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Subject: "Optimal" Football Pickoff Strategy Posted by: Sludge - [20421222] Sun, Aug 27, 15:55 Here is my initial post in the Select football forum. I thought with the Pickoff game right around the corner, I would contribute in that arena since it is, quite frankly, something I would like to think I'm good at. At least, I'm good at developing strategy for it. This year, there are a few rule changes that have the potential to change things around quite a bit. First, you can now pick a game which you would like to receive double points, whether good or bad. Secondly, bonus points are now awarded for getting 11 or more of the games correct. 50 points for each correct pick over 10. Finally, on weeks 4, 8, 12, 16, and the Super Bowl, there will be no information about the picks given until after the picking deadline. Ignoring those two for now, here is the "optimal" way to play the game. (I'll explain why optimal is in quotes a bit later.) Let's start by considering a specific game. To keep it generic, let's just call the teams 1 and 2. Somewhere out there, there is a quantity that I'll call P1 that gives us the probability that Team 1 will beat Team 2. Unfortunately, we don't know, and will never know, the value of P1. (Another way of viewing P1 is that it is the fraction of times that Team 1 will beat Team 2 in game after game after game with the same players under the same conditions. The game is only played once, so we'll never know P1.) Because of this, we have to estimate P1. More on that later as well. Suppose X1 is the percentage of participants that have selected Team 1. Then, if you select Team 1, the expected (i.e. average) points you will receive is given by: E1 = (100-X1)*P1-X1*(1-P1) Fact: E2, the expected points for selecting Team 2, is just -1*E1. So the "optimal" selection is to choose the team with the positive E. Simple enough, right? Here's where the "optimal" in quotes comes from. Like I stated before, we don't know P1, and have to estimate it. Because we are using an estimate of P1, we are actually obtaining an estimate of E1. That is, it's not going to be exactly correct. The better the estimate of P1 is, the better we will be able to estimate E1. So, it's only optimal if you have the best available estimate of P1. There are many ways of estimating P1. Last year, I used the point spreads in the games and developed two models to estimate P1 based on that spread. There are some other places that you can find these things. (Unfortunately, that is where my kindness in sharing this information stops. I want to win just as bad as anyone else.) Now it's time to address the rule changes. 1 - Doubling a game. Simple. Just double the game with the largest expected points. 2 - No information. This one is a bit tricky. In this case, we don't know X1 (or have a good, Saturday night, idea of its value), so we have to estimate it as well. I have a few ideas how to do this that I'm not going to share right now, but I believe it can be done simply enough. Use your estimated X1 to compute E1, and away you go. 3 - Bonus points. This is the trickiest of them all. If you are only going after bonus points, the optimal thing to do is to select the favorites in every game. If it is a good week for favorites, then you might get some bonus points. Unfortunately, the games that you get wrong just might cancel out the bonus! (Especially if there are some big upsets that week.) We can, with some tedious work, estimate the expected number of points for your entries for that week given your picks and the estimated P's. I mean some VERY tedious work. Probably not worth it. It is my opinion that going for bonus points will be a very dangerous thing to do. If you go for the bonus every week, I have a feeling that the upsets that you didn't pick will obliterate the bonuses that you would have gotten. If you get any bonus points, just consider it icing on the cake. Finally, a word of warning. If you choose to use this method, be prepared for some frustrating weeks. This is the Turtle in the race. Slow and steady does the trick. I was extremely surprised that I actually got the highest point total for the last week last year. (I suspect it was because of a change in the picking patterns with people trying desperately to make up ground.) Don't expect to be in the top 10 every week using this. Don't expect to win using this. Regardless how good our estimates are, regardless how much statistical theory goes in to this, the games still have to be played by the folks on the football field, and there are still only 17 full weeks of football that are played. As we all know, anything can happen. Sorry for the long post. Any thoughts, comments, or trash talking are certainly welcome. | ||||||
