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I'm playing this video game where people can get kills, deaths, and assists , and all this is recorded on a stats website. The stats website gives you a rating by directly manipulating these numbers.

In the first entry, I have 26 kills, 5 deaths, and 19 assists. The KDA ratio the website gave me was 29.8. At first thought, I guessed that the formula was ratio = (kills*5 + assists)/deaths.

But then the second entry threw me off. 21.33 Kills, 1.33 deaths, and 4.33 assists. And the ratio outputted here is 24.58.

Is there a good approach to figuring out the formula or function when the inputs and outputs are given?

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I know with only two entries, there can probably be multiple formulas, but the way data is weighted / calculated should also make sense to apply a rating to a player. So I'm just wondering if this is possible to figure / how to figure it out. – krikara Dec 16 '12 at 4:57
1. The more datapoints that you have, the more likely you will be able to find a reliable estimate of your score. 2. If you have some idea of the general form of the equation, you can use regression to estimate the unknown quantities in your equation. – Daryl Dec 16 '12 at 5:08
You've already given enough data to determine the values of a and b in any formula of the form KDA=(akills+bassists)/deaths that would fit your data - and it implies a negative value of a! (to first approximation, b=8 and a=-.1) - this suggests that your 'meta-formula' is the wrong formulation to use. – Steven Stadnicki Jul 3 '14 at 19:46

Well, an easier method I think is (if you can get more data) is to just plot it. You might just "see" what is happening with a reasonable number of points plotted. This will also help with guessing the form of the fitting function if you want to use regression.

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You should be able to use a regression to figure out the function based on the fundamental type of function that you want. For example, if you want an linear function, you would be able to find some equation in the form $y=mx+b$.

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