SaberSmart
  • Home
  • Blog
    • Throwback
  • Playoff Odds
    • MLB >
      • 2019 >
        • Total Playoff
        • Win Division
        • Win WildCard
        • Expected Wins
      • 2018 >
        • Total Playoff
        • Win Division
        • Win WildCard
        • Expected Wins
      • 2017 >
        • Total Playoff
        • Win Division
        • Win WildCard
        • Expected Wins
    • NBA >
      • 2018 >
        • Total Playoff
        • Expected Wins
      • 2017 >
        • Total Playoff
        • Expected Wins
  • About
    • Contact
    • Comment Policy

Living in the Past: Predicting Super Bowl 51

2/3/2017

Comments

 
Picture
With the Super Bowl between the Patriots and Falcons coming up on Sunday, the internet is flooded with probabilities of which team will win as well as a myriad of other prop bets. Currently, the Patriots are favored by three points and the predicted score is estimated to be around 28-25.

Nate Silver of the FiveThirtyEight blog, using a pretty intense simulator, has the Patriots at 61% of winning the Super Bowl with the Falcons consequently at 39%. His forecast is based on 100,000 simulations of the season with updates after every game. His model uses Elo ratings, a complicated measure of strength based on head-to-head results and quality of opponents, to calculate a team’s chances of winning their next game.

To check these probabilities, we developed a basic simulator incorporating only the final scores from games played by the Patriots and Falcons during the regular season and playoffs so far.
Patriots
Falcons
Points For
Points Against
Points For
Points Against
23
21
24
31
31
24
35
28
27
 0
45
32
 0
16
48
33
33
13
23
16
35
17
24
26
27
16
30
33
41
25
33
32
24
31
43
28
30
17
15
24
22
17
38
19
26
10
28
29
30
23
42
14
16
3
41
13
41
3
33
16
35
14
38
32
34
16
36
20
36
17
44
21
​The points scored by each team represents their offense. The points scored against each team represents their defense. Fitting a probability distribution to each of these four scores allows us to randomly sample from each statistic and determine an appropriate total score for each team over as many Super Bowl simulations as we want. The two most common probability distributions for sports scores are the Poisson distribution and Negative Binomial distribution. To decide on which to use, let us examine the histograms:
Picture
The spreads are all over the place due to their relatively small sample sizes. Here are the descriptive statistics:
 
Mean
Variance
​Patriots Offense
28.38889
93.31046
Patriots Defense
15.72222
64.09477
Falcons Offense
34.44444
81.20261
Falcons Defense
​24.83333
50.02941
Since the means and variances are not the same, we can probably rule out the Poisson distribution. As another blow to the Poisson distribution, the Negative Binomial has been proven to accurately describe scores in baseball, soccer, rugby, and college football. Because of this analysis, we decided to model the scores above using the Negative Binomial distribution.

The Negative Binomial requires two inputs, the size or dispersion parameter (the shape parameter of the gamma mixing distribution) and the probability of success where prob = size/(size+mean). Since we know the mean of each statistic, we will compare 1000 samples of various sizes to see which one fits the best.
Picture
The highest single game score by a team is 72 points, by Washington in 1966. Thus we can rule out sizes with scores higher than that, which is anything around a size of 4. By the looks of the graphs, both size 50 and size 100 seem to be decently accurate, at least for the Falcons Offense. It turns out the difference in the final results between the two are negligible so because of this, we will just use a size of 100 to describe all of our distributions. Now we are ready to simulate the Super Bowl!
.
For each simulation of the Super Bowl, we took a single random sample from each distribution to get a number describing each of the Patriot’s offense, Patriot’s defense, Falcon’s offense, and Falcon’s defense. Then we took the mean of the Patriot’s offense score and the Falcon’s defense score to obtain a score representing the Patriot’s total points and the mean of the Falcon’s offense score and Patriot’s defense score to get a score of the Falcon’s total points. Then we compared the two, threw out ties, and recorded who won.

After simulating 100,000 Super Bowls in this way, our method returned the Patriots winning 61% and the Falcons winning 39%. The average score by the Patriots was 27 points and the average score by the Falcons was 25 points. These results are on-par with Vegas odds and matches almost exactly the winning probabilities that Nate Silver came up with. This shows that even a basic simulation can come marginally close to the results produced by more complex simulations probably trained on more data and information. Try this out with scores from other sports teams!

As usual, find all of our code on GitHub.

The SaberSmart Team
Comments
comments powered by Disqus

    Archives

    August 2019
    July 2019
    January 2019
    October 2018
    September 2018
    August 2018
    July 2018
    June 2018
    April 2018
    February 2018
    December 2017
    November 2017
    October 2017
    September 2017
    August 2017
    July 2017
    June 2017
    May 2017
    April 2017
    March 2017
    February 2017
    January 2017
    December 2016

    Categories

    All
    Analytics
    Big Data
    Computer Science
    Economics
    Essay
    Football
    Gambling
    History
    Mathematics
    MLB Teams
    NBA Teams
    NFL Teams
    Philosophy
    Super Bowl
    Triple Crown
    World Series

    RSS Feed

    Follow @sabersmartblog
    Tweets by sabersmartblog
 Support this site by clicking through the banner below:
  • Home
  • Blog
    • Throwback
  • Playoff Odds
    • MLB >
      • 2019 >
        • Total Playoff
        • Win Division
        • Win WildCard
        • Expected Wins
      • 2018 >
        • Total Playoff
        • Win Division
        • Win WildCard
        • Expected Wins
      • 2017 >
        • Total Playoff
        • Win Division
        • Win WildCard
        • Expected Wins
    • NBA >
      • 2018 >
        • Total Playoff
        • Expected Wins
      • 2017 >
        • Total Playoff
        • Expected Wins
  • About
    • Contact
    • Comment Policy