Watching a bit on statistics, and they're talking about experimental probability. I know I'm just drowning myself in a sea of statistics, but if Scottie Pippen is shooting 83% at the free throw line for the season, but 75% for the game, does it really mean he's even likely to make a free throw next time he gets sent to the line? (By even more I'm assuming them mean >83%)
Semantically I guess the experimental probability he'll make it is higher than 83%, whereas as a pessimistic fan I figure he's having an off night and is going to pull his numbers down.
Heh. (I say 'Heh' because I was just thinking about your first question the other day.)
Somewhere I read something by a statistician that the whole notion of 'winning streaks', etc. in sports is an illusion - nothing but random variences in some probability-dependent outcome. (i.e. along the lines of the idea that if you flip a coin enough times, you'll occasionally end up with stuff like ten heads in a row). But I dunno - the thing we call a 'streak' occurs so much in sports - you hear stuff about athletes being "in the zone" in some psychological sense than can give them a streak off success, etc. But then I wonder how, mathematically, you could prove that there' more involved in just random chance when, say, a basketball team has a 'run' of, say, 15 unanswered points in a game.
if Scottie Pippen is shooting 83% at the free throw line for the season, but 75% for the game, does it really mean he's even likely to make a free throw next time he gets sent to the line? (By even more I'm assuming them mean >83%)
Nuh-uh.
OK, let's say Scottie's free throw % is exactly 83% at the beginning of the game in question. Now lets say in the game he makes 9 out of 12, giving him a 75% for the night. In a strictly probabilistic sense, you would not expect him to do better than 83% "make up" for the lower than 83% run he just had. (Are you familiar with the "random walk" idea in probability?)
OK, let's say that when we now look at Scottie's free throw %, taking into account the current game, it would now be, say, 82.998%. We would now expect (in a probabilistic sense) that he would continue to shoot at 82.998% overall, as this is now his shooting %, (taking into account all the available data). Of course, even in a purely probabilistic sense, there'd still be random variations, so we'd expect that new % to fluctuate up and down as well. But assuming no change in Scottie, his shooting % would tend to converge around his actual probability of getting a free throw, even if that probability is unknown (i.e. his shooting % based on his actual playing would converge around his (unknown) probability of getting a free throw, due to the sample size getting larger and larger).
Of course, all this is based on a theoretical idea of his making and missing shots being a purely random phenomena, ignoring the actual complexity of the real world (he might be in a bad mood on the night when he makes 75%, etc).