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Super Bowl 50: The Panthers are Still Underrated

The Carolina Panthers and Denver Broncos are your Super Bowl 50 participants. I believe not only will the Panthers win, but they should do so handily. Why? Because math.


I wrote an article last week about using the Pythagenpat formula to project 2016 records. Well, we can use that same formula for in-season results as well. However, we can’t just use the regular season Pythagenpat from last week’s article, because we have more games we can add to the results of the Panthers and Broncos.

The Panthers have been simply dominant in the playoffs, which has increased their Pythagenpat win percentage from 0.817 to 0.831. Meanwhile, Denver has also won two difficult games and their Pythagenpat win percentage has increased from 0.629 to 0.632. In other words, the Panthers are indeed a favorite, as current gambling lines reflect. So how much does Pythagenpat like the Panthers?

Using the Pythagenpat win percentages, we can use the Log5 formula to predict the expected win percentage for the Panthers. The formula gives us the result that the Panthers have a 74.1 percent chance of winning. In other words, a very good chance they win the Super Bowl. How do we translate that into a point differential?

Normal Distribution

According to my research, gambling  lines have been normally distributed with a mean of zero (meaning on average Vegas is correct with their lines), and standard deviation of 13.4 over the past decade.

Distribution of Gambling Spread vs. Actual Spread Since 2005


If we revert back to statistics 101 for a moment, you might recall the 68-95-99.7 rule, which lets us know what percentage of values lie within one, two, or three standard deviations of the mean for a normal distribution. We can use exactly this type of method to calculate how many standard deviations it would equate to a 74.1 percent chance of a Panthers win. We get 0.642 standard deviations, which translates to 8.6 points away from the mean of zero.

In other words, Pythagenpat likes the Panthers by 8.6-points on a neutral field. Don’t take this as betting advice, because there are a lot of other things that factor into setting lines. The point is Pythagenpat really really likes the Panthers.

I think that’s fair. The Panthers went 11-5 against the spread according to Vegas Insider, and 2-0 in the playoffs. They have simply been underestimated all year.

More Sabermetrics

Pythagenpat is what sabermetricians call a first-order win. To get a more accurate prediction using sabermetrics, we could do two things (the details of which is for another article, another day). First, we could calculate something called second-order winning percentage, which uses a calculation of how many points a team should have scored based off of certain statistical metrics. This helps account for both luck1 and the order in which the statistics happened, and represents a truer picture of a team’s strength. Second, we can then get a metric called third-order wins, which adjusts second-order winning percentage for strength of opponents faced. This is a much better predictor of future games (like the Super Bowl).


Third-order wins should bring the Broncos a bit closer to the Panthers than Pythagenpat alone, but probably not close enough for where the line currently stands at Panthers -4.5.2. If you are playing any sort of fantasy sport for the super bowl, lean on those Panthers players. They are likely to win, and could even do so comfortably according to sabermetric predictions.

  1. good or bad  (back)
  2. As of Monday, January 25th  (back)

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