Friday, May 04, 2007

The importance of Game 5

Throughout NHL playoff history, after a series is tied at 2, the team that wins Game 5 has gone to win nearly 80% of the time.
The next game in tonight's Buffalo-New York and tomorrow afternoon's Detroit-San Jose match-ups is absolutely pivotal (although there's a good chance you didn't need the above quote to spell that out).

I'm curious: Do any of the various stat gurus that read this blog know what the importance of every game in a series equates to?

(The only one I'm absolutely sure of is that the team that wins Game 7 wins 100 per cent of the time.)


At 1:17 p.m., May 04, 2007, Anonymous Indrew said...

I don't have the historical stats, but so far in these playoffs, the team that has won game one has come out on top of all 9 of the completed series'.

One could argue that Ottawa, San Jose, and Buffalo have a good chance of winning their respective series, so a perfect 12-12 to start things off is possible

At 1:22 p.m., May 04, 2007, Anonymous BDH said...

One could also argue that Detroit has a pretty good shot in a best of 3 with home ice...

At 2:12 p.m., May 04, 2007, Anonymous Indrew said...

"One could also argue that Detroit has a pretty good shot in a best of 3 with home ice..."

Very true. I for one wouldn't bet money on either team. I have no idea how it will end.

At 3:38 p.m., May 04, 2007, Blogger JavaGeek said...

Not sure if this what you're looking for. I just used the who wins historical outcomes for the NHL.
Game 1:
0-0: 50.0% -> 68.3% = +18.3%
Game 2:
1-0: 68.3% -> 86.5% = +18.2%
0-1: 31.7% -> 50.0% = +18.3%
Game 3:
2-0: 86.5% -> 98.6% = +12.1%
0-2: 13.5% -> 29.6% = +16.1%
1-1: 50.0% -> 70.4% = +20.4%
Game 4:
3-0: 98.6% -> 100% = +1.4%
2-1: 70.4% -> 90.7% = +20.3%
1-2: 29.4% -> 50.0% = +20.6%
0-3: 1.4% -> 9.3% = +7.9%
Game 5:
3-1: 90.7% -> 100% = +9.3%
2-2: 50.0% -> 79.1% = +29.1%
1-3: 9.3% -> 20.9% = +11.6%
Game 6:
3-2: 79.1% -> 100% = +20.9%
2-3: 20.9% -> 50.0% = +29.1%
Game 7:
3-3: 50% -> 100% = +50%

At 3:57 p.m., May 04, 2007, Blogger J. Michael Neal said...

It should be noted that most of the numbers Javageek posted show that the series outcome is pretty much a binomial distribution with P set to .5. In other words, it looks very much as if, in aggregate, each game is close to a 50/50 proposition regardless of what the current series situation is. I have to go to work in ten minutes, so I don't have time to sort through it right now, but let's look at the specific example that James brought up.

If a series is tied 2-2 going into the fifth game, it will automatically be 3-2 after that game. With two games remaining, and if it is a straight up 50/50 proposition as to who wins each game, we would expect the distribution of outcomes for those two games to be .25 for each case of one of the teams winning both of them, and .5 for each team winning one. Of course, if the team that's up in the series wins game six, which they should 50% of the time, game seven isn't played, but that doesn't matter for this analysis.

In other words, with a binomial distribution where p=.5, we would expect the team that wins game five to win the series 75% of the time. The data show that they win about 79% of the time. That could well be in a 95% confidence interval around 75%, though I'd have to know how many instances of a series tied 2-2 there are to know for sure. In practice, I would expect there to be a slightly greater than 75% chance of the team up 3-2 winning the series, because the expectation is that the team that has won more games is the better team. That effect is likely to be small, in aggregate, since five games is such a small sample size, but it's there.

(That's different from saying that the team that has a better regular season record has more than a 50% chance of winning each game, since that's based upon a sample size of 82, rather than five. In each case, we have different prior knowledge.)

So, I absolutely agree that game five of a series is pivotal. The one thing I would caution people about is drawing any inference about the overall quality of the teams based upon that outcome. To answer that question, the amount of additional knowledge you have after the fifth game played is negligible.

At 4:56 p.m., May 04, 2007, Blogger Nick said...

Lies, damn lies and statistics.

James, you've been talking a lot of statistics this year. When you look at overall averages, I'm not surprised it comes out that way - but when you're looking one individual series, the standard of deviation takes over... If the Rangers were to win game 5 and you said "The Rangers now have an 80% chance of winning the series" I'd take those odds.

I would venture to say that game 4 was a more important game to win for Detroit than game 5 will be, but it's still huge.

Go wings.

At 5:21 p.m., May 04, 2007, Blogger James Mirtle said...

I just find them to be interesting talking points, Nick. It's definitely not gospel, and there's a lot to be said for momentum, etc., when breaking down a series.

The blog's just a good repository for things I read that are interesting; often they happen to be statistics, I guess.

(I'd actually intended to do a "The importance of Game 4" post but never got around to it.)

At 5:40 p.m., May 04, 2007, Blogger JavaGeek said...

There are three pieces of information in the historical averages:
1. Binomial
2. Home ice
3. Team strength

For two teams: 70% (Team A) and 30% (Team B), Possibilities after game 5:
p(A comesback from 2-3) = 49%
p(B comesback from 2-3) = 9%
p(A needs to comeback) = 30%
p(B needs to comeback) = 70%
Implies p(win 3-2) = 1-p(comeback 2-3)
1-(0.30*0.49+0.7*0.09) = 1-0.21
= 79%
Note: The better team accounts for 70% of the comebacks with only 30% of the opportunities.

It should be noted that team A has a 78.4% chance of winning the "3 game series". The odds increase to 91% with a win.

Of course the trick question is "who is the stronger team?"

At 7:59 p.m., May 04, 2007, Blogger Nick said...

The dudes on Vs. are dropping the 80% statistic. Sometimes I wonder how much stuff they lift from blogs.

At 8:44 p.m., May 04, 2007, Blogger Art Vandelay said...

I have a 100% percent certainty of being confused.

At 1:01 a.m., May 05, 2007, Blogger J. Michael Neal said...

I just find them to be interesting talking points, Nick. It's definitely not gospel, and there's a lot to be said for momentum, etc., when breaking down a series.

On the list of things that I want to study about hockey if I ever have the time and the discipline to do it, momentum ranks very highly. Both in-game and between-game momentum interest me. To start, I'm curious as to whether they actually exist.

In studies of baseball, any evidence for momentum is very hard to come by. Both hot teams and hot hitters are very hard to make predictions about. It is very clear that both get on hot streaks that are statistically significant, but you can only recognize these streaks in retrospect; the predictive value of having been hot for determining if you will stay hot is near zero. In other words, your hot streak can end at any time, and is just as likely to end right now as it is to end next week.

I suspect that momentum has a stronger impact in hockey, at least within a particular game. I also suspect that the effect still isn't very strong. I could easily be wrong about that, being biased by having seen the data for baseball.

That's why conducting the research is so much fun, of course. Who knows what you'll actually find.

At 1:34 p.m., May 05, 2007, Blogger JavaGeek said...

But in the NHL, when teams find themselves a man down and their penalty kill units score the rare shorthanded goal; there is no greater momentum swing. []

RE: In game momentum.
I have been able to show that a short-handed goal increases your odds of winning a game more than even strength goal or power play goal does. I have to work out some of the mess of this theory as it is quite complicated. But momentum certainly exists.

At 1:31 p.m., May 06, 2007, Blogger Nick said...

is a shorthanded goal the cause of the win or a indicator of something else going on in the game?


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