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Subject: Statistical Question Posted by: The Beezer - [191202817] Tue, Mar 13, 10:10 Is there a good way to turn an expected point spread into an expected winning percentage? For example, if I think Tennessee is a 2-point favorite over Charlotte, what % of the time should I expect Tennessee to win based on that spread? Thanks in advance! | ||||||
| 1 | Sludge ID: 18116195 Tue, Mar 13, 10:28 |
Yes. You can "buy" a half point for, I believe, an extra 10% on the bet. (Been a while since I figured this.) You can then convert that to the probability of a team favored by "X" points winning. Those probabilities are:
Unfortunately, I wouldn't trust them much past 10 points. Another method is to collect historical data regarding outcomes for past basketball games and build a model to predict the probability of a team winning. Unfortunately, time is short, and I don't know if such data exists in a format that can be quickly used. Or... you can just go to a site like Massey and look at his probabilities. Or you can go to Team Rankings and look at theirs. Or any number of sites. | |||||
| 2 | The Beezer ID: 191202817 Tue, Mar 13, 10:39 | Thanks, Sludge. Exactly what I was looking for! For what I'm doing, these factors should more than suffice. I'm doing 1 set of picks off the Sagarin ratings using expected returns, and then another based off the gut. Should be interesting to see who wins this "man vs. machine" battle... | |||||
| 3 | The Beezer ID: 191202817 Tue, Mar 13, 11:05 | 1 more Q; do you have to formula to generate that? I know it has something to do with natural log, but I'm just missing something obvious and can't seem to nail it down. Thanks! | |||||
| 4 | Sludge ID: 18116195 Tue, Mar 13, 11:31 | Formula to generate what? The listings I gave? It doesn't involve natural log at all. I'm not even sure, now that I think about it, that these would even apply to point spreads in basketball. | |||||
| 5 | The Beezer ID: 191202817 Tue, Mar 13, 11:34 | That would explain why I can't find it. :) Thanks anyway. | |||||
| 6 | steve houpt ID: 51291010 Tue, Mar 13, 12:13 |
Here is something I came up with a few years ago. Converted Massey or someone elses formula to use with Sagarin ratings. Do not ask how I came up with numbers. It was so long ago, I don't remember. Not sure of 'statistical' accuracy any more (if there ever was any). But it is relative when looking at all teams. TEAM A=1/(1+10^((((SAGARIN TEAM[B]-17.79)^1.724) - ((SAGARIN TEAM[A]-17.79)^1.724))/400)) TEAM A = 95.00 TEAN B = 90.00 TEAM A = .755 (have to convert to 75.5%) NOTE: 5 points favorite does not always mean 75.5% probability of winning in this method. Based on probability that Duke is less likely to blow/lose a game over a team they are favored by 5 points than a Winthrop is. TEAM A = 75.00 TEAM B = 70.00 TEAM A = .711 (71.1%) Does not work with rating below 17.79. | |||||
| 7 | Toral ID: 452461218 Tue, Mar 13, 12:18 |
Thanx, Sludge! Whoops, that wouldn't work for football? I've been looking for a chart like this in football for a long time. Inhabited gambling usenet groups and couldn't get one (maybe no one would give it to me.) Would a football chart be different? Toral | |||||
| 8 | Sludge ID: 18116195 Tue, Mar 13, 13:00 |
Toral - That's one of the lists that I actually used for football pickoff. It didn't perform very well. The historical model has always been the winner (in the two years, anyway), even over the computer rankings. I suppose I could open up a bit and share that one. :) (It could be refined even more by looking at even more historical data. I believe the data I used covered only 5-6 years.
