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super bowl squares

Get excited, the Super Bowl is coming, which means Super Bowl Squares are coming! It’s time to start thinking about the value of each cell in the square. You can let players pick cells, but it’s more fun to randomly assign them. That still allows trading cell for the skill player, but doesn’t leave a hobbled 2-2 cell lying around for some sucker to pick. Either way, it’s good to know the expected value of each cell.

There’s several approaches one can take. Last year, before the SF-BAL game, Minyanville published an article on how to value Super Bowl Squares which I’ll use as a reference.

One can start with historical data, but as noted, the game changes over time. Perhaps one can try more recent data, such as all the games played this season by the two teams, or even all games by all teams.

Sidebar: I’ll pull one quote from the above article for further discussion. “Safeties make a dramatic change to the square values; there seems no reason to assume they should be more common in Super Bowls.” This is a dangerous thought process, particularly for a financial site. One may not know why an event happened, but the event did happen. For that matter, the discard outliers until the data fits our theory methodology is used in several unnamed other fields, with equally sad outcomes.

We can also simulate the game in a variety of ways. There’s some hints in the article about the inputs you need. Simulating on a drive by drive basis is pretty easy, which is the approach I’ve taken.

There’s Lua code in sbsquares.lua. It prints out the relative values of each cell, normalizing to 1.0. Values over 1.0 are good. There’s one square each for the published Minyanville square (note that it’s for last year’s SF-BAL game), a very simple simulation, and historical data. For the historical data, because there’s so little data, I reflected the scores, such that a 7-3 result counts as 3-7.

For the simple simulation, I assigned probabilities which should be calculated more accurately. Each team gets the ball 10 times. 30% of the time they score, and 60% of the scores are touchdowns. Without looking at too much data, those numbers sound about right. I don’t recommend the sounds right methodology, either, but it’s just a starting point to get some code running.

results

Without having to run the code, here’s the result:

simulation
\      0      1      2      3      4      5      6      7      8      9
0  4.880  2.160  0.270  3.220  4.090  0.240  1.630  4.740  0.670  0.640
1  1.820  0.760  0.070  1.270  1.420  0.090  0.670  1.930  0.250  0.270
2  0.260  0.060  0.010  0.180  0.140  0.010  0.060  0.170  0.030  0.020
3  3.400  1.420  0.100  2.390  2.140  0.150  1.070  3.470  0.580  0.350
4  3.540  1.450  0.180  2.200  2.680  0.110  1.140  4.030  0.470  0.400
5  0.210  0.050  0.000  0.090  0.180  0.010  0.060  0.230  0.040  0.010
6  1.550  0.700  0.060  1.050  1.280  0.050  0.530  1.840  0.200  0.220
7  4.970  2.090  0.170  3.350  3.530  0.220  1.910  4.920  0.930  0.490
8  0.710  0.400  0.020  0.460  0.460  0.010  0.360  0.830  0.120  0.050
9  0.410  0.140  0.020  0.360  0.370  0.020  0.230  0.640  0.090  0.060

minyanville
\      0      1      2      3      4      5      6      7      8      9
0  5.159  1.065  0.352  4.046  2.555  0.181  1.879  4.755  0.469  0.823
1  1.336  0.316  0.110  1.028  0.794  0.165  0.606  1.200  0.198  0.302
2  0.549  0.179  0.027  0.500  0.435  0.064  0.323  0.472  0.070  0.133
3  4.588  0.959  0.292  2.766  2.208  0.202  1.580  3.801  0.336  0.720
4  2.835  0.864  0.222  2.118  1.282  0.177  1.099  2.651  0.309  0.484
5  0.442  0.132  0.079  0.274  0.269  0.047  0.193  0.360  0.110  0.067
6  2.576  0.673  0.217  2.016  1.403  0.199  0.852  2.246  0.297  0.421
7  4.869  1.093  0.190  3.562  2.431  0.213  1.682  3.737  0.421  0.746
8  0.576  0.295  0.082  0.535  0.403  0.089  0.311  0.518  0.070  0.118
9  1.157  0.427  0.098  1.035  0.706  0.100  0.605  1.115  0.166  0.196

previous results
\      0      1      2      3      4      5      6      7      8      9
0  0.000  1.064  1.064  1.064  0.000  2.128  2.128  3.191  0.000  2.128
1  1.064  0.000  0.000  0.000  3.191  3.191  1.064  3.191  1.064  1.064
2  1.064  0.000  0.000  0.000  1.064  0.000  0.000  1.064  0.000  1.064
3  1.064  0.000  0.000  0.000  2.128  0.000  2.128  2.128  0.000  0.000
4  0.000  3.191  1.064  2.128  0.000  0.000  0.000  5.319  0.000  1.064
5  2.128  3.191  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
6  2.128  1.064  0.000  2.128  0.000  0.000  2.128  1.064  1.064  1.064
7  3.191  3.191  1.064  2.128  5.319  0.000  1.064  4.255  0.000  1.064
8  0.000  1.064  0.000  0.000  0.000  0.000  1.064  0.000  0.000  1.064
9  2.128  1.064  1.064  0.000  1.064  0.000  1.064  1.064  1.064  0.000

Without any particular effort to tune the numbers, my simulation comes out fairly close to whatever Minyanville did, at least to the extent that most of the highs and lows are in agreement.

outcome

As for the real game, 34-31, the simulations valued that cell rather poorly.

And as for safeties, why yes, there was another safety in last year’s Super Bowl.

In 2014, there was a safety 12 seconds into the game.

Posted 17 Jan 2014 04:43 by tedu Updated: 10 Oct 2014 00:34
Tagged: math programming sports