Well, this year's playoffs have been interesting so far, haven't they? It was the first year since 1937-38 in which none of the previous year's semifinalists won a playoff series. It was also the first year since 1925-26 that no "Original Six" team won a playoff series. Since my favourite team was both in last year's semifinals and was an "Original Six" team (it's thirty-six years now - how much longer is it going to be?), I now have lots of time to write another one of these articles. Instead of attempting to write on a complex subject and getting bogged down (thus explaining the huge delay since the last one), I'll look at a slightly simpler topic that came to mind a short while ago:

At the start of the playoffs a few weeks ago, several commentators commented on the importance of winning the first game of a playoff series, the implication being that winning the first game of a series gives a team some sort of psychological advantage. Being at least a little suspicious of "psychological advantages", I waited for someone in the mass media to either debunk this idea or at least to argue against it, but no-one did. So, I guess that leaves insignificant me to do so.

Objectively, there is some advantage to winning the first game of a playoff series. After all, you're up 1-0 in the series instead of being down 1-0, and you now only have to win three out of the next six games, while your opponent has to win four out of the next six. If you sweep the series, then you obviously had to have won the first game. The question I want to answer, however, is whether the advantage obtained by winning the first game is completely explained by the simple fact that they've won a game, or is there some other advantage?

Let's look at a series between two evenly-matched teams that win
or lose games completely at random. Since, in the playoffs, there are
only two possible outcomes for each game (either one team or the other wins),
and there are six games after the first game, there are 2^{6} = 64
possible combinations of win/loss sequences for the rest of the series
(obviously not all of these will occur in a real series because the series
would be over after one team wins four games, but for the current purpose
we can ignore this fact).

Since the team that wins the first game needs to win three out of the next six games in order to win the series, the probability that the team that wins the first game will also win the series is

= ^{40}/_{64} = 65.625%

Pulling out the trusty ol' calculator again, ^{171}/_{268}
is about 63.8%. As we calculated above, the "ideal" probability that a
team that wins the first game of a series will win the rest of the series
is 65.625%. Since these two numbers are quite close,
So, in conclusion, there is no psychological advantage to winning the
first game of a best-of-seven series. There appears to be no advantage
to winning the first game than the fact that
a team that wins the first game now only needs to win three more,
instead of four. Also, the winner of the first game is only a moderately
good predictor (i.e. less than 64%) of who is going to win the series.
A much better predictor would be the winner of the last game of the series.
## Bibliography

Assuming two even teams that win or lose games at random, the
probability that the team that wins the first game of a best-of-seven
series will also win the series is
65.625%, slightly less than ^{2}/_{3}.

Since most of series in the Stanley Cup playoffs are not played between two evenly-matched teams that win or lose games at random, we need to look at what effect this assumption has on this number. This assumption is actually comprised of two parts. The first part is that the two teams are even, which they most likely aren't. A stronger team will (a) more often than not have home-ice advantage for the first game, (b) be more likely to win the first game anyway and (c) be more likely to win the entire series, and so the correlation between (b) and (c) will almost certainly be positive. As to how strong this positive correlation is, I won't worry about that yet. To save typing from here on in, let's call this the "stronger team" effect. The second assumption is that the teams win or lose games at random. If there is some psychological advantage (or, to be fair, disadvantage) to winning the first game, then the wins and losses would not be distributed at random. To save some typing, let's call this the "psychological" effect.

I'm now going to look at all of the best-of-seven series over the previous
twenty years,
and calculate the percentage of series winners who won the first game
of the series. But what will the number that comes out the bottom mean?
Well, if we find that about ^{2}/_{3} of
series winners also win the first game of the series, it either means
that the "stronger team" effect cancels out the "psychological" effect,
or that neither of these effects are significant. If the number is a
good deal lower, then there is likely some sort of *negative*
"psychological"
effect. If it's a good deal higher, then this is either due to one or
more of the "stronger team" effect or a *positive*
"psychological" effect.

So, let's crunch some numbers and see what happens. I've dug out the series results for all best-of-seven series for the past 20 years (until 1986-87, the preliminary round was a best-of-five affair, so I've ignored those series), and compared the series winner to the team winning the first game of the series. I was going to list each results for each series for the past twenty years below, but I felt that it was pretty boring reading. So, I've removed it from this page and separate page listing each individual outcome. Moving right along, here are the year-by-year summaries:

Year | # of game 1 winners who won series | # of game 1 winners who lost series | Total |
---|---|---|---|

1982-83 | 6 | 1 | 7 |

1983-84 | 4 | 3 | 7 |

1984-85 | 4 | 3 | 7 |

1985-86 | 4 | 3 | 7 |

1986-87 | 7 | 8 | 15 |

1987-88 | 10 | 5 | 15 |

1988-89 | 8 | 7 | 15 |

1989-90 | 9 | 6 | 15 |

1990-91 | 6 | 9 | 15 |

1991-92 | 11 | 4 | 15 |

1992-93 | 9 | 6 | 15 |

1993-94 | 9 | 6 | 15 |

1994-95 | 10 | 5 | 15 |

1995-96 | 12 | 3 | 15 |

1996-97 | 10 | 5 | 15 |

1997-98 | 13 | 2 | 15 |

1998-99 | 9 | 6 | 15 |

1999-00 | 11 | 4 | 15 |

2000-01 | 10 | 5 | 15 |

2001-02 | 9 | 6 | 15 |

Totals | 171 | 97 | 268 |

- National Hockey League, The National Hockey League Official Guide & Record Book, various years.
- The Internet Hockey Database, http://www.hockeydb.com/.

For questions or comments, please e-mail James Yolkowski.

This article is Copyright © 2002, James Yolkowski. You may reprint or reproduce this article, as long as this paragraph is also reproduced. The original article and others like it can be found at http://www.sentex.net/~ajy/hockey/.