And, like I mentioned, I can't really think of many (any?) passes that SHOULD have been picked.

This is a good observation, because it's a reminder that this isn't just a math question using box score stats. You have to use not only stats, but information that doesn't make it into the stat line, like how many INTs have been dropped.From a mathematical approach, here's how I would figure Campbell's odds of throwing an INT against an average NFL team.

I'd use everything I knew about Campbell heading into the season (his college experience, his draft position, his NFL experience, his NFL stats so far, my subjective impression of his abilities, the offensive scheme he's in, and so on) to estimate his "true" (i.e., expected long-term) INT/attempt ratio for the 2008 season. This would be based mostly on previous results from other QBs who IMO were similarly talented and in similar situations, etc.

In fact, to make the next step work, I'd have to estimate the probability that he falls into each of several ranges -- i.e., there's a 10% chance he'd fall into the 0.038-0.040 INT/attempt range, an 8% chance he'd fall into the 0.035-0.037 INT/attempt range, and so on. Again, we can do this using previous results from other QBs we believe to be similar.

From that point, I could use pure stats and math (without watching any games) to update my estimate of his 2008 INT/game ratio after each game using Bayesian inference analysis.

To jump ahead to one implication, I know that each time I update my estimate, it will be in between (a) my previous estimate, and (b) his results from after I made my previous estimate.

So if my original estimate was that he'd throw 0.036 INT/attempt, and then he goes out on his next 30 attempts and throws 0.033 INT/attempt, I know that my updated estimate after his most recent performance will be lower than 0.036 INT/attempt and higher than 0.033 INT/attempt. This is an implication of the math involved, and is what is often referred to as "regression to the mean."

So here are two points I think are worth noting.

1. Since Campbell has generally thrown fewer INTs than expected this season, our estimate of his "true" INT/attempt should be higher than his actual past INT/attempt on the season so far.

2. Number one is only mathematically provable if our only information comes from the stat box. If we've actually watched the games and can update our estimate using information not included in the box score, it's theoretically

*possible* that our best current estimate is that his "true" INT/attempt is actually lower than his actual current INT/attempt, notwithstanding the fact that he's outperformed our original expectations.

All of the subjective judgments involved (pertaining to both our estimate of Campbell's abilities before the season, and our evaluation of his play that's not reflected in the box score) make this a hard question.

And so far, that's not even taking into account about his specific matchup versus Pittsburgh.

Trying to come up with an appropriate line (to compare against the one offered by the book) is really too much work to do if you're not devoting full-time to it like it's a real job.