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A thought experiment

by Chase Stuart on September 22, 2012

in Strategy, Theory, Thought Experiments

Yeah, yeah, Football Perspective turned 100 today, blah blah blah. I have something on my mind and I need the wisdom of this crowd. Below is a thought experiment.

You are highly incentivized to correctly guess how many interceptions a quarterback threw in a specific game. If you can answer it correctly within the one-tenth of an interception, you win. (You can assume this is the average of 100 games, if you like, but the point being your answers should not be limited to whole numbers.)

I will inform you that the quarterback in question threw exactly 13 incomplete passes (or each of the 100 quarterbacks threw exactly 13 incomplete passes).

Now, before you guess as to the number of interceptions thrown by this quarterback, I could also let you know how many pass attempts the quarterback had. But I don’t have to. Do you want to know how many attempts he threw, or is that information irrelevant?

If it *is* relevant information that you want to know, how does that knowledge affect your answer? If you knew he threw 45 passes, will you now project him to have more interceptions or fewer interceptions? Please vote in the poll below, but I’m just as interested in your comments. So get to commenting!

[poll id="6"]

{ 12 comments… read them below or add one }

Singer September 22, 2012 at 1:37 pm

I like this thought experiment because I am interested in what others would answer. There are a few elements at play here.

First, there is the question is of QB accuracy. If we know that one QB completed 32/45 and another QB completed 12/25, the former QB is more accurate than the latter. It seems reasonable to infer that greater accuracy would yield a lower INT rate. While we can’t know the rate of INT/incompletions for each QB, the latter QB might have more INT because he has lower accuracy and the same number of incompletions as the former QB.

Second, there is the question of QB quality. Here, I would interpret the difference in attempts as meaning one of two things. First, it is unlikely that a QB who is 32/45 has gotten benched in a game because he has such a high number of attempts. 25 attempts for the other QB could signal that he was benched partway through, perhaps because he was throwing too many incompletions or interceptions. Alternatively, it could signal that the 12/25 QB had a strong supporting cast and did not need to attempt as many passes, while the 32/45 QB was chasing the whole game (hence the higher number of attempts) and had to make riskier throws. In general, the completion rate of both QBs would lead me to guess that the one with more attempts is a better player.

Third, and most importantly, is that there are a contextual factors that would help answer this question. We don’t know anything about the teams, the previous games’ statistics for either QB, etc.

Also, interceptions are a low probability event, and you are placing them within a small sample (1 game). So even a better QB (as evidenced by the completion percentages) could throw more picks on a given day.

If we were guessing over the course of a large sample, I would say that QBs that are 32/45 would throw fewer interceptions than QBs that are 12/25 because a) they are more accurate, indicating a better ability to avoid interceptions and b) they have signaled that they are less likely to be borderline quality players because of the number of attempts they have in a game.

Bottom line: I would choose the first answer, but I would note that there is a LOT of important context missing here. Also, just because you have set up the thought experiment this way, I would assume that you picked two specific QB performances where the result is counter-intuitive.


Danish September 22, 2012 at 2:04 pm

After 5 minutes of pondering I think I’m going with “irrelevant”. On one hand throwing a lot of picks terminates drives and keeps you from throwing more passes. On the other throwing picks will have you facing a deficit, leading to more pass attempts. On average I’d think it evens out.

Anecdotally there are about as many “John Skelton” games with an ugly 12/25, 3INT as there are “Drew Brees” games 32/45, 3INTs.

Allthough, I can certainly be swayed to either side…

(Happy anniversary)


Richie September 22, 2012 at 4:30 pm

It just doesn’t seem like enough information, but I would assume the guy who went 12/25 likely threw more interceptions than the 32/45 guy.


Shattenjager September 22, 2012 at 4:59 pm

I would go with irrelevant. Interception rates have a huge element of randomness, more than any other QB rate stats, so it’s difficult to predict them based on pretty much anything other than the league averages.


Cos September 22, 2012 at 6:10 pm

Given the data provided, it is irrelevant. INTs depend on so many factors that without knowledge of team, off scheme, wr skills, def, score, historical qb data, etc. Thus, my chances of guessing the correct number are still 1/130 whether I know the PA or not.
That said, if I knew the QB was 65% (32/45) accurate but I have no reason to back this up…just a feeling. Maybe the point is to show that QB accuracy or PA has zero cooralation to INT rates.
Or maybe I’m just way wrong.