| 60 | Sludge ID: 1440310 Mon, Sep 11, 12:01 |
Species - That may be true, but if remember last year correctly, you had to look pretty far down at me last year after the first week of competition as well. I also seem to recall everyone hurting their neck looking UP at me by the time the dust had settled and St. Louis had won the Superbowl. In all seriousness, however, going by the numbers I gave above, (which are, keep in mind, estimates based on MY belief) I had about a 20% chance of going below -100 points. So it's not at all surprising to me that it happened. | |||||
| 61 | Species ID: 58412510 Mon, Sep 11, 12:06 |
Sludge - I'm glad you can chuckle at my playful jab! I think walk would remind me that my "kicking you while you're down" is really my own inferiority complex when I look at your obviously superior "optimal" statistical methond! ;-) I know you'll be there all year. | |||||
| 62 | Madman ID: 44633210 Mon, Sep 11, 13:31 |
Wow. Now I feel like I'm starting to understand what's going on here. One more possible difference, Sludge -- that you've mentioned before -- is our predicted probabilities. After seeing the stark difference in mu's, I'm betting that my predicted probabilities were much closer to the Collective's than yours were. As the predicted probabilities approach the Collectives, the favorites strategy should become more and more attractive. I really tanked it in week 1, as well. Unfortunately, I can't attribute it all to bad luck. In retrospect, I made some serious strategical flaws, although I'm still agnostic on the success of my main algorithm. The distributions you posted there would seem to indicate that it (my algorithm) was signficantly flawed. Aaargh. What's critical is the 30% chance of a 200 point game with your strategy. That means that even a top 6% draw with the favorites strategy will be dwarfed much more quickly than my predictions of a half-season advantage. Of course, this assumes that someone can't actually do better than Vegas at predicting winners . . . Finally, this distribution does or does not include the doubling option? I take it not. That would probably increase the variance of the Sludge-method more than the favorites-method, no? | |||||
| 63 | Sludge ID: 1440310 Mon, Sep 11, 14:26 |
Madman - You are correct in assuming it does not include doubling. That was beyond what I wanted to look at. Optimally, you just double the game with the highest E. That also applies to picking favorites. In the "optimal" solution, however, you typically double a game where you pick the dog, and there is a very large difference in the pick percentages. Losing a doubled pick doesn't hurt you much, but if you get it right, you get mega points! (As I did on the Oakland-Indy game for one of my entries, and for the Washington-Detroit game on another.) If you are picking favorites, and you double, the inverse is true. If you double a closely split game, the hurt will equal the gain. If you double a drastically split game, then the hurt will far outweigh the gain. I don't really have an intuition as to the relative increase in the variances. Give me a situation where the % picking a team is close (but not equal to) to the probability of that team winning, and I'll run my program on it. | |||||
| 64 | Sludge ID: 1440310 Mon, Sep 11, 16:53 |
Another example... Consider the following setup:
This is certainly a case, Madman, where my method would not be optimal. The optimal choices are:
I italicized the only dog that you would pick in this case. This is more along the lines of your reasoning. As usual, we were saying pretty much the same things but attacking the problem from different angles. The fundamental difference in our two approaches is that I believe that the pick percentages are not good estimates of the actual probability of a team winning (and, in fact, tend to overestimate the probability of the favorite winning), while I get the impression that you are more favorable in your opinion of the pick percentages. | |||||
| 65 | The Pink Pimp ID: 406421522 Mon, Sep 11, 23:46 | wow | |||||
| 66 | The Pink Pimp ID: 406421522 Tue, Sep 12, 00:22 |
Ok, I do have one question for Sludge. When do you enter your picks? Sunday morning? Saturday night? etc | |||||
| 67 | big V ID: 237481122 Tue, Sep 12, 00:32 |
Whew!! I thought all you needed to play this game was a little football knowledge and a willingness to stick to your initial decisions. Guess I will have to recruit some friends to make "fake" picks early to screw up the percentages. Good luck all Big V | |||||
| 68 | Sludge ID: 1440310 Tue, Sep 12, 07:50 |
