Thursday, November 6, 2014

ESPN Analysts Display Lack of Probability Knowledge

Yesterday, on ESPN's Sport Center, they were going on about how badly the Los Angeles Lakers are doing so far this year, going winless in their first five games.  One point they brought up was the upcoming schedule for them, with Kobe Bryant and company favored to lose each of their  next eight games.  There were actual percentage probabilities given for the Lakers to win each game, with the figures hovering around the 30th and 40th percentiles.  Then one of the announcers got to the point of all this, which is that they may well lose all eight games and start the season off at 0-13.  I beg to differ...

I didn't get all of the percentage predictions of each game (I wonder how they even arrived at them), but I think I'm being pretty conservative at saying they averaged about a 35% winning probability given for each game (it's probably higher).  That means that the losing probability for each game is .65: for the Lakers to lose all eight of their next games, you would need to take that probability to the eighth power:

(,65)(.65)(.65)(.65)(.65)(.65)(.65)(.65)=.032 , or 3.2%

In other words, even though the Lakers may be heavy underdogs in each of the next eight games with only a 35% average chance of winning each one, the probability of them losing ALL eight games is only 3.2%!

This is a glaring example of how otherwise very intelligent and educated people can falter the minute they go any distance in interpreting statistical data or anything dealing with probability.  Will the Lakers actually lose their next eight games?  Maybe, but it's not very likely given the input data...