Wednesday, May 23, 2007

A lesson in probability

Why is everyone so stunned about the NBA draft?

Basically, for those that don't know, what happened is the two teams with the worst record, Memphis and Boston, were the most likely to get the #1 and #2 picks, but in the drawing ended up getting #4 and #5. They are surely depressed, because a #1 or #2 pick would have meant Greg Oden or Kevin Durant, both future stars.

Everyone, including Greg Oden (the likely #1 pick and a sure superstar), seemed surprised.

But why? The draft works like this. The 14 teams that don't make the playoffs all have a shot at one of the first three picks in a random drawing. Each team gets a number of ping pong balls out of 1001 total based on their records. The team with the worst record gets 25% of the balls, the team with the second worst record 20%, and so on until the last team which has only 5 balls. Do the math real quick (I won't bore you) and you realize that even the team with the worst record had less than a 50% chance of getting one of the top 2 picks.

Here's a chart I just found from the Celtics.

So really it shouldn't be much of a surprise at all that some teams jumped into the top three from lower. Sure it was a 1 in 19 shot for the Blazers to get the #1 pick, but take all the longshots together and it's not a surprise.

Then there is discussion about how Memphis and Boston had purposely lost just to get the top picks and how it backfired. Karma and moral discussion aside, this doesn't mean that tanking is not strategically optimal. Just because they didn't get one of the top picks doesn't mean increasing their chances of getting one of those picks wasn't a good idea. Of course they wanted a higher chance of getting one of the top picks. Likewise maybe a team like the Bucks would have gotten a higher top pick had they had the extra 94 balls the worst record would have provided them over the 3rd worst record. It's all a random draw (assuming they don't rig, which the NBA does according to conspiracy theorists). You can't look at it after the fact and say losing was or wasn't a good idea.

People not understanding the basics of probability and statistics is a problem. Not a problem like cancer or poverty, but a problem nonetheless because it casues politicians, the media, voters, businessmen, NGOs, and lots of otherwise smart people to make bad decisions at times.

But congrats to the Blazers and Sonics for the luck of the draw. And karmic curses to the Hawks for getting the #3 pick, assuring the Suns it won't be theirs.

Update: Here's Bill Simmons' long awaited column in response. Funny and witty, as always.
Also, I realize I may have committed my own error- generalization. Surely there are people that weren't surprised.

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