PP - I usually start Friday afternoon since my picks will affect the percentages, of course. Then Saturday, I double check them. Sunday, I triple check them. Usually, I'll only end up changing one or two total from my three entries. Big V - Go right ahead. Just keep in mind that at 500 original participants, it takes 2500/(495-x) picks to move the percentage up a single point, where x is the original number of picks. So, if 80% of 500 pick a team, you would need ~26 of your closest friends to make a minor swing. At 3 entries per (assuming you are honest), that's ~5 friends. If the total is 50%, you only need ~10, or 3 friends. Then you have to get them to make their picks on Sunday before the games to have any effect. When was the last time you tried to get one of your friends to do anything at a specific time, much less 3 to 5? Then, once they get interested in the game, and realize there's $500 at stake, they might just decide to break the bloc and go for the dough. | |||||
| 69 | big V ID: 237481122 Tue, Sep 12, 13:37 |
Oops!! I forgot the ;)! Besides I was talking about getting a couple of friends to move the very early percentages before the other 400 people make their picks. I still believe that all of this statistical analysis is a waste of time. The best strategy in my opinion is to pick all of the teams you expect to win and double the one game you believe in the most, without regard to percentages. The only exception being games that have no clear favorite in your opinion. In those games wait until the last minute and pick the underdog. For me 2 games fall into that category week 3 (Pitt-CLe and N.O-Sea). All other games I already know which team I am picking no matter what the percentages. The only time I can get my friends to do anything at a specific time is to offer to buy the first round and even then a couple of them are late. | |||||
| 70 | philliephan ID: 5843138 Tue, Sep 12, 13:44 | Actually the optimal strategy the last two weeks may have been to take my picks and reverse them. | |||||
| 71 | Guru ID: 330592710 Tue, Sep 12, 14:00 |
In the past (including last year), it has been rare for percentages to move more than a point or two from about Friday on. Remember, too, that next week (week #4) will be a blind week. There will be no percentages announced until after the freeze. | |||||
| 72 | Sludge ID: 1440310 Tue, Sep 12, 14:19 |
big V - Waste of time or not, it landed me a spot in Guru's HOF last year. If that's not enough to convince you, then take a look at post #25. If you don't like 10 games, increase it to 100, or 1000, or 1,000,000. The point remains the same. Picking a team with inflated pick percentages will result in a net loss over time. Inflated pick percentages result when people "pick all of the teams you expect to win" without carefully weighing the possible risks versus the possible rewards. | |||||
| 73 | Sludge ID: 1440310 Tue, Sep 12, 14:28 |
Guru - Do you have the final standings from last year? I'd be curious to see a listing of the points per correct pick for the top finishers. I think it'd be a good measure of efficiency. | |||||
| 74 | Species ID: 58412510 Tue, Sep 12, 15:23 |
Sludge - your last point in post #72 was my downfall last year. I stubbornly stuck to (more or less) the "who I think will win" strategy until it was too late. big V - I think a mixture of both stats and "feel" is necessary to win. Sludge's method obviously did work last year and I know he'll be in the running this year -- too bad Guru didn't offer this kind of prize money last year, eh Sludge? | |||||
| 75 | Guru ID: 330592710 Tue, Sep 12, 15:32 |
Last year, you won with 1936 "raw" points (no bonus points, no doubling). You had 120 correct winners, out of a possible total of 201 games. If this year's bonus point scheme were applied, you would have earned 400 bonus points. You also won by a pretty big margin. The second place finisher had 1470 points, picking only 78 winners. He concentrated on upsets, as you may recall, and never had 10 winners in any week. The fifth place finisher had 1241 points, also on 120 correct picks. He would have had 600 bonus points. | |||||
| 76 | Sludge ID: 1440310 Tue, Sep 12, 15:46 |
No kidding, Species. I tried to get Guru to build in a "Grandfather Prize" to be awarded to the winner of last year's contest, but he wouldn't go for it. Have you no sympathy for a guy with a new baby and a new house, Guru? How can you say "No" to this face? Just look at the poor boy, he's starving to death! (Oh well... I had to try. Sorry for deviating from the "selectness" of the forum.) I think that "feel" is a bit overrated in contests like these, Species. I prefer to call it (a) expertise or (b) luck. | |||||
| 77 | MikeMaz ID: 33433912 Wed, Sep 13, 07:06 | Cute kid Sludge , after finishing right behind you last year your sludge2 team had the exact same 15 picks this week as I did ( including doubling the same game). I'd be willing to bet they were the only 2 exact entries. Weird stuff. | |||||
