Comments on: Are there ideal numbers to have in a basketball "Square pool"?
http://ask.metafilter.com/210828/Are-there-ideal-numbers-to-have-in-a-basketball-Square-pool/
Comments on Ask MetaFilter post Are there ideal numbers to have in a basketball "Square pool"?Sun, 18 Mar 2012 16:58:47 -0800Sun, 18 Mar 2012 17:10:51 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: Are there ideal numbers to have in a basketball "Square pool"?
http://ask.metafilter.com/210828/Are-there-ideal-numbers-to-have-in-a-basketball-Square-pool
Math/sports question! I entered a "Square pool" (purely theoretical money at stake :) ), for the NCAA basketball tournament. I am curious if there are better numbers to have, and why that would be the case. More information inside. <br /><br /> This type of pool is very popular for the Super Bowl. You create a 10 x 10 grid, and people purchase squares (let's say five bucks a piece.) Once all the squares have been purchased, you randomly assign digits 0-9 to the rows and columns, as well as a team. Each square corresponds to the last digit of the score. So if the super bowl ended 42-35, Giants beating the Patriots, the person who had the square Giants 2, Patriots 5, would win.<br>
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Now in football, there are clearly a few numbers which are better to have. By virtue of the scoring opportunities in football, you're obviously going to do OK with numbers like 7, 4, 1 or 0. Numbers like 5 and 2 don't come up as frequently, just because these require less likely scenarios like kicking four field goals to get to twelve points.<br>
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However, I am curious if there are ideal numbers to have for the <strong>basketball version</strong> of this pool. So far this year, there have been a couple number combinations that have come up more than once. I am guessing this is just random odds, but I was wondering if anyone who knows statistics or probability or just plain math better than I do might be able to offer some advice or theories about which numbers would be better to have in a pool like this for basketball.post:ask.metafilter.com,2012:site.210828Sun, 18 Mar 2012 16:58:47 -0800JoeGoblinfinalfourncaabasketballgamblingpoolBy: no regrets, coyote
http://ask.metafilter.com/210828/Are-there-ideal-numbers-to-have-in-a-basketball-Square-pool#3040601
I'd be happy to be corrected, but I think <a href="http://en.wikipedia.org/wiki/Benford%27s_law">Benford's Law</a> might apply. I don't know how strong an effect it would have, but I'd guess low numbers over high numbers if you put a gun to my head.comment:ask.metafilter.com,2012:site.210828-3040601Sun, 18 Mar 2012 17:10:51 -0800no regrets, coyoteBy: milqman
http://ask.metafilter.com/210828/Are-there-ideal-numbers-to-have-in-a-basketball-Square-pool#3040622
Benford's Law would apply to the _first_ digit of a different type of counting phenomena. In this case, you could take a pretty good crack at the first digit being 6, 7, or 8 probably 90% of the time. The last digit (the one you are looking for here) is going to be far more random.<br>
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If I were going to venture a guess, I would do so by first looking up the final scores to all of last years games, mod 10-ing them and looking for a pattern.<br>
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We did something like that <a href="http://ask.metafilter.com/193301/Ive-got-a-beer-riding-on-this">here</a>. Good luck.comment:ask.metafilter.com,2012:site.210828-3040622Sun, 18 Mar 2012 17:33:32 -0800milqmanBy: Pinback
http://ask.metafilter.com/210828/Are-there-ideal-numbers-to-have-in-a-basketball-Square-pool#3040627
Shouldn't be too hard to find out - grab the scores for a few years worth of games in the particular league, ditch all but the least significant digit, and do a histogram of the frequency of each combination.<br>
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The only real trick beyond that would be to account for which team won. Assuming that the assignment of teams to an axis is random, you shouldn't need to - but if not (e.g. lowest team alphabetically is always on the Y axis) then you may be subject to some unaccounted-for bias (i.e. do teams starting with A-L, or "odd-numbered" alphabetical names, win/lose more often?)<br>
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On preview: basically, what milqman said.comment:ask.metafilter.com,2012:site.210828-3040627Sun, 18 Mar 2012 17:39:30 -0800PinbackBy: Pinback
