage should show up in the first game of the series between the better-rested and maxed-out teams, provided we go back far enough to get a large sample of games to look at.

Let's go back 20 full playoffs, so we'll look at 1990-2010.

Over that time, there were 71 series in which at least one participant had just won a game seven to advance. Coming off a seven-game win, teams were 29-42 in the first game of the next series, a .408 win percentage.

We're not done, because some of those series included two teams coming off seven-game series. When a seven-game series winner plays a "better rested" team in the first game of the next round -- a team that advanced in four, five or six games the round before -- the seven-game series winner is 19-32, a .373 win percentage, in 51 games.

So far, that's pretty powerful evidence of some kind of advantage.

But we're still not done. If a second round matchup features a first seed and a sixth seed, we would expect the six seed to lose the first game often, no matter how many games it took it to get there.

We can suss out the number of "upset losses" in those 51 games. The easiest way is by looking at whether the seven-game series winner was on the road -- and therefore, lower-seeded. Fifteen times in those 51 games a higher seed lost to a lower seed, a nominal "upset."  Looked at from the other direction, a lower-seeded team lost (as expected) 17 times out of 32 total losses. We can't fairly attribute those losses to facing a better-rested opponent -- it's just as likely that they were facing a better opponent.

So, 15 times in 20 years a team took seven games to dispatch an opponent, and then it lost Game 1 of the next series to a lower seed. We need to see how that compares to upsets under other circumstances. The chart below sets all this and more out, but let's walk through it first.

First, let's look at the 47 series over the same 20 years which matched two teams that both won the previous round in either five or six games. Twenty-three times the lower seed prevailed in Game 1. The higher seed went 24-23.

Then, let's look at the 19 series over the same period where both teams were coming off either a sweep or a five-game series win. There were only five upsets in game one under those circumstances, the high seed going 14-5.

Finally, we have to consider the overall number of Game 1 upsets in the second round or later over those 20 years. Sixty two of 140 game ones in the second round or later were upsets, based on seed. The high seed, in every series after the first round in the last 20 years, has gone 78-62 in game one.

In the chart, "UPSET%" isn't (as you can probably tell) the winning percentage of the lower seed. Rather, to true up the percentages with what we did for teams coming off seven-game series, we look at the number of upset losses as a percentage of all possible outcomes.

In other words, it's upset losses divided by (all wins + all losses).

Here's how I think we can fairly summarize the data:

Longer series in the previous round do contribute to upsets. Compare the upset percentage when both teams are coming off four- or five-game wins to the rest of the numbers. There are far fewer when both teams are well rested.

But a team coming off a seven-game series playing a better-rested opponent is only about five percent more likely to be upset than if both teams had gone either five or six games the series before (29.4% vs. 24.5%). That amounts to one extra game-one upset in every 20 series.

There is certainly an advantage to being well-rested, but its effect in the results of the next series -- or at least, game one of the next series -- is usually overestimated.

Bonus nerdity!  Below you see the game one W-L of each team over the last 20 years when it is coming off a seven-game series win, minimum three such games. This does not exclude series in which both teams were coming off 4-3 wins.

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