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I am using a SRS spreadsheet (Not necessary to know I believe, but it is as mentioned in this article) to determine team strength in various sports. This system allows me to predict an average score for both teams and what the variance of the score is for both teams.

I am running this in google sheets, and have been brute forcing the probability, by using a sheet with the sequence of numbers (0.0025, 0.005, 0.0075, 0.001 ... 0.9975) in the top row and first column and subtracting the distribution of one team from another for each cell.

The problem is this process results in over 150,000 formulas being updated at once every time an input into my formula is changed (i.e. Change one of the teams, the location of the game, etc.)

Is there a formula that can be used instead of attempting to brute force out a sample?

For example;

Team A has an average predicted score of 26.0 and a variance/standard deviation of 11.12

Team B has an average predicted score of 29.3 and a variance of 7.81

The random score is determined for each by using a CDF.

Is there a formula that can predict the odds of Team A having a better score than Team B assuming the random variables are independent?

For reference, my extent of knowledge is Calculus 1 (Specifically, taking AP Calculus in my senior year of high school)

Rickstar
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  • (1) What's an "SRS system"? (2) In what form are these distributions represented? (3) How is the "input changed"? (4) The mathematical procedure is called a convolution. That's a good search term to find plenty of closely related threads here on CV. – whuber Sep 08 '22 at 19:28
  • Hi. Welcome to CV. As @whuber mentioned, please make your post self-contained and please abstain from using acronyms which are not known universally. A more research and clarity in the post would be appreciable. – User1865345 Sep 08 '22 at 19:35
  • @whuber Thank you for the response, I added in some clarifying information, but to summarize what I added. (1) A system used to determines a value for each team based on points scored, I don't believe it is necessarily helpful, but I figured I'd add just in case someone here randomly knew it. (2) These distributions are CDF. (3) When I refer to an input changing, I am referring to the location of the game (which adds or subtracts from the means of both teams) or one of the teams participating. (4) Thank you for pointing out convolution, but I don't think I see how that helps me Icould be wrong – Rickstar Sep 08 '22 at 20:32
  • The convolution remains the solution. However, your description of your data is so vague that I cannot provide additional clarification about how you should compute it. – whuber Sep 09 '22 at 13:22

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