| 78 | Sludge ID: 20421222 Sun, Sep 17, 12:00 |
Week 3 "Optimal" picks based on three different estimates of probabilities of winning and 8:00 am pick percentages: Car over Atl Cle over Pit Det over Tam GB over Phi Jac over Cin NE over Min NYJ over Buf Stl over SF SD over KC Oak over Den Chi over NYG NO over Sea Mia over Bal Was over Dal 137.843468 Atl over Car Pit over Cle Det over Tam GB over Phi Jac over Cin NE over Min NYJ over Buf Stl over SF SD over KC Oak over Den Chi over NYG Sea over NO Bal over Mia Was over Dal 120.806327 Atl over Car Pit over Cle Det over Tam GB over Phi Cin over Jac NE over Min NYJ over Buf SF over Stl SD over KC 0 Oak over Den Chi over NYG Sea over NO Bal over Mia Dal over Was 131.209711 | |||||
| 79 | Sludge ID: 20421222 Sun, Sep 17, 18:32 |
Argh!!! I just can't seem to get enough of those close ones! Where are you at, New England? Oakland? Chicago? Pittsburgh? Steelers looked like Keystone Kops out there today. Another good week for picking favorites. | |||||
| 80 | biliruben ID: 278231313 Sun, Sep 17, 20:21 |
Sludge - I matched you pick for pick, unfortunately, except for Buffalo (sentimental favorite). Luckily I forget to pick last week, so I have only decended into the "Sludge-probability-Abyss" once. ;) | |||||
| 81 | Sludge ID: 20421222 Sun, Sep 17, 22:37 |
Well, what can I say except what I've said several times already? They still have to play the games. I just wish to hell I'd start getting some of the close ones. Last week was even worse than this week. It seemed that I had 5 or 6 games that could have gone either way in the 4th quarter, and all I needed was half of them to put up a decent score. I don't think I got a single one right. This week, I think I got two - Green Bay and the Jets. | |||||
| 82 | big V ID: 237481122 Mon, Sep 18, 14:33 |
My go with your gut feeling method didn't work very well this week (+42 pts with Washington tonite). I still have 452 pts for the season so I am not totally ready to change my method of picking. Was just wondering how you number crunchers are doing so far since I don't know your team names. Also a quick thank you to Guru for providing such a helpful site. Everybody take the time to click two ads please. | |||||
| 83 | Sludge ID: 1440310 Mon, Sep 18, 15:27 |
Bad... very bad. Just page down the standings (page WAAAAAY down) and find the "Sludge" entries. I don't find it surprising that I am finishing with negative points (recall, above, I gave myself about a 37% chance of doing so). I also don't find it surprising that I finished negative two weeks in a row (~14% chance of doing so). I do find it very disapointing, however. Alas, that's the way it goes. I am very fond of the quote, "Yous rolls the dice and yous takes your chances." It's very appropriate here. One of my wife's entries finished on the positive side (although just barely), with a little help from me. | |||||
| 84 | Madman ID: 44633210 Mon, Sep 18, 15:47 |
I'm sucking wind. Most of my teams are just under zero net, I think. I'd have to look it up for sure. As I said before, this is not all luck. I screwed up a few times in week one (doubled poorly chosen teams). Live and learn. I have three teams, each with a different strategy. One I run on instinct. One I run totally by the numbers (Mine are somewhat different than sludge's, however. I have less accurate predictions for P1 than he does. In addition, because I am potentially targetting bonus points, in certain weeks (defined by a rough idea of the probability of getting 10+ wins), I am somewhat more likely to choose favorites (although I don't do this indiscriminantly -- this is all defined better, but I don't want to get into it. It could be silly; if not, it's my competitive advantage.)). The third I run based on the predicted probabilities mostly, but give myself some room to play around. That is the team that is doing the best right now. Unfortunately, it has Dallas tonight. Sludge I am really getting swamped in other stuff. I see your point with the algorithm. It's fastest to do it your way, I think, when you consider the difficulty of programming the alternatives. In Excel, I would (but have not) essentially programmed it to consider all 2^15 possibilities, and add up the probability of 10+ wins. It doesn't look like it requires another 2^15 calculations, but it, of course, does (because the aforementioned probability comes from adding up 2^15 things). The algorithm change I was describing was that if you assume a finite set of combinations for probabilities (i.e., 50%, 52%, 55%, 60%, 70%, 80%), you could calculate all the possible probabilies (of 10+ wins) ahead of time conditional on the number of each of the selections (i.e., 5 50% games, 2 48% games, 2 52% games, 6 60% games). When you are running through your 2^15 strategical possibilites, then you lookup the corresponding probability. But, if you are modelling P1's as a continuous variable (which you likely are), then you have a whole host of these possibilities -- the probabilities that correspond to +/-0, +/-.5, +/-1, etc. which might make that method prohibitive. Plus, you'd have to develop an efficient "lookup" algorithm, which might, in and of itself, take a lot of computing power. | |||||
