Pool player win probabilities help

[Brock Windsor]

Suppose I have a 5 player runningback pool and handicap the following numbers for expected yards rushing:
Player A 80 yards
Player B 75 yards
Player C 70 yards
Player D 65 yards
Player E 60 yards
The bet is "which player will have the most yards rushing for the week". How do I calculate fair odds for each player to win? What additional info do I need? (ie standard dev yardage for each player or should I use an averaged std dev.?) Sorry if this was covered elsewhere. I'm assuming any answer will have a formula that can be applied to any pools type wager. Thanks.

[Brock Windsor]

Putting some more thought into this... My thought is I should profile what a winning result would be (i.e. 80 yards has a 50% chance of winning, 75 yards has 50%-X% chance of winning) and then calculate the probability of each player achieving one of those results to get their probability of winning. Am I on the right track? anyone?

[cyberbabble]

I don't think you can do it analytically (formula).
You probably would need to use a simulation method. Get some history on the players. Get an average/standard deviation for each guy. Pick a probability distribution function. Write a program to generate a series of matches using random numbers and the probability function. Keep track of the results of each match. After repeating for a many times, you would get a win % estimate for each guy. Use win % to value bets.

[Waterstpub87]

I don't think you can do it analytically (formula).
You probably would need to use a simulation method. Get some history on the players. Get an average/standard deviation for each guy. Pick a probability distribution function. Write a program to generate a series of matches using random numbers and the probability function. Keep track of the results of each match. After repeating for a many times, you would get a win % estimate for each guy. Use win % to value bets.

Monte Carlo Method, always good. I'm new to it but, let me see if this helps out.

If you knew the STDEV, you could go into excel and try to figure this out.

For your example, Say A with 80 Stdev of 10, B with 70 Stdev of 10.

For A type into a cell =norm.inv(Rand(),80,10), and you should get a semi random number based on the data. Drag that down 100x and you should have a column of numbers which would indicate projected results. Start another column with B same formula =norm.inv(Rand(),70,10), drag down 100x. Column C Type =If(A>B,1,0), Drag that down and sum up the total and that is the winning percentage. Do that 10x, which is easy because anytime you move the mouse, the data would change .

I did this and got 81, 79, 75, 78 and 70 for an average of 76.6, so off of that I would price it on a head to head match as -314 and +314 vig free.

If you wanted to do it as a pool, simply make more columns and make a formula where is gives you the winner of each series, calculate the total per set, run it a couple of times and price it that.

I might be completely off, but that seems like it should be on the right track.

[cyberbabble]

Very good, I learned a new spreadsheet trick.

I read the original problem to be that you get odds on each player to beat the other four players in the group in a given week, not a head to head matchup. Like betting on the winner in a horse race.

Use your spreadsheet, create a column for each player. Each row would be a game. Each row(game) would have a winner out of the five players. Count the number of rows won by player A, number of rows won by B, etc. This would give a win % for A, win % for B, etc.
You could decide which player to bet on using the calculated win % and quoted odds to win for each player.

If betting on head-to-head matchup, your way looks good to me.