tag:blogger.com,1999:blog-5204092591876211047.post6458258660396003746..comments2016-07-29T03:02:20.310-04:00Comments on Advanced NFL Stats Community: Kelly Criterion on 4th downUnknownnoreply@blogger.comBlogger7125tag:blogger.com,1999:blog-5204092591876211047.post-80834610244642438412013-01-15T20:02:02.118-05:002013-01-15T20:02:02.118-05:00I might be totally misunderstanding the concept of...I might be totally misunderstanding the concept of a 'bankroll' as used by the author, but could the bankroll simply be the number of remaining 4th down attempts in a given game?<br /><br />Here's an example I was imagining: It's a tie game at the final two-minute warning and your team has a 4th and inches call on your own 30. WP total and EP total both indicate that you should definitely go for it. Personally, I'm about sticking to the numbers.<br /><br />However, at this point, with only two minutes remaining, you likely only have one more (4th down) bet to make: this one. If you fail, you're likely to lose your stack. <br /><br />If you were faced with the same decision on your opening drive, then you might be more tolerant of variance knowing that you're likely to have future opportunities to bet.Luthernoreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-41155838359905942212013-01-09T18:32:20.332-05:002013-01-09T18:32:20.332-05:00In blackjack, if the odds say you're better of...In blackjack, if the odds say you're better off hitting, you hit. The Kelly Criterion indicates how much you should bet - not whether you should hit. You don't conserve your influence over the gain by electing not to hit - you conserve your influence by limiting the size of your bet. It's not that hitting only makes sense in the long run. It's that it doesn't make sense in the short run to blow your entire bankroll on a bet that has good odds but isn't certain.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-58005594920717300812012-12-27T20:31:54.735-05:002012-12-27T20:31:54.735-05:00Great look at the idea of "football capital&q...Great look at the idea of "football capital" that coaches have and probabilities, interesting stuff tunesmith.Topher Dollhttp://www.milehighreport.comnoreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-52768491437639101542012-12-21T12:56:25.075-05:002012-12-21T12:56:25.075-05:00I've thought about this a little, and may have...I've thought about this a little, and may have posted to the effect elsewhere, but applying the Kelly Criterion to fourth down decisions is incorrect: The Kelly Criterion is appropriately used in situations where you can (1) choose how much to wager, and (2) make as many wagers as you like. For a fourth down decision, neither of those is true: You only get one chance (barring penalties) to convert, and it's always the entire game that's on the line.<br /><br />In addition, the normal EV models (ones that are<br />about the chance to win the game) by their nature<br />already incorporate the potential future opportunities to win the game. Assuming that the conversion chance, EV model, and primacy of winning the game are all correct, there's no valid justification not to go for it (or punt, depending on the numbers)<br /><br />Instead of a poker analogy, here's a blackjack one: Early in a deep deck game, you've got 10,6 and the dealer's showing a 7. Do you hit, or stand? Does it make any sense stand as the "safe low risk option"? Or to conserve your "influence over this particular game"? Or to make some variance calculation using the marginal chance to win by hitting? Or do you think 'hitting only makes sense in the long run'?<br /><br />No! Assuming you like money, as soon as you're confident that your chance to win by hitting is better than your chance to win by standing you hit.<br /><br />The same way, if it increases your chance to win, you should go for it on fourth down. Now, in blackjack, our predictive model is very strong, and in fact, relatively common knowledge. By comparison, we're not really that certain how good our football model is, and it's relatively specialized knowledge.<br /><br />After musing, I find myself thinking that the fourth down decision may be more about discounting behaviors than about variance aversion.<br />http://en.wikipedia.org/wiki/Hyperbolic_discountingNatenoreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-47319372551870540412012-12-21T00:15:50.934-05:002012-12-21T00:15:50.934-05:00I guess in football the problem with using the Kel...I guess in football the problem with using the Kelly criterion is that this is a one size fits all model at the moment with regards to WP and thus the team doesn't have a calculable edge. The scenario would be more adequate if a team like the 2000 ravens had a huge edge running the ball and stopping teams but were down 5 points on their own 20 yard line on 4th and 1 with time running out but still plenty left. Perhaps 3rdQ with 4M left. They should punt even if it is lower EV than to go for it because of risk management. In this case they will be likely down 8 points, possibly even 12 or 13 if they fail and they would have to deviate from their gameplan and take more risks to get back to even in time. That means passing the ball and they simply are not built to do that well. They would have a lower EV passing than running I believe, and of their high risk fails they soon cut their effective bankroll down to beyond where they can recover. If they punt they get the ball back and they keep running and have a chance to eventually put up a TD.<br />The Kelly criterion would be relevant in poker if you had entire bankroll at risk. Say you were 80% to win with aces. You would want to risk 60% of your bankroll. To lose 95% requires a 2000% gain to compensate. If you win 4 times in a row then lose the 5th by doubling up the amount at risk where are you at with 90% of bankroll at risk each time? 80% 40%? You can try this yourself and see that "less" is sometimes more. I am not entirely convinced this plays a role in this particular example in football... A few reasons...<br />1)it's not as if a team has any traditional form of economic risk or value that can be wagered. Risk perhaps the same, but if you were 90% to convert a first down, how could you increase the weightings and risk more? If you were 30% how could you risk less? You can take other or lower variance strategies and balance the variance, but how do you measure that?<br />2)The bets cannot be made at will. I'd you fail a 4th down you can't simply take a loss and immediately try again. There is a time limit. True, WP adjusts and function as bankroll and as time decreases the bankroll may decrease or increase if you have a lead or not, but still.<br />3)defining the bankroll cannot easily be done.<br />I think risk management is still important, and Kelly criterion is a great tool of risk management, but finding actual utility for it in this case may be a bit more difficult.Mikenoreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-34933194485026216072012-12-20T23:52:09.792-05:002012-12-20T23:52:09.792-05:00Other thing about Kelly criterion or bankroll mana...Other thing about Kelly criterion or bankroll management is it requires you to have an edge. The idea is that you give up maximum EV in the short run to reduce the volatility of a decision to reduce your risk of ruin to zero. The Kelly criterion is designed for an unlimited amount of bets or maximizing your long term growth as The number of bets approach infinity. In the lotto example it would be more relevant if you could bet the same exact lotto conditions $1 at a time, or millions at a time. But the ticket drawn would have to be random otherwise you could guarantee a win by buying enough tickets and avoiding duplicates. Now if you had $1B simply buying 500M tickets wouldn't guarantee you a win, or even $1B. So you would actually reduce the amount you risk. However only betting a dollar wouldn't yield you a very large return on that $1B bankroll even if the ticket itself is EV. The idea of the Kelly might be to find a balance. Sometimes you have an absolute minimum bet allowed, such as a $1 ticket and do if your bankroll takes a hit you can't start using $.01 tickets. Sometimes your bankroll isn't large enough to justify the minimum bet because if you keep repeating that bet you will go broke due to volatility.Mikenoreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-5219698054167807572012-12-20T21:13:16.654-05:002012-12-20T21:13:16.654-05:00Just got my question answered from math.stackexcha...Just got my question answered from math.stackexchange.com . To be 99% sure of reaching cumulative expected value in that scenario, you have to take the bet 1520 times.tunesmithnoreply@blogger.com