| 85 | Eat Acid ID: 408451815 Mon, Sep 18, 15:54 | Somehow I've cobbled myself into ninth place in this game. The only rule I think I've established is that I will always double a 0-35 percent game. The reward is greater and the risk is minimized. I also only pick a favorite if I'm pretty dawgone sure they are going to win the game. This might hurt me in bonus points, but the big negative scores from missing a 60-80 more than balance that out, IMHO. If Wash wins I'll get 50 bonus for this week, combined with 50 from last week doesn't look too bad. Those ones in the middle (40-60) are the ones that will make or break me, so far I've been fortunate. | |||||
| 86 | Madman ID: 44633210 Mon, Sep 18, 23:48 |
Eat Acid this is likely buried in the posts above, but your strategy is almost identical to Sludge's. To recap why: Gurupies are going to consistently over-bet on the favorites. That means that Sludge's method will find the underdogs to be more attractive (there's been 1-2 exceptions each week, I think). This is essentially the strategy Sludge has been advocating. Especially since Gurupies are over-betting on favorites, the risks to those picks are just too huge despite the presence of potential bonus points (to paraphrase his argument -- sorry Sludge). The only other difference that I can see is the he uses historical statistics to give him the best odds possible (but past performances are not guarantees of future returns), thus you might bet on different combinations of the games in the middle ground. But, I should note that Gurupies don't over-bet on the middle ground games nearly like they do on the big ones, thus he's more apt to mix and match favorites in the middle, as well. That strategy is definitely sound. | |||||
| 87 | Eat Acid ID: 458331919 Tue, Sep 19, 19:33 |
Wow, the monday night game threw me for a loop. I really thought Wash was going to be better than they are. The blind picks are going to make things interesting this week, I'm going to have to do some thinking about these games. Madman, thanks for summarizing the arguments for me, I have a little more confidence now. My theory for this week right now is that since this week is blind the percentages will be less drastic, making wins extremely important. People will see that 70-90 percent of gurupies think that one team will win a game, and their off the cuff response will be to go with the masses. With blind picks more intuition is necessary, which should spread the percentages more equally. Of course this might mean people will pick the obvious choice off W-L's, and thus chuck my theory out the window. Thoughts? | |||||
| 88 | Madman ID: 44633210 Tue, Sep 19, 19:58 |
I have no idea how Gurupies are going to be this week. Either of your explanations seems very plausible. But, to flesh out the 'other side', a bit more, the Gurupies can get the Vegas lines, and these same lines are good predictors for the percentages that bet on either team. For example, a team favored by 6 would have had 70-75% Gurupie support (off the top of my head). So, I really don't know. If I had to bet on the way people were going to bet, I'd bet that if you looked at the final percentages three years from now and had to figure out on which weeks the gurupies had inside information and which weeks they didn't, that you couldn't figure it out. In other words, I'm guessing the percentages look very similar to what they would have without the inside information. | |||||
| 89 | Ref ID: 1442849 Fri, Sep 22, 15:23 | Does doubling affect the pick %? I looked for this answer and apologize if it's been covered before. | |||||
| 90 | Species ID: 58412510 Fri, Sep 22, 15:47 | Ref - no, not at all. It doubles your risk/reward personally, but only adds one more pick to the pot..... | |||||
| 91 | Eat Acid ID: 3188232 Sat, Sep 23, 02:08 |
