tag:blogger.com,1999:blog-38600807.post3715563222883908739..comments2023-11-05T04:16:44.937-05:00Comments on Advanced Football Analytics (formerly Advanced NFL Stats): The Weekly League: Notes and Ideas for Week OneUnknownnoreply@blogger.comBlogger20125tag:blogger.com,1999:blog-38600807.post-29903047394127375472010-09-09T00:20:52.957-04:002010-09-09T00:20:52.957-04:00Here's another application of marginal vs. ave...Here's another application of marginal vs. average values. A new player doesn't have to be above average to help make his team better. He just has to be better than the player he is replacing. He can still be the worst player on the team, but as long as he is better than the player he replaces (who in this example, obviously was the worst as well), he has raised the team average. <br /><br />Yes, a player can be below average when joining a team, but still bring the average quality of the team up.<br /><br />The reverse happens, too. This is probably easier to understand. A superstar that suddenly leaves and is replaced by a mere star means the average quality on the team went down even though the new player is above average at his position.<br /><br />In both cases, it's the marginal value of the player that counts, and the marginal value depends on circumstances. In this case the marginal value is determined by comparing the value of the player with the value of the player being replaced, not their value compared to averages.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-31315428913611588862010-09-08T16:22:34.673-04:002010-09-08T16:22:34.673-04:00I was going more for the Fonz. (Actually, I'm ...I was going more for the Fonz. (Actually, I'm trying to go for the House thing. Total jerk, but you can't ignore his analysis.)Brian Burkehttps://www.blogger.com/profile/12371470711365236987noreply@blogger.comtag:blogger.com,1999:blog-38600807.post-67809261293034584452010-09-08T15:46:20.430-04:002010-09-08T15:46:20.430-04:00"YEAHHHHHHHHHHHHHHHHH!!!"
Oops, sorry, ..."YEAHHHHHHHHHHHHHHHHH!!!"<br /><br />Oops, sorry, a bit of a CSI Miami moment there.<br /><br />"I think I have zeroed in<br />*puts on sunglasses*<br />on what they are maximising"Iannoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-11349405939756026132010-09-08T15:43:02.928-04:002010-09-08T15:43:02.928-04:00The sneak preview is that I underestimated the imp...The sneak preview is that I underestimated the importance of running by looking at average efficiencies. (I was wro...wro...wro...ng.) I think I finally figured out what coaches are maximizing, since they don't appear to be maximizing yards, net points, or even WP. I also found solid evidence of minimax play in the run/pass mix, where we could find none before.<br /><br />That's not to say, coaches are doing things right after all. It's that I think I have zeroed in on what they are maximizing.Brian Burkehttps://www.blogger.com/profile/12371470711365236987noreply@blogger.comtag:blogger.com,1999:blog-38600807.post-7397790805116041202010-09-08T15:11:29.086-04:002010-09-08T15:11:29.086-04:00I can't wait for this post on Brian's new ...I can't wait for this post on Brian's new thoughts for measuring the effectiveness of the running game. Should be interesting - any sneak previews?Iannoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-88320801596550963282010-09-08T11:28:42.746-04:002010-09-08T11:28:42.746-04:00Yeah, I think you're right. Most of the time, ...Yeah, I think you're right. Most of the time, we can utility is approximately linear in EP, with the notable exceptions being times when you become a lot more risk-averse.<br /><br />And I do agree that WP is linear, or at least as far as we're concerned. The cute side of little economist me wants to point out that it's not clear exactly what the owners or coaches are maximizing or that we don't know how WP feeds into an owner's profits, but linear WP sounds right.Andynoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-36500154124004032282010-09-08T11:24:00.452-04:002010-09-08T11:24:00.452-04:00In engineering terms, it's a matter of where y...In engineering terms, it's a matter of where you draw your system boundaries. EP is linear under the assumption that on any particular drive, a team's goal is to maximize its expected net point advantage. <br /><br />There are obviously parts of the game where that breaks down, like toward the end of a game, when you don't care whether you win by 1 or by 100, (which is why Carson limited some of his analysis above to the first 3 qtrs with the score w/in 10 pts).<br /><br />That's where WP comes in. WP is always linear within the system boundary of the game as a whole. A WP of 0.40 is always twice as good as a WP 0.20. And a WP of 0.80 is always twice as good as a WP of 0.40.Brian Burkehttps://www.blogger.com/profile/12371470711365236987noreply@blogger.comtag:blogger.com,1999:blog-38600807.post-79202915713388835022010-09-08T11:16:56.333-04:002010-09-08T11:16:56.333-04:00Would love to know the underlying payoff matrix, o...Would love to know the underlying payoff matrix, or at least how the coaches perceive it.