Quick Math Lesson

Bloggified by Jake on Friday, May 14, 2010

A few weeks ago, when the Coyotes were playing the Red Wings in the first round of the Stanley Cup Playoffs, one of the commentators mentioned during Game 5 of the series the importance of winning the fifth game. It seems that in the last 10/15/whatever arbitrary number of years they selected, the team that won the fifth game in a series that was tied 2-2 after two games went on to win the series "almost 80% of the time." The actual number was just a tic above 78% in thirty-some-odd series.

The implication was that winning Game 5 gives a team the momentum it needs to break through and win the series. The commentators tried to give the win a psychological spin. The pressure is off the winners and the losers have their backs to the wall.

But let's just look at it mathematically.

Let's assume two teams are evenly matched to an degree that the outcome of any game between the two will be a virtual coin flip.

In Game 6, there are two possible outcomes. The 3-win team wins 50% of the time and the series is over, and the 2-win team wins 50% of the time and the series goes to a seventh game. In the case of the latter, 50% of the time the team that won Game 5 will win and take the series, and 50% of the time the team that won Game 6 will win and take the series.

So, 50% of the time the team, that wins Game 5 will win in Game 6, and 50% of 50% (also known as 25%) of the time, it wins Game 7. Translation: Without factoring in any variables of home ice, player strengths and weaknesses, fatigue, etc., the team that wins Game 5 should win 75% of the time! All it takes is one team to lose Game 5 and win the series to bring that 78% down to 75%. So, what I'm saying is your mystical, psychological edge is bullshit.

I only bring this up because today I heard all the buzz about the Bruins, who'd won the first three games of their series with the Flyers only to now need a win in Game 7 to avoid elimination. When you combine all of the playoff records of hockey, baseball, and basketball, only three teams have come back to win a series in the 276 times that their opponents jumped out to a 3-0 lead.

That's because the team with the 3-0 lead has a 50% chance of winning games 4, 5, 6, and 7, any of which eliminate the team that lost the first three games. So 50%+25%+12.5%+8.25%=95.75% of the time the 3-0 should win the series just by random chance. Factor in that a team that gains a 3-0 lead on its opponents over three games is likely a better team with better players, better coaches, or whatever other edge you might be able to attribute. They also are more likely to be playing Game 7 on home ice. Factor in those variables and it's no surprise that they win 98% of the time instead of the predicted 96%

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