Numbers game of 5-, 7-game series
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Last week, talking about his team's series against the Philadelphia 76ers, Boston Celtics coach Jim O'Brien voiced a common concern among NBA coaches and players. "Five-game series are too short," he told the Boston Herald. "You put a lot into the year getting to the playoffs, and you want to be able to play a seven-game series because I think a seven-game series really proves who's the better basketball team."

O'Brien's got a lot to think about, such as how to keep Allen Iverson from getting 42 points again in Game 4 Wednesday night, so he should stop worrying about how short that first-round series is. Because he's wrong.

A best-of-7 series doesn't really prove anything different than a five-game set.

Simple mathematical probabilities tell the story. This handy chart was published by James H. King back in 1994:

Probabilities of stronger team winning games
Likelihood of a stronger       Length of series  
team winning any game |   3 5 7 9
55% |   57% 59% 61% 62%
60% |   65% 68% 71% 73%
65% |   72% 76% 80% 83%
70% |   78% 84% 87% 90%
75% |   84% 90% 93% 95%

In this particular series, the Celtics, it can be argued, are marginally better than the Sixers. (They won six more regular season games than the 76ers, but lost 3-1 in head-to-head matchups.) So let's say the Celtics' chance of winning each game is 55 percent. As the chart says, 59 percent of the time, the Celts will win a five-game series. Lengthen it to seven games, and they'll win 61 percent of the time.

In other words, in the case of the Celtics against the Sixers, only once every 50 years would it matter whether they were playing five games or seven games in a series.

Or, if you are the kind of Celtics fan who bleeds kelly green and knows Larry Bird's middle name, perhaps you think the Celtics have a 75 percent chance of winning any particular game. In that case, as the chart shows, the difference between a five-game series and a seven-game series is only three percent. In other words, there is hardly any difference at all between a five-game series and seven-game series, no matter how big the gap between the two teams.

In a way, O'Brien is providing his team (and himself) an excuse to lose. He's saying that we know our team is better, but if we lose this series it's because of bad luck.

You know what? The coach is showing some insight there because, when it comes down to it, only two basic factors decide how a series will go -- the quality of the two teams, and a big set of imponderables called luck. But don't tell anyone, because then all of us sportswriters will be out of a job.

Note: For more, see the (issue) 1992 article by E. Lee May Jr., in the academic journal Mathematics Teacher, "Are Seven-Game Baseball Playoffs Fairer?"

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Jeff Merron