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| 9 | The Beezer ID: 191202817 Tue, Mar 13, 13:05 |
Thanks for the formula, Steve. Since I just finished the numbers using Sludge's numbers above, I'll save them for next year. :) BTW, I found the formula for Sludge's numbers, in case anyone wants to apply it without rounding spreads. It's (spread+5)/(spread+10). Ex: 5 point spread= (5+5)/(5+10)=10/15=0.666667 as above. | |||||
| 10 | Sludge ID: 18116195 Tue, Mar 13, 13:19 |
steve h - That looks like the formula given on Massey's page for computing probabilities using the Sauceda rating system. (Here) It looks like you've just converted the Sagarin ratings into a Sauceda rating to do the computation. Recall how you did the conversion? Regression? | |||||
| 11 | Sludge ID: 18116195 Tue, Mar 13, 13:22 |
Beez - That would be it. I don't recall if I simplified it down to that simple formula when I originally computed them. I'm notorious for finding the formula (simple or not) and using it as is. | |||||
| 12 | steve houpt ID: 51291010 Tue, Mar 13, 13:58 |
I have that formula in an 8 team bracket. Getting bigger was too hard for my spreadsheet (and brain). Using that and Sagarin recent ratings (not full season) I came up with the following chances of making the Elite Eight (3 wins) out of a million tournaments. Number of times making it to the Elite 8 has no 'direct' effect on chances against other teams that are predicted to make it in different brackets. EAST (upper) Duke_____ 956,654 UCLA_____ 18,182 Ohio St__ 13,938 5 others_ 11,226 EAST (lower) KY_______ 578,758 BC_______ 311,829 USC______ 51,365 Iowa_____ 24,483 Creigh___ 23,170 3 others_ 10,394 MW (upper) Illinois__ 590,187 Kansas____ 330,815 Tenn______ 32,321 Charlotte_ 23,592 Syracuse__ 16,811 4 others__ 6,274 MW (lower) Arizona__ 756,186 Miss_____ 106,362 Wake F___ 90,664 Xavier___ 22,365 ND_______ 16,641 3 others_ 7,512 SOUTH (upper) Mich St__ 753,697 Okl______ 99,440 VA_______ 89,069 Calif____ 22,686 Fresno___ 20,076 Gonzaga__ 13,064 2 others_ 1,698 SOUTH (lower) Florida__ 501,794 UNC______ 310,788 Prov'nce_ 74,105 Temple___ 46,295 Texas____ 48,856 Penn St__ 11,504 2 others_ 9,658 WEST (upper) Stanford_ 770,548 Indiana__ 163,499 Cinci____ 31,577 St Joe's_ 14,958 4 others_ 19,418 WEST (lower) Maryland_ 712,919 Iowa St__ 123,111 Arkansas_ 96,764 WISC_____ 49,680 Georgt'n_ 13,419 3 others_ 4,107 READ AT OWN RISK. | |||||
| 13 | steve houpt ID: 51291010 Tue, Mar 13, 14:11 | Sludge - I cheated. Didn't have a spreadsheet that would do regression. Worked equation backwards, substituting different variables until I got lowest error for whatever I wanted at the time to get similar results at various points. | |||||
| 14 | The Beezer ID: 191202817 Tue, Mar 13, 17:15 |
Had some free time this afternoon, so I played around with Steve's formula and used it to determine my winning percentages. I'm doing my expected values now, and I wanted to confirm my thinking on something. When I'm comparing team A and team B, if team A is the favorite, then I need to consider 3 factors: expected gain from team A if they win, expected gain from team B if THEY win, and the penalty to A if they lose to B. Since the second and third values are the same, I believe this means that the expected value of A winning should be twice the expected value of B winning. Does this sound correct? I started doing it just comparing expected A and expected B directly, and my bracket so far looks pretty normal. Is there a flaw in my thinking somewhere here? Thanks in advance! | |||||
| 15 | Sludge ID: 18116195 Tue, Mar 13, 19:37 |
Expected Winnings of Team A = (Gain for A should they win)*(Probability A Wins) + (Gain for A should they lose)*(Probability A Loses) Note that "Gain for A should they lose" will be a nonpositive number. | |||||
| 16 | Sludge ID: 18116195 Tue, Mar 13, 20:16 |
Here ya go, steve h et al. The regression equation to convert from Sagarin ratings to Sauceda ratings: Sauceda = -424 + 19.8 * Sagarin To compute probabilities, see the link to Massey's page I gave above. Enjoy. | |||||
| 17 | The Beezer ID: 191202817 Tue, Apr 03, 21:56 | Well, I just wanted to thank Sludge and steve houpt for the help on the statistics. Using Sludge's table and s.h.'s formula with the Sagarin ratings, I managed a 5th place finish! Thanks tons guys! | |||||
| 18 | HooeyPooey ID: 1631545 Wed, Apr 04, 05:17 | Thanks you guys... some how I managed 611th place. :) | |||||
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