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Should be simple enough, but I can't get my head around the math required.

Let's say you have Team 1 (80 overall) vs. Team 2 (70 overall).

Using only those two variables, what's the best/fairest way of determining a winner? Obviously, the higher the overall, the better the chance Team 1 should have to win.

I've been trying to look up answers, but unfortunately I don't exactly know the word or phrasing of what I'm trying to figure out.

Just looking for a logic, or if someone can point me in the right direction of searching, that would be great.

Edit: Basically, in a match of Team 1 vs. Team 2, how can I calculate the winner when the only stat I'm given is the overall of each? Overall meaning the teams overall rating out of 100. (think sports team, the players ratings average is the teams overall rating).

jsquadrilla
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    Your question is confusing. Are you asking what is the *probability* that Team 1 will win if Team 1 has a "rating" of 80 and Team 2 has a rating of "70"? – Scott Mitchell Dec 21 '12 at 20:01
  • Yeah, what do these numbers mean? If you give us a formula for those scores, we can propose meaningful models. Right now, these could mean literally anything. – Patrick87 Dec 21 '12 at 20:03
  • It should be depending on how many Games they both play each other isn't. – Sunil Bojanapally Dec 21 '12 at 20:05

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The question is unclear because you haven't defined an criteria for how the winner is selected. If the winner is the team with the highest overall ranking then it's pretty straight forward, team one wins. If you're doing some sort of weighted drawing -- like the NBA draft lottery -- where the team with the higher score has more chances of winning the drawing then you'd just think of it like pieces of paper in a bowl. Team 1 gets 8 pieces, Team 2 gets 7 pieces. There are 15 pieces in the bowl and Team A has 8/15 or 53% chance of having one of its pieces picked out. Add in a Team 3 with say a 30 ranking so they get 3 pieces of paper. Now there are 18 in the bowl and Team 1 has a 8/18 or 44.4% chance of winning.

If that's what you're after then you can write a formula for picking weighted random winners -- random choices but where one team has a greater chance of being selected than another.

wunderdojo
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  • The winner won't always be the team with the higher overall ranking, but they should have a higher probability of winning. – jsquadrilla Dec 21 '12 at 20:08
  • Example: NHL games, Leafs vs. Penguins. Penguins have a higher overall on paper, but the Leafs could still win. – jsquadrilla Dec 21 '12 at 20:08
  • @jsquadrilla The rest of this answer is probably about as good as you can do without more information: assume that ratings are comparable 1:1 and draw randomly from a bag with the right proportions. There's an element of randomness, and evenly matched teams have an even chance of winning. – Patrick87 Dec 21 '12 at 20:13
  • @Patrick87 Could you explain that a little more? Assuming Team 1 and Team 2 are both equally rated, they would have a 50/50 percentage of winning the game. Team 1 is rated higher than Team 2, so the percentage split would be changed. I'm just trying to understand the math behind it. – jsquadrilla Dec 21 '12 at 21:12
  • @jsquadrilla The part of the answer that the probability as proportional to the score is what I'm referring to. – Patrick87 Dec 21 '12 at 22:59
  • Check out this post for multiple PHP solutions to generating weighted random selections: http://stackoverflow.com/questions/445235/generating-random-results-by-weight-in-php – wunderdojo Dec 22 '12 at 21:42