I think I found the actual reference from my entry level statistics course in college. Something referred to as binomial probability; taking a trial of results with at least 2 outcomes, and measure of success and failure. I recognized this approach when I studied the Favorite Toy method by Bill James, which is now more properly termed The method is supposed to measure the probability of reaching a milestone amount, mainly applied to baseball. It’s a matter of taking 3 different numbers, and ranking them, applying the value to the number, and dividing the value of the rank to the sum of the numbers being used. For example:
We’ll assign 1 a value of 1, 4 a value of 2, and 3 a value of 3.
We multiply the numbers to each other (1×1), (4×2) (3×3) and then add these results.
So our total is
1 x 1 = 1
4 x 2 = 8
3 x 3 = 9
And we divide that number, 18, by the sub total of rank (1+2+3 = 6) to get…3
The number that is key is 3, as the likelihood of the result that follows 1, 4 and 3 based on the rank. This can be applied in a number of situations.
So it is that I looked to this method for determining a future scoring outcome for the Super Bowl, to see if I can predict the score and the flow of the game. What I did, after a few years experimenting on this, was to take the quarterly scores for and against of a team’s games,looking at each boxscore of the regular season and playoff game. Applying the Favorite Toy method, the Game 1 scores have the least rank, and the conference championship games the most rank. I had to add up the week numbers (basically 1 through 18, which equals 171), and then divide that by the series of products that resulted from multiplying all those quarterly scores. I then produced a 2nd series of numbers by simply doing a sum total of the quarterly scores, no binomial coefficient to mess with here. Finally, I did a median of the 2 sets of numbers to use as the basis for the comparatives.
For this post, I’m comparing the two Super Bowl teams and measuring who is scoring and allowing scores at a rate quicker or slower at a particular quarter of a game. In this way, not only am I attempting to predict a score, but also the very flow of the contest.
I’ll spare the heavy work, and give you the core results and the comparatives here:
After 18 games, here is what the Broncos scored based on the sub total:
1Q: 7.77 2Q: 9.72 3Q: 8.61 4Q: 10.88. Total of the sub totals are 36.98
1Q: 3.55 2Q: 7.27 3Q: 5.77 4Q: 7.44 Total: 24.03
Using the binomial coefficient, the scores are a bit different. It’s how different that matters:
1Q: 7.97 2Q: 9.38 3Q: 5.92 4Q: 10.04 Total: 33.31
1Q: 3.02 2Q: 6.18 3Q: 5.21 4Q: 8.05. Total: 22.46
And for the median of the 2 results for the Broncos, the basis for the study:
1Q: 7.87 2Q: 9.55 3Q: 7.26 4Q: 10.46 Total: 35.14
1Q: 3.28 2Q: 6.72 3Q: 5.49 4Q: 7.74 Total 23.23
When comparing the 1st 2 sets of numbers, I am comparing the statistical trend, the sub total to the binomial. The binomial result is what’s current. In this way, we see that the Broncos’ is scoring a few more points in the 1st, a few less in the 2nd, a lot fewer in the 3rd, and less in the 4th.
In points allowed they are allowing less in the first and 3rd, a good deal less in the 2nd, and then it softens up in the 4th.
The trend: I gathered by getting the net score of the sub total for each quarter, PF and PA, and comparing to the binomial. If the sub total is greater, or more positive, this means a negative trend is occuring.
1st quarter: +0.73
2nd quarter: +0.75
3rd quarter: -2.13
Now we pause and look at the Seahawks numbers. First the sub totals:
1Q: 4.16 2Q: 8.50 3Q: 5.38 4Q: 7.33 Total 25.37
1Q: 1.38 2Q: 6.38 3Q: 2.66 4Q: 4.16 Total 14.58
1Q: 4.33 2Q: 8.71 3Q: 4.67 4Q: 6.98 Total: 24.69
1Q: 1.41 2Q: 5.63 3Q: 2.49 4Q: 4.75 Total: 14.29
And the median of these, the numbers we’ll run with:
1Q: 4.24 2Q: 8.60 3Q: 5.02 4Q: 7.15 Total: 25.01
1Q: 1.39 2Q: 6.00 3Q: 2.57 4Q: 4.45 Total: 14.41
1st quarter trend: +0.14
Seahawks scoring a bit more lately in the first, a bit more in the 2nd, much less in the 3rd, and less in the 4th.
On defense, they give up a few more in the first, much less in the 2nd, a bit less in the 3rd, and soften up in the 4th.
Now for the real marriage: We’ll take the median of 2 of the median lines, specificaly Denver’s points for and Seattle’s points against, and then vice versa. We’ll do the median of those results further to finally get the point total we seek. And….we’ll do a final comparative as to how the scoring should go:
First the median of the Broncos’ points for and the Seahawks points against:
7.87 9.55 7.26 10.46 (Bronco offense)
1.39 6.00 2.57 4.45 (Seattle D)
4.63 7.77 4.91 7.45 = 24.06
Now vice versa:
4.24 8.60 5.02 7.15 (Seattle offense)
3.28 6.72 5.49 7.74 (Denver D)
3.76 7.66 5.25 7.44 = 24.11
Considering the quarterly trends and the marriage of medians, my predicted final score is Seattle 26, Denver.24
Both sides should come out firing and that momentum will be present, with Denver doing best, in the 2nd quarter. 2nd half will be much more defensive, and Seattle will have its biggest impact in the 3rd. Both sides are very even in the 4th, so the end-of-3rd quarter result should be the best indicator.