A-Rod total home runs bet

[Tweety]

Early in the season, I made a bet with a friend of mine on A-Rod's regular season home run total for this year. I bet my friend $1,000 that A-Rod would hit fewer than 52.5 home runs this year.

Obviously, I'm underwater on this bet right now. My friend has made me an offer to get out of the bet. I won't say what his number was right away- I'd like the mathematicians of this forum to do their best to price out what his marked to market p+l is on his position, and give me the number.

Obviously determining the fair value isn't all that easy. You can pro-rate his home run rate over the rest of the year, but do you use his home run rate this year or his career home run rate? Also, you have to look at the opposing teams he'll be facing between now and the rest of the season and the caliber of their pitching, you have to factor in injury risk, and then you have to factor in the risk of him getting benched if the Yanks clinch. Lots to think about here.

I'd like to see what people here come up with, then I'll let everyone know what his offer was and we can see if it's good. Today is Thursday and the yanks are idle. So I have until game time tomorrow to decide.

Thanks in advance for helping me out with this.

[crockpot]

do you use his home run rate this year or his career home run rate?

the true answer lies somewhere in between. i know if i'm projecting a-rod's HR rate next year, it's going to be considerably lower than his 2007 figure.

honestly, this is too complex of an analysis for one bet, unless the $1000 is really important to you (in which case you shouldn't be betting that much). if i had to, i'd estimate the probability using a binomial distribution with a HR rate 40% of the way between a-rod's projected and actual 2007 figures, and assuming he plays maybe 85-90% of the remaining games. once you crunch that, you have the fair value of your bet.

if you expect to be making similar bets in the future, feel free to expand on this, but i doubt it will come up.