nice how did u come up with tht formula
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The formula is the only way I can think to quantify a teams defensive capabilities while simultaneously factoring out strength of schedule. It has its flaws. For example, it doesn't take into account any human variables, weather, or even home field advantage. it is strictly "this team scores this much on average, the target team (49ers + Panthers) held them to this." It makes a ton of assumptions, but because it deals in averages over time, it becomes more accurate as the season progresses.
So have you retrotested and if so how has your model done?
The model works much better for teams that do not have high variance in the differential between Points Against Target and Points Against Season Average.
The Panthers have differentials of (-13.8, 3, -17.6, 1.3, -13.3, -5.7, -2.5, -12) This have a an average of -7.575 and a standard deviation of 7.67! So if a team averages 27.3 points per game, 68% of the time, they will score between 11.83 and 27.4. scoring on average 19.725 points against the Panthers. Because the standard deviation of 7.67 is so high, it leaves us with a wide margin of possibility being statistically possible.
Teams with a smaller variance like say the 49ers (-1, 3.2, 0.2, -9.7, -15.3, -0.7, 1.5, -0.8) with an average of -2.825 and a standard deviation of 6.3 meaning that the Panthers who score on average 25.5 points per game, would have a range of 16.375 to 28.975 (68% of the time) with an average of 22.675. (They also have a HUGE outlier, there game against the Texans, but we shall save outlier detection and winsorized means for another time)
So Technically speaking, the game has a 68% chance that the scores fall
Panthers 16.375 - 28.975
49ers 11.83 - 27.4
Though that isn't a strong statement, it is extremely helpful in determining my bets for the weekend. I only bet 2 or 3 games a week, and I am pretty solid.