bostonfred
Footballguy
Joe, Are you disagreeing with my example that the 4 INTs game was a bad game? That it was more than one standard deviation from Manning's norm for the season?Hi bf,
I guess it can be anything you want it to be. I think it's more along what MT said when he started:
I'm suggesting that, with the small sample sizes of playoff games along with high standard deviation of weekly QB performance in general, any kind of "playoff choking effect" we find will probably have no more statistical significance than the pastrami effect.
Is 4 INT's outside the normally high standard deviation? Well, He averaged .6 INTs per game that season and never threw more than 2 INTs that season, so his normally high standard deviation for 2003 was .72. Which means that one would expect him to get .6 INTs per game, would be between 0 and 1 INTs 68% of the time, and would be between 0 and 2 INTs
But that's a small sample size since it's just a 16 game season, so let's look at his 112 career games where he averages closer to 1 INT per game (mostly in his first two seasons, but in the interest of accuracy and fairness, we'll use all the data points we can). He's only had one other 4 INT game through all the data points in his seven year career. His average was 1.07 INTs per game. His standard deviation is .98. That means that Manning's 4 INT game was three standard deviations from his entire career - meaning it should happen less than one third of 1% of the time. As a sanity check, those numbers played out fairly regularly during his regular season performance - he had just one 4 INT game in 112 regular season games, which is perfectly within the expected bounds.
So there's about a .3% chance of that game happening, and it happens in the playoffs? That's pretty statistically unlikely. But he could be really unlucky. Then again, his completion percentage was 2 STDev's away from his career norm, which should happen about 5% of the time.
Can we agree that a game that bad, even in a small sample size, was extremely unlikely to happen? And that it did happen?