Wednesday, December 2, 2009

Basketball Math Fail

Today's miscreant: The Boston Globe's Celtics Notebook. The offending paragraph reads:
Rasheed Wallace has eight technical fouls in 18 games, which would equate to 36 over a full season. That number is astronomical, of course, especially since the NBA suspends players one game for each technical after the 16th.
First of all, the NBA does no such thing. It does suspend players one game for every other technical, starting with the 16th. (See the NBA Rule Book, Rule 12, Section VII.) But that's not the math fail in this instance. The math fail is figuring that Wallace would get 36 technicals over a full 82-game season, when by their own admission, he wouldn't even play 82 games because of the suspensions for all those technicals.

So how many technicals would he get, if he were to get them at the same rate for the rest of the season, and he didn't miss any games to injury or other reasons besides the suspensions from the technicals?

At the current rate, Wallace would pick up his 16th technical in his 36th game, meaning he would be suspended for the team's 37th game. (We'll assume that Wallace doesn't appeal any of his technicals or suspensions.) He would then pick up four technicals in every nine games he played in thereafter. For the sake of argument, let's say he picks up the even-numbered technicals (16th, 18th, 20th, etc.) in the fifth and ninth game of every cycle of nine games he plays in. Since each of those technicals would carry with them a one-game suspension, these cycles would actually span 11 games for the Celtics.

As a result, Wallace would pick up those even-numbered technicals in the Celtics' 42nd, 47th, 53rd, 58th, 64th, 69th, 75th, and 80th games, in each case being suspended for the next game. That technical in the 80th game
his 32ndwould be his last, since he'd only be able to play in one additional game, and we'll charitably assume that he wouldn't get called for a technical in that one. So he'd get suspended for nine games in all, drawing 32 technicals in 73 games.

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