I gotta take Wash again this week, even though in the past two they have combined to hit me with negative 150, plus costing me 100 bonus points. This squad is just too good on paper to be as bad as they have been on the field. I think they will key on Barber and Dayne, and let Deion/Champ/Green make the plays in the secondary. I am terrified of the STL/ATL game, because of the percentages, if I had two entries I would definately split them. Oakland is going to put my Brownies in their place this weekend, and the obvious Tenn/Balt favorites should handle their respective foes easily. I like Tampa at home over the Jets, and am torn on the Jax/Indy game. At least that one will be a pretty even split, although that makes it all the more critical to be on the right side. This game definately makes me watch more football, and more intensely than I normally do, which is good and bad, I suppose. I just need to make my profs understand the gurupie mentality. :) | |||||
| 92 | azdbacker ID: 3743019 Sat, Sep 23, 05:35 |
Sludge, first off let me preface my statement by saying that your strategy is far and away the closest I have seen to an 'optimal' strategy. Second, farbeit (is that a word?) for me to question the thinking of a Hall of Famer and an obvious mathematical genius. That being said... The only flaw that I see in your strategy, is that you are using the 'Vegas' line as your basis for prediction. Therefore, you are assuming that the Vegas line is w/o bias. It is not. For five years now, I have beaten the Vegas line at a 52-58 % clip, and this year I am 21-7 or 75% against it. The reason for this is that the sole purpose of the Vagas line is to ensure that approximately half of the people bet on each side. Therefore, public opinion is obviously a great factor in the making of a pointspread. To make your strategy truly optimal, you need to come up with your own pointspreads, and then figure the %'s based on that. The only way to do that is to make your own Power Ratings. I'm certain that for someone with your mathematical skills, you could easily come up with something equal or better than the Sagarin ratings, which I assume you're familiar with. I have my own, and I come up with 3-5 games a week that are off by 3 or more points than I believe they should be. If I'm winning over 50% of my picks over a 5 year period, that means my spreads have to be more acurrate than Vegas', and I'm sure you could do at least as well. Either way, my power ratings do agree that 'dogs are undervalued. According to my ratings, there is a group of 14 teams where games between them hinge on home field advantage, many of which would be 'obvious' picks for the general public. For example, Buffalo is a 1/2 point favorite over the Rams in my Power Ratings. As I said, I'm sure yours would be better. So quit using the Vegas line as a crutch, and make your own Power Ratings, for the love of God, and your optimal strategy will truly be optimal. There is another thing we are missing here, and the reason it's not here is the inability to quantify it, but there are just certain situations where a team is more or less likely to win due to emotional reasons, and this is why a purely mathematical approach will not, IMO, beat an intuitive picker, with a sense of the week-to-week of the sport, who starts from a solid mathematical base. On Wisconsin | |||||
| 93 | Eat Acid ID: 3188232 Sat, Sep 23, 06:02 |
Madman/Sludge, in my efforts to understand this game better I checked out the spreads and am going to agree with you that they are probably a decent indicator of how gurupies will pick during blind weeks. A couple jump out at me though, and I'd like your thoughts. Chicago -2 vs. Detroit----No way in hell that the gurupie majority takes 0-3 Chicago in this game. I'll bet on a 65% Detroit majority. And I'll be on the other side of it, these teams are both terrible, might as well minimize risk. Denver -6.5 vs. KC----- I guess this one depends on how good you believe Gus Frerotte is. I really cannot see 70-75% Denver on this one, but I hope it is. Probably closer to 60-40, unless we gurupies are less informed than I think, which is tough to do considering all the Griese/Terrell update threads. Tampa -7 vs. NY-----As I already stated I like Tampa to win, but I think some will be swayed by the lofty W-L of the Jets. Around a 60-40 split. The rest will probably shake down pretty close. Or at least thats what my secret algorithm (crystal ball) tells me. :) | |||||
| 94 | Sludge ID: 20421222 Sat, Sep 23, 08:28 |
azd - Yup. You are 100% correct. Let me just say that the Vegas line isn't the only predictor I use. So far, it hasn't helped much, but it's not the only thing. I also do not factor in things such as emotion and injuries. I simply don't have the time with juggling my two SW teams, running a non-internet fantasy league, juggling another non-internet fantasy team, juggling my SW baseball teams, etc... etc... (I could always sound like Mathis and use my new kid as an excuse. See #76 for a picture.) Eat Acid - Not going to argue. Especially on the Denver-KC game. At the same time, however, Gus isn't going to be expected to throw a lot, I would guess. If he can make a couple of passes here and there, then Anderson and the OL should be fine. That's really what they've relied on so far this year, anyway. | |||||
