The NBA conference finals brings with it one of the best sideshows in sports: the NBA draft lottery, in which 14 grown men stand around awkwardly for half an hour to figure out how a bunch of ping pong balls bounced. We*, the viewing audience, are treated to a half-hour special containing some 15 minutes of talking heads speculating wildly, 2 minutes of commisioner David Stern reading franchise names, and 5 minutes of awkward interviews with team representatives. Fascinating.
* - Maybe "we" is the wrong pronoun; I mean, I didn't watch it.
But while the presentation of the lottery may not be especially compelling, the lottery itself sure is. The lottery teams (i.e., those that miss the playoffs) are ranked in inverse order of record, with the worst teams receiving the best chances of a high pick. So the team with the worst record has a 25% chance of winning the lottery, the second-worst team has a 19.9% chance of winning the lottery, and so on down to the 14th-worst team (the last team out of the playoffs) who has a 0.5% chance of winning the lottery. The whole list of probabilities for this year's draft is available here.
Some have argued (with varying degrees of seriousness) that the lottery system is rigged*, and point to the fact that the worst team in the league hasn't won a lottery since the Orlando Magic won and picked Dwight Howard in 2004. But I want to stress this again, because it's important: the team with the highest probability will still lose the lottery (i.e., not get the first overall pick) 75% of the time.
* - In fact, a certain popular sports columnist with an affinity for Boston teams and Teen Wolf went so far as to list the teams most likely to benefit from the rigged lottery. The only thing is, he picked five total teams with a combined probability of 43%. There's a really good chance one of those "suspicious" teams was going to win, even without foul play.
And how likely is it that something with a 75% probability will happen eight times in a row? Well, we can use the same formula we did for Pujols' homerless streak:
P(no win in 2005)*P(no win in 2006)*...*P(no win in 2012) = (.75)(.75)...(.75) = .75^8 = .1001
So call it 10%. That's not crazy.
Since 1999*, two of the 14 lottery winners have had the worst record in the league that season. The difference between 14% and the expected 25% seems large, but look: this is a very small sample size. In 14 samples, you would expect an event with a probability of 25% to happen on average some 3.5 times. So we're talking, what, one unlucky bounce here or there, and we're right on average.
* - Before 1999, the Raptors/Grizzlies' expansion agreements did weird things to the probabilities, so let's ignore that for the sake of simplicity.
On the other hand, since 1999, seven* of the 14 lottery winners had a less than 10% chance of winning the lottery. That seems odd, but remember: there are several teams in the lottery each year with a less than 10% chance of winning. In fact, there are about 10, and the odds of one of these winning the lottery in any given year come out to a combined 27%. Still, the odds of this happening seven times out of 14 are something like 60-to-1 (1.7%). It's enough to raise a unibrow, but still: very small sample size.
* - This includes the Cavs' win last year even though they had the worst record in the league, since the pick they won with technically came from the Clippers in a trade.