<br /><br />On a related note about the value of average--It's finally sunk in with me that that average running gains (yds per carry, or even EPA/carry) may be a very poor measure of the effectiveness of a running game. More in a subsequent post.Brian Burkehttps://www.blogger.com/profile/12371470711365236987noreply@blogger.comtag:blogger.com,1999:blog-38600807.post-75159318753895530362010-09-08T11:14:15.627-04:002010-09-08T11:14:15.627-04:00About the linearity of the utility curves, it isn&...About the linearity of the utility curves, it isn't clear to me why EP or WP have linear utility. The argument against EP entering utility linearly is just that if I care about winning a game, then EP must have a very nonlinear relation to winning depending on the current point differential. If you're already up or down by a ton, one EP has a low marginal benefit, whereas in a close game, one EP has a high marginal benefit.<br /><br />Perhaps it's different if you're considering EP over a season instead of over a game.Andynoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-45748211022796323342010-09-08T11:09:52.822-04:002010-09-08T11:09:52.822-04:00Brian, it sounds like your understanding is genera...Brian, it sounds like your understanding is generally right about the average vs. marginal issue, although I would say the real problem is lack of a model to inform our data. We do not know exactly the 'production technology' (in economics lingo) of runs versus passing. That is, we do not actually know or observe the full payoff matrix of the offense/defense game where by full, I mean literally every possible choice. <br /><br />So we're stuck using data to estimate a much much simpler model. In estimating, we make an assumption that the average will give us a good guess of the marginal. This assumption is bad (there are obviously diminishing returns), but it is the best we can do without making ridiculous assumptions about the functional form of the payoff matrix.<br /><br />I think the right way to present this is to admit that marginal vs. average distinctions may be problematic, but that given our limitations, this is the best we can do.Andynoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-66728776092808662892010-09-08T10:51:12.014-04:002010-09-08T10:51:12.014-04:00Agree on the sample size point. This is how I thin...Agree on the sample size point. This is how I think about marginal vs average in football:<br /><br />Football is very artificial in its construction. The marginal cost of any one play is always the same: one down. The marginal production is what's coming next. The question is, how do we estimate that? What is the best practical measure of expected future performance available to us? The average.<br /><br />And as I mentioned above, the marginal utility of a thing differs from its average utility only when the utility curve is non-linear. In most cases here (EP, WP, etc.), the utility curve is a straight line. In other cases (game prediction model), I use a logistic probability curve, so that very high inputs in a model diminish in effect as teams would theoretically approach a 1.000 or 0.000 winning percentage.<br /><br />Keep in mind teams are not acquiring a basket of goods. Teams do not grow tired of gobs of extra running yards during a season because they already have a lot of them, the same way I might get bored with a bunch of extra TVs in my house. The first TV is great. The second is convenient. But after that, I'm just looking for places to put them and would prefer having a laptop or some other good to another TV. <br /><br />I'm not an economist, so maybe I'm off base. But someone will have to explain it to me.Brian Burkehttps://www.blogger.com/profile/12371470711365236987noreply@blogger.comtag:blogger.com,1999:blog-38600807.post-36187808359248848372010-09-08T10:33:01.230-04:002010-09-08T10:33:01.230-04:00@Brian about marginal vs. average:
This cannot be...@Brian about marginal vs. average:<br /><br />This cannot be quite right. Or more precisely, if you're correct, and the average is everywhere the marginal, then advice cannot be "pass more", it must be "pass exclusively".<br /><br />That is, when people talk about run/pass mixes, they are implicitly assuming some form of diminishing returns so as a team runs more, it becomes less and less effective. Or, the marginal value is different (below) the average value.<br /><br />To respond to another comment by the first anonymous, I absolutely agree about incorrect comparisons of averages of two groups that have different sample sizes, although I think the problem is more fundamental than the selection/game theoretic issues Anonymous raised. It is just basic statistics that the variance of averages are declining in sample size. Comparing low carry RBs to high carry RBs without adjusting for the change in degrees of freedom will lead to erroneous conclusions.Andynoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-34591802644131966532010-09-08T10:24:36.748-04:002010-09-08T10:24:36.748-04:00Game probabilities will be running this year. I ne...Game probabilities will be running this year. I need to wait for a couple wks to go by to get some decent data, however. They will likely be at NYT again, either the print or online edition. I'll link to them here either way. Still not sure, though. My agent, Drew, is telling me to hold out for more money and another guaranteed year, but Toni Monkovic is no Dan Snyder.Brian Burkehttps://www.blogger.com/profile/12371470711365236987noreply@blogger.comtag:blogger.com,1999:blog-38600807.post-25821539787219296922010-09-08T10:02:03.444-04:002010-09-08T10:02:03.444-04:00Are you guys going to be doing the weekly picks li...Are you guys going to be doing the weekly picks like last year that ran on NYT? Those projections turned out great and were a huge asset towards me winning many a pool last year.<br /><br />Also really like the format of this write up. Look forward to it this year.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-66193154489876428292010-09-08T08:52:51.851-04:002010-09-08T08:52:51.851-04:00Re: marginal vs. average