| 95 | Madman ID: 44633210 Sat, Sep 23, 15:21 |
azd I understand your desire to not wade through all my posts, but I'd like to point out that I made exactly that same point in post 17. To rephrase, the Vegas lines are a measure of a team's popularity. The Gurupie line is a measure of a team's popularity. Why should the Vegas line be more reliable than the Gurupie line? (OK, this year, yes, because of the bonus point scheme Gurupies are going to be "suckered" into going for bonus points and skewing the percentages. But this argument was in general.) Eat Acid I'm a KC fan, so I can't give advice on how normal people rank KC. But with respect to your other two picks, I tend to agree on the CHI/DET game, although I like CHI. The TAM/NYG game -- I have hope the Collective will be jumping on TAM. Remember, there has been a ton of media hype about this one. But I'm very uncertain, and therefore haven't decided who to go with on that one. | |||||
| 96 | Madman ID: 44633210 Sat, Sep 23, 15:37 |
Man, would I like to be able to self-edit that last post! (But I can't since I'm in Netscape) NYG. Good grief. With all the hype about Keyshawn, etc. HA! Man, I make so many stupid typos, it's a wonder anyone pays attention to what I say . . . YOU GET THE IDEA. | |||||
| 97 | Madman ID: 44633210 Sun, Sep 24, 17:44 |
OK, I should have seen this before. azdbacker Whether the Vegas lines are biased or not is largely irrelevant to Sludge's method. All he needs is a positive correlation between his variable of choice (Vegas lines) and the resulting outcomes. The first step in his method is to predict a team's winning percentage by taking the historic Vegas line vs. the historic winning percentage of that line. The only limitation of his method is that the variance around his predictions is greater if the Vegas lines get weird. To illustrate. Let's say that the "real" point spreads on a different groups of games are 0,3,6 (call these type 1, 2, and 3 games). But, Vegas over-weights the favorites, to make the observed spreads to be 1,4,7. After the games are over, it is observed that 50% of type 1 games were predicted correctly (in terms of the winner), 60% of type 2 games, and 70% of type 3 games. Would his predictions be better if he used the "real" point spreads or the Vegas ones? Well, if he uses the Vegas ones, his regressions will find that every 3 points of Vegas-point spreads maps into a 10% higher chance to win a game, and that a point spread of 1 gives a 50% chance to win. If he uses the "real" spreads, he finds the same slope coefficient (3 points into 10% higher chance), but finds that a zero point spread = 50%. In other words, there is absolutely no difference. He can consistently use either set of initial point spreads. Of course, this is conditional on various technical regularity conditions holding. But I think the concept is general enough to make the method fairly immune to the criticsm you and I were raising, azdbacker. But unless underdogs start winning at their historical rate, this whole point is moot. AAARGH! | |||||
| 98 | Sludge ID: 20421222 Sun, Sep 24, 18:18 |
Madman - I couldn't have explained it better myself. | |||||
| 99 | Eat Acid ID: 318412418 Sun, Sep 24, 18:41 | A rough week for me. I'm slightly negative with 8 wins. The KC game saved me, the Tampa game killed me. I need Wash/Indy to come through or I'm going to plummet to the bottom. | |||||
| 100 | Guru ID: 330592710 Sun, Sep 24, 18:43 | Especially the AAARGH part... | |||||
| 101 | Sludge ID: 20421222 Sun, Sep 24, 22:49 |
Now we're talkin'. 370 points with only 7 picks correct. Now THAT'S how it's supposed to work. (I'm talking about my "Sludge 2" entry, which is the one based on the point spread model. The one based on my "other" estimate got a whopping -425 for the week.) Here's hoping for many more weeks like this. Interestingly enough, because of the dependencies of my predictions of the pick percentages and winning probabilities, I picked nearly all consensus underdogs. I believe that's a reflection of the tendency of the gurupies to overestimate the probability of a favorite winning. Only picked one consensus favorite, Philadelphia. | |||||
| 102 | Madman ID: 44633210 Sun, Sep 24, 23:48 |
