Baseball Probability game

[MrDaveyHavoc]

Hello all,

A little backround. I work part time in a restaurant which for better or for worse is not always very busy. I often kill time by watching baseball on gamecast or mlb.tv. Recently, I hired this kid who wants to gamble on everything, but has no real idea about the math of it. I devised a fun way to pass the time would be to wager on the outcome of an at bat for the game we are watching.

The game goes something like this. We each pick a team (for instance, tonights Yankee-Oriole matchup) I get all the Yankees and he gets all the Orioles. When they are at bat, we wager on the outcome. Hit or Walk vs. out. HBP, sacrifice, etc = push.

My question is this- Lately I have been wondering how to adapt the game so that it is even regardless of the side taken. What sort of odds would you have to give the batter? I am just looking for someone to help me spell it out mathematically. I know it is batter dependent, so a formula would help, and to quicken the process i guess we could plug in league average batters (or I can use league average and pick and choose which side based on who is up and over/under the line to take advantage of my dim friend, but that's neither here nor there [img]/images/graemlins/smile.gif[/img]

Anyway thanks for all the feedback, I appreciate the time.

PS I rarely make first posts so if this is in some way violating a forum policy please move/delete as necessary.

[DeliciousBass]

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I get all the Yankees and he gets all the Orioles. When they are at bat, we wager on the outcome. Hit or Walk vs. out. HBP, sacrifice, etc = push.

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Based on this...I have no idea what you guys are doing.

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Lately I have been wondering how to adapt the game so that it is even regardless of the side taken. What sort of odds would you have to give the batter?

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Based on this...the simple way to do it would be to give odds based on the batter's OBP.

Barry Bonds for example has an OBP of .496, for the sake of the argument, he's a coin flip. He's going to reach base 50% of the time and make an out the other 50%. As a bettor I would want +100 on "Bonds makes an out" and -100 on "Bonds reaches base". (would actually just say "Even")

Bonds' teammate Barry Zito has an OBP of .133 (we'll say .100). When he gets to the plate I should be looking at +900 on "Barry Zito reaches base" and -900 on "Barry Zito makes an out".

So your formula should be something along the lines of (someone step in if this is way off):

((1/OBP)-1)*100 This gives you the odds for the player reaching base.

Using Bonds we get ((1/.5)-1)*100 = 100
Throw a plus sign in front of that number and you get the payout for the player reaching base...a negative and the price for a bet on an out.

In the unlikely event of a player with an OBP above .500...You run it through the first formula and then take answer = x and (100/x) * -100 for the price on the player reaching base and the opposite for the payout on an out.

Using Excel with the OBP in A1 your formulas are:
B1: =((1/A1)-1)*100
C1: =IF(B1<100,(100/B1)*-100,B1)

Of course none of this takes into account the pitcher, the other team playing, the situation the batter finds himself in, whether or not HIV has any action on the game, Charlie Manuel, the fact that you feel guilty about taking the Yankees and most of the busboy's rent money, etc.

Edit: To say, as a bettor I would want one of those bets on Bonds to be wrong in my favor. I should have said, "In a perfect world" because those bets will always be -110 and -110 in the book.

[MrDaveyHavoc]

Thank you very much for the informative reply. I appreciate it.

[AaronBrown]

Here's another way to do it, that does not require uneven odds or knowing the batting statistics.

Divide the batters into pairs. You could do even/odd (you get the first batter, he gets the second, you get the third and so on) or you could take the Yankees in order and he could take the Orioles, so you compare the first Yankee batter to the first Oriole and so on.

Rank the possible outcomes from grounded into double play, out no runners advance/fielder's choice, out runners advance, walk, single, double and so on. You can make the categories granular or not as you like.

For each pair, the person whose batter does better wins. So if you have the leadoff hitter and he walks, and the number two hitter stikes out; you win. If the number three hitter gets a single but the number four gets a home run, he wins. If both do the same, it's a push.