Andrew September 22, 2012 at 9:07 pm

I don’t necessarily know how relevant this information is, but I would say that, all other things being equal, which is how I’m treating this, the QB who throws more passes has a higher chance of throwing more picks. If, on the other hand, we threw that assumption of equality out the window, I would still say that the QB with 45 attempts likely threw more interceptions. For those of you assuming a QB who throws more is higher quality, I can accept that. However, even if his interception percentages are lower than the QB who had 25 attempts, volume could doom him (unless the interception rates are particularly far apart). Additionally, he may be behind and thus more inclined to risk taking. On the other hand, the other QB could either have a very strong running game and not have to throw, or is perhaps just bad, in which case his attempts are limited and reduce his odds of throwing an interception. And the final factor to consider is that interceptions are affected by a myriad of circumstances outside of the control of the QB. His receiver may bobble the ball or run a bad route, or a defensive linemen could tip it into the air. Furthermore, the team he is playing against is a huge factor, as a better pass rush will lead to more hurried throws, hopefully leading to interceptions. Also, the quality and style of the opposing defensive backs impact interception rates. There is a reason that the guy who leads the league in interceptions is almost never the top cover CB in the league, but rather a gambler like Nathan Vasher or DeAngelo Hall. Thus, on the whole, guessing the number of interceptions in a given game with the given information is virtually impossible, but still fun to try. I like this thought experiment. These should happen more often.


Ian S September 23, 2012 at 2:37 am

I have said change my answer so the one who threw more passes has more ints. Only thing around it I can think of though, is whether an int counts in the 13 incomplete passes. In my mind, I separate out an incomplete pass from an interception, so that an incomplete pass is not something that is ‘not a completion’.


David September 23, 2012 at 7:43 am

My initial reaction was that more information is better, but then I thought a little more. I have one datum in the first instance (number of incompletions) and three data in the second (number of incompletions, number of attempts, completion percentage). Does more data help?

I then had a quick look at correlation coefficients for each of the data to number of interceptions (the desired output). Using just 2011 regular season numbers, it turns out that completion percentage has a low correlation (where I thought it would be high), and that number of incompletions is better than number of attempts.

So, based on that, I would still prefer to know the number of attempts, as it gives me more data points against which to produce a regression analysis, which would be my best bet for estimating the number of interceptions – but it’s less helpful than I thought it would be


Red September 23, 2012 at 11:08 am

In any single game, I would guess that a QB’s interception % is almost entirely random, with any skill being drowned out by the effects of luck and game context. Therefore, more attempts would mean a greater opportunity for INT’s, regardless of how good the QB is, and regardless of how many passes he completed. I don’t think CMP % and INT % are very closely related, as there are plenty of innaccuate QB’s with low INT rates (Tebow, Cassell, McNabb), and there are accurate QB’s with relatively high INT rates (Favre, Warner).

Anecdotally, it seems like the innacuracy of certain QB’s actually aids them in avoiding interceptions. When Tim Tebow’s passes land 20 yards away from his receiver, or go sailing into the stands, it’s nearly impossible for the defense to make an interception. When McNabb tosses his patented one-hoppers off the turf, those passes are also nearly impossible to intercept. Conversely, Kurt Warner’s passes were almost always placed within close vicinity of his receivers, which of course means they were also in close vicinity to the DB’s, thus creating more chances for interceptions.


Nathan Jahnke September 23, 2012 at 12:17 pm

On one hand, I’m guessing the collection of quarterbacks who have a completion percentage that high are more accurate passers than the collection of quarterbacks who have a completion percentage that low, and in general more accurate passers have less interceptions.

On the other hand, if I assume that the quarterback with 25 attempts isn’t benched(which I guess I can’t do that, but this is where my thought process went), if a quarterback only throws the ball 25 times in the game, chances are they are winning the game, and running the ball late to not need a lot of passing attempts. If someone throws 45 attempts in a game, more often then not they are losing the game and passing the ball a lot late to try catching up. Winning quarterbacks throw less interceptions than losing quarterbacks in the average case, so then the quarterback who threw a lot of passes and probably lost also probably threw more interceptions.

Either way, I think the information is relevant. If I can assume the 25 attempts is the teams only 25 attempts, and there wasn’t another QB to play, then I will guess the 25 attempter had less interceptions.


sn0mm1s September 23, 2012 at 12:45 pm

My gut says the 25 attempt guy would have a slightly higher number of interceptions per game – but a much higher INT%. A QB going 12/25 is probably less accurate than a guy going 32/45. Which means his incompletions are probably “worse” than the more accurate QB. However, at the pro level that difference is still pretty small so 13 incompletions from one player is probably pretty similar to 13 incompletions from another player. I think an interesting stat might be INTs per Incompletion. I would bet that it is pretty constant across all tiers of QBs.


Tim Truemper September 24, 2012 at 10:05 am

Lots of good comments. I’m going to use Shattenjager’s comments as a basis. Int.’s are overall random occurrences, though based on what we know about good vs. bad QB’s, a lower int rate tends to go with the former. Let’s just go with the notion that int rate and completion rate are roughly the same for all levels of QB play. I would say that the number of attempts is irrelevant, but with this nagging and contrary caveat. We would intuitively think that more attempts would create more opportunities for int’s (overall). But if you are completing more passes, this in converse reduces the chance that int’s occurred. Is it a wash between these two numerical factors? We probably would know if we compare percentage completion rate to int percentage rate (as compared to total attempts). Thus, we need to read the POPIP article by Chase and consider its merits to this hypothetical.


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