Congrats, Sludge. This was a week for the underdogs to do somewhat better. In fact, going all underdogs was going to be my strategy on the statistically based team for exactly the reason you said. However, I out-thought myself this week, and convinced myself that a bunch of people would pick the Jets because they were 3-0. So, I stuck with TB. In other words, I tried to get too fancy with non-scientific psuedo-sociological babble by trying to out-guess what the masses were going to do. That's the same logic that made me go with Indy. We'll see if it backfires there. So, although I have started to recover, I'm still waiting for my first 200 point week. Although my top team did climb into the top 100 this week (the mix of stats and intuition). Finally. My pure stats based team just made it over zero this week. Wu-hoo! Should we start a new thread for pickoff? This one is getting kind of heavy. | |||||
| 103 | Eat Acid ID: 318412418 Mon, Sep 25, 21:44 |
Well, post 93 shows how much I know. Sludge, I have to agree now that the point spread is a terrific indicator during blind weeks. If Indy can win at least I'll have 50 bonus points to console me from the Tampa debacle. -83? Sheesh!And the -110 I got from doubling Chicago, double sheesh! I really thought the majority would kick that percentage down, gotta go with the spread more, then I probably would have doubled a better game. I know I wouldn't have doubled a 55, that's for sure. | |||||
| 104 | Sludge ID: 1440310 Tue, Sep 26, 07:48 |
Eat Acid - You brought up some good and salient points. Just as two bad weeks of bad scores by "the" method doesn't prove that it's a bad one, one week of good scores doesn't prove that it's the best one, either. (Just to clarify, it *IS* the long-run optimal method *IF* you can estimate the probabilities of winning better than anyone else. Who's to say that my estimates are any good, however?) | |||||
| 105 | azdbacker ID: 3743019 Thu, Sep 28, 22:56 | BUTT, great thread. Madman, you are absolutely corect in number 97, I should have seen that myself. | |||||
| 106 | CanEHdian Pride ID: 426351415 Wed, Apr 18, 17:54 | BUTTED for Tranceformer. Try to wrap your head around this! | |||||
| 107 | biliruben Sustainer ID: 49132614 Wed, Sep 10, 2003, 16:51 | If anyone wants a headache... | |||||
| 108 | Astade ID: 376502816 Thu, Sep 11, 2003, 00:19 |
biliruben, thanks for BUTT-ing this thread. I went ahead and read through this entire thread (took me a good hour!!!). I was wondering if Sludge or Madman could offer up some help: I just downloaded a Monte Carlo Simulator and wanted to know if either of you (or anyone else) had run an MC simulation on the 'optimal' versus 'favorite' strategies? if so, do you still have the data and what were the parameters that you incorporated? if not, do you have any suggestions for other scenarios to study? if you guys aren't comfortable sharing, it's cool but it would be great to cross-check with someone else. thanks | |||||
| 109 | Sludge Sustainer ID: 5781086 Thu, Sep 11, 2003, 08:29 |
I'd certainly be happy to share if I had done it. But I haven't, and I won't. I'll tell you why. In order to perform the MC simulation, you will have to simulate some football games, their spreads, and how people will pick those football games. I just don't see any good realistic way of doing it. Some bootstrap methods might be acceptable, though. The second roadblock is that the implementation that I've written up (with an incredible amount of cooperation with Madman), as slick as some of the coding is if I do say so myself, still takes a couple of minutes when dealing with a 16 game schedule. (It is a matter of seconds with a 13-15 game schedule, and one might be tempted to only consider those cases, but that would be ignoring the increased impact bonus points would play with a higher number of games. It would also be faster on a quicker machine - mine's 550 - but not to the point where MC simulations can be run.) But there is no doubt that the 'optimal' method described is optimal (in the sense of maximizing points) given that you know the probability that Team A will be Team B for all A and B. Even if you don't know that probability (of course, we don't), it is still optimal if you can estimate that probability better than anyone else. (Another criterion to maximize over might be to minimize the variance of the point distribution conditional on a positive score. Something I've thought about doing recently, but haven't yet.) I will be more than happy to give you some advice, though. The standard deviation of the score distribution is very high every week. Last week, I computed it as around 224 points. To be on the safe side, let's assume that it's around 300 every week. If you were doing a classical 95% confidence interval for the average score per week, the error would be +/- 145.5 points (2*300/sqrt(17), assuming, for simplicity, a 16 game week for 17 weeks). That is absolutely HUGE meaning if you are to do some MC simulations, that's a whole lot of seasons to simulate. (At a standard error of 200, for comparison's sake, it's +/- 100.) | |||||
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