In football, marginal ut...Re: marginal vs. average<br /><br />In football, marginal utility is the "next expected gain" from a certain type of play or by a certain player or team. Averages, for the most part, do the trick. They can be represented in many ways (yds, EP, WPA, etc.). The great thing about EP and WPA is that they are linear utility curves, and therefore next expected = marginal.Brian Burkehttps://www.blogger.com/profile/12371470711365236987noreply@blogger.comtag:blogger.com,1999:blog-38600807.post-43238291528906728172010-09-08T04:20:38.789-04:002010-09-08T04:20:38.789-04:00Anon - It's a good point about how things are ...Anon - It's a good point about how things are at the margins, but I think one of the assumpions we make is that of repeatability i.e. if I run the same strategy I should get the same outcomes. For example, if I've already run a 50:50 split of plays for the first 8 games and got 6 yards per pass and 4 yards per rush, I expect to get the same stats if I run a 50:50 split for the remaining 8 games.<br /><br />At the margin, we're concerned with how the next play will go. But if I assume my past performance is indicitive of future performance then the expected value of the next run/pass will be either 6 or 4 yards. This isn't a bad assumption really - after all, if a 50:50 split have so far given me 6 per pass and 4 per run, we have more reason to suspect this in the future than some other values (for example, there's no reason for my passes to suddenly start to average 4 yards if I change nothing).<br /><br />Your point is not invalid though. That's why, when sites like these say "passing gets more yards than rushing, therefore we should pass more" they never actually say exactly what run/pass balance to go with. You can't tell what would happen to a team's passing efficiency if you change their strategy mix. But the point about using averages is that it collects all the 'margins' from previous plays run under the previous strategy, giving an indicator of all the past margins. In the future, with the same strategy, we expect the same margins again.Iannoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-757837367829359782010-09-08T03:50:59.789-04:002010-09-08T03:50:59.789-04:00More pleaseMore pleasej holzhttps://www.blogger.com/profile/13428814047654767163noreply@blogger.comtag:blogger.com,1999:blog-38600807.post-68370863094683854632010-09-08T00:50:15.306-04:002010-09-08T00:50:15.306-04:00So much of the analysis I see on this blog confuse...So much of the analysis I see on this blog confuses average values with marginal values. For example, the high average net yards per pass is interpreted as a reason to pass more. I'd believe this if I saw some analysis that showed the marginal value of passing higher than the marginal value of running, but simple averages don't do it. The marginal value is situational dependent and includes time remaining, variability of outcomes, opportunity costs, as well as game theory (what strategy your opponent chooses). <br /><br />I'm stunned that Cistulli compares the average values of Adrian Peterson's plays (a large sample size) with players of higher averages but a very low sample size (Jeff Dugan with a sample size of six). By this logic, Clint Longley is a better quarterback than Roger Staubach because of his famous Thanksgiving game. <br /><br />Adrian Peterson's yards might be low because he runs the ball on third and short and helps to run out the clock at the end of games. The marginal value of two yards when it's third and one is quite high. Many coaches would take a certain two yards over a play that averages four yards but has a wide range of outcomes. Also, Petersen might be used a lot so as to increase the marginal value of passing--defenses have to expend resources in stopping him, leaving more opportunities for passing. If you only use him two or three plays a game, there isn't much reason to design a defense to stop him. You can concentrate on Favre's passing.<br /><br />I'm a newcomer to this blog, but I'm not convinced yet about all the rah-rah about passing. I agree that the rule changes have made passing marginally more attractive, hence the rise in the percentage of pass plays in a game over time. Maybe there should be more passes, I'm very open to the assertion (particularly with even more rule changes that help the passing game), but don't cite average values to prove it. Optimization theory involves marginal, not average values.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-38600807.post-89096959875302296482010-09-07T23:56:05.743-04:002010-09-07T23:56:05.743-04:00A quibble; Peterson may have been quite valuable i...A quibble; Peterson may have been quite valuable if we assume that A) most other running backs would have been horrible behind the same line and B) the Vikings were going to be running the ball a lot no matter what. Is condition A true? I can only guess, but it certainly is my impression that Peterson generates a lot more long runs than most running backs are able to. But I agree that your overall point is more important; the Vikings should have been throwing more.Jeremiahhttps://www.blogger.com/profile/12054254727747120279noreply@blogger.comtag:blogger.com,1999:blog-38600807.post-38390102332291506502010-09-07T23:32:34.205-04:002010-09-07T23:32:34.205-04:00Good start.Good start.Alexnoreply@blogger.com