We were watching game four of the Stanley Cup finals between Edmonton Oilers and Carolina Hurricanes. Before the game started, the commentators quoted a stat to highlight the importance of the game. They said that 10 of the last 13 teams that won game four of the final series went on to win the Stanley Cup.

It sounded a little strange. At the very least it is more likely that the team that wins any one match will be more likely to win the series. I decided to look at it and see if it really is a silly stat to quote.

Winning combinations
There are 32 winning combinations in a best-of-seven-games series.

There is one way to win a series in four games and 100% of teams that won game four win the cup.
1 1 1 1

There are four ways to win the series in five games. Three quarters of teams that win game four win the series.
1 1 1 0 1
1 1 0 1 1
1 0 1 1 1
0 1 1 1 1

There are ten ways to win a series in six games. Sixty per cent of the combinations show a game four win.
1 1 1 0 0 1
1 1 0 1 0 1
1 1 0 0 1 1
1 0 1 1 0 1
1 0 1 0 1 1
1 0 0 1 1 1
0 1 1 1 0 1
0 1 1 0 1 1
0 1 0 1 1 1
0 0 1 1 1 1

There are twenty ways to win in seven games and ten of them (50%) include a game four win.
1 1 1 0 0 0 1
1 1 0 1 0 0 1
1 1 0 0 1 0 1
1 1 0 0 0 1 1

1 0 1 1 0 0 1
1 0 1 0 1 0 1
1 0 1 0 0 1 1
1 0 0 1 1 0 1
1 0 0 1 0 1 1
1 0 0 0 1 1 1

0 1 1 1 0 0 1
0 1 1 0 1 0 1
0 1 1 0 0 1 1
0 1 0 1 1 0 1
0 1 0 1 0 1 1
0 1 0 0 1 1 1

0 0 1 1 1 0 1
0 0 1 1 0 1 1
0 0 1 0 1 1 1
0 0 0 1 1 1 1

So, there are 20 of 35 combinations that have a game four win. So that’s 57% which is less than the 77% in the stat. Those combinations don’t account for different probabilities of series length or of particular combinations.

Distribution of games

Here are the combinations from the last 13 finals series.

2003-2004 0 1 0 1 0 1 1
2002-2003 1 1 0 0 1 0 1
2001-2002 0 1 1 1 1
2000-2001 1 0 1 0 0 1 1
1999-2000 1 0 1 1 0 1
1998-1999 0 1 1 0 1 1
1997-1998 1 1 1 1
1996-1997 1 1 1 1
1995-1996 1 1 1 1
1994-1995 1 1 1 1
1993-1994 0 1 1 1 0 0 1
1992-1993 0 1 1 1 1
1991-1992 1 1 1 1
1990-1991 0 1 0 1 1 1

Hey those five series sweeps can really skew the statistic. Five of the thirteen have all games won by one team.

If we look at the distribution of series length.

7 games - 3

6 games - 3

5 games - 2

4 games - 5

So if we multiply this series length distribution by the proporation that have gamef our wins we get:

3*50% + 3*60% + 2*75% + 5*100% = 9.8

So is 9.8 close enough to 10 to show that the game four win is just random variation within the distribution? Oh, whatever.

I went into the grade three class yesterday for the first time in several weeks. They had had standardized tests earlier in the week, so Thursday was a more relaxed day.

I made paper airplanes with groups of two and three. I helped the girls set up the stereo at a window so they could practice their choreography for the upcoming talent show.

• “That song is inappropriate for our age group. It says ‘grab your chest.’”
• About one group’s dance “People would be yawning by now.” “They told us you’r supposed to do something different every eight beats.”
• I got a photograph of me and all 19 or so kids. They are all giving me rabbit ears.

In the afternoon the kids made “cootie catchers,” which is a folded paper fortune game. You fold it from a square of paper and then mark the four outside flaps with colours, eight inside triangles with numbers and under each number there is a fortune. Based on the choice of colour the user moves the quarter of the catcher with thumbs and forefingers by each letter of the colour and then counting the number. That is how the fortune is chosen. Kids made fortunes like: cool, you will win $1,000, you will marry [this person], sexy. Then there were “you’re gay,” and “perv;” some kid may get suspended.

I hope to see the kids one or a couple more times before school ends. Then it is summer vacation.