[DanT]

Interesting topic heading post. Thanks for posting this, Discuss Thrower.

In data through Week 9 of 2012, both Alex Smith and Aaron Rodgers had 25 opportunities for a 4th quarter comeback during their career. Smith was successful in 10 of those, while Rodgers was successful in 4.

For statistical significance testing of these data as presented, we would have to assume that the game results from the same QB are uncorrelated, which isn't quite right. But our results based on that assumption probably won't be too much different from what we would get if didn't have to make that assumption. In order to do the fancier analysis, we would need access to such information as how the QBs did in specific seasons (assuming that the probability of a given QB being successful varies from one season to the next as the QB matures and as each year's team gets better or worse).

Nevertheless, the Chi-square p-value for the difference in success proportions (computed by me, in Stata) is 0.059. This is not quite statistically significant at the conventional p < 0.050 threshold, so we wouldn't be able to claim that the differences we've seen so far in games reflect true differences in these QBs underlying probability of being successful. The plausible values for the true underlying difference (Smith minus Rodgers) in success probabilites that would be consistent with these data range from Rodgers being just barely better to Smith being a lot better (95% CI for difference in success proportion = -0.0001 to 0.49 ).

In the 17 opportunities against opponents with 0.500+ records that each QB coincidentally had, Smith was successful in 7 of those (41%), while Rodgers was never successful (0%).