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September 12th, 2013, 08:07 PM   #1
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Question about simulating finishing order

This isn't really for anything important, but every now and then my brain gets locked on something and won't let go.... you know how it is, I'm sure.

I started thinking about how video game rating systems work, and set out to devise my own simple version of one, just so I could test it and simulate some games.

So say it's a racing game, with 4 players. Video game rating systems are meant to attempt to measure the "true skill" of a player, so for my simple version I'm going to assume that it does accurately enough.

I want to simulate the finishing order of 4 players with the following ratings of "true skill." The rating numbers themselves are arbitrary for now, but I've tried to disperse them in a way that there should be an obvious trend in how they finish, leaving the last two closer together to attempt to see more "flip-flopping" of positions than the first two.

Player A - 1500
Player B - 1250
Player C - 1000
Player D - 900

How do I calculate the probability of each of the 24 (4!) different possible finishing orders?
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September 12th, 2013, 09:25 PM   #2
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Re: Question about simulating finishing order

To clarify,

These ratings are meant to be relative. Meaning if they really represent the true skill of a player, then Player A is ~18% better than Player B. The numbers themselves should be scalable. (At least that's how I think it should work in my brain)
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