http://ask.metafilter.com/210828/Are-there-ideal-numbers-to-have-in-a-basketball-Square-pool#3040631
On consideration: if the axis for the team is determined by something like home vs away status, or some other 'theoretically randomised by the league, but potentially outcome-biasing' factor, then definitely factor it in.comment:ask.metafilter.com,2012:site.210828-3040631Sun, 18 Mar 2012 17:43:30 -0800PinbackBy: JoeGoblin
http://ask.metafilter.com/210828/Are-there-ideal-numbers-to-have-in-a-basketball-Square-pool#3040633
Some more info:<br>
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-In the basketball pool, one axis is for the Lower seed number (favored team), and the other is for the higher seed number (underdog). <br>
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-As far as I can tell, in the pool I'm in, the only number that matters is the final score. My initial instinct is to believe that having the same number on both axis, 6-6 or 9-9, is a disadvantage, since a game would have to end by a ten point differential to make this happen, but this may just be an uniformed opinion. (A friend is in a pool that sidesteps this by having the score at the end of regulation count, so a tie is a possible outcome.)<br>
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I am mainly curious to see if the basketball strategy impacts the result at all, since many of these games seem to end with the team that is losing fouling a lot in the final two minutes and then taking faster, riskier plays that don't pay off as much when they get on offense. My numbers are Underdog: 0 and Favorite: 1, which I thought might work out OK, but it hasn't hit yet. I wonder if having numbers that are further apart might be better.<br>
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Anyways, thanks for any insights you can provide!comment:ask.metafilter.com,2012:site.210828-3040633Sun, 18 Mar 2012 17:44:46 -0800JoeGoblinBy: Homeboy Trouble
http://ask.metafilter.com/210828/Are-there-ideal-numbers-to-have-in-a-basketball-Square-pool#3040967
<a href="http://www.amstat.org/publications/jse/jse_data_archive.htm">This site</a> (search for "basketball") has a link of old NCAA basketball scores you can play around with. (They're old enough that the first link I found to the dataset was a gopher link.) It covers ~1700 games to 1995, and unless the game has changed significantly, here's a few quick datapoints:<br>
- Scores ending with 7, 5 and 2 are less common; scores ending with 0 and 9 are slightly more common. 7 was the least common; 9.1% of the scores (obviously 10% is the expected outcome) and 0 the most common, 10.8% of the scores. So it's still pretty even.<br>
- Your opinion about the axis is correct; results where the difference in digits is 0 make up 6.7% of the results. The most likely are 2 points off (14.2%), followed by 1 point off (12.4%) and 4 points off (12.0%).<br>
- The most common two-digit combo is 9-4 (e.g. 84-79, 109-104). It occurs 2.8% of the time (you'd expect 2.0%). The next most common are 0-2 (2.7%), followed by 0-6 and 4-6 (2.6% each). The 0-1 combination occurs 2.2% of the time. The dataset doesn't say who the underdogs and who the favourites are. The worst combo is 7-7 (0.8%), followed by 3-3 (0.9%).<br>
- In a 68 game tournament, you would expect about 1.47 games to end 0-1; while more will end with underdog 0, favourite 1, I'd expect at least a third to go the other way (which could be Underdog 81, Favourite 80; but also Underdog 80, Favourite 91). <br>
- If I had to pick, Favorite 2 Underdog 0 would be my choice. But you could do a hell of a lot worse than your choice.comment:ask.metafilter.com,2012:site.210828-3040967Mon, 19 Mar 2012 00:19:48 -0800Homeboy TroubleBy: JoeGoblin
http://ask.metafilter.com/210828/Are-there-ideal-numbers-to-have-in-a-basketball-Square-pool#3041557
Thanks for running the numbers! I guess part of the offset in probability of the higher probability numbers you cited probably come from the identical digit sets - whose outlier status can be explained by the rules of the game.<br>
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I didn't doubt that the numbers would probably be fairly even, but was curious if any freaky discrepancies would arise. Looks like it's a fairly normal set of data. Thanks for your help!comment:ask.metafilter.com,2012:site.210828-3041557Mon, 19 Mar 2012 13:20:56 -0800JoeGoblin