OK Sharps, need some legitimate help for a bowling bet.

[indio]

All things being equal (lane conditions, good health, etc..) for our contest, we have Joe and Fred who bowl in the same league. They have averages which have been created by the last 2 years of games, which is around 250 games for each. Let's say for arguments sake that their averages are spot on.

Joe has an average of 190, Fred has an average of 210.

What's an accurate vig-free ML for a standard one game/10 frame contest between the two?

[Fall778899]

Fred -300

[indio]

Fred -300

Do you have a math based formula to predict that Fred will win 75% of the time, or is this a "gut feel" line?

[buby74]

Get their standard deviations, square them, add them together, take the square root and that gives you the standard deviation of the difference in scores. Divide this by the difference in the averages and this gives you a z score of the difference which allows you to work out the probability. This approach assumes the scores are normally distributed which is a reasonable starting assumption.

[indio]

Get their standard deviations, square them, add them together, take the square root and that gives you the standard deviation of the difference in scores. Divide this by the difference in the averages and this gives you a z score of the difference which allows you to work out the probability. This approach assumes the scores are normally distributed which is a reasonable starting assumption.

Appreciate the input, although some of it is foreign to me. But for this problem, assuming all we have are the averages, and not the actual scores that made up the averages, is there any way to create an approximate chance of Fred beating Joe with strictly the averages? We can assume that both bowlers may have rolled the maximum 300 at some point, although obviously Fred is much more likely to have achieved this feat. And both bowlers I'm sure have the occasional clunker of a 155 in their history, but I guess I'm trying to get an approximate probability with limited information. Having some experience in the bowling world helps someone to come up with a decent approximation. Fall778899 gave us Fred -300, I was thinking Fred -240 myself, so I'm just curious what the consensus is by bowlers, gamblers, and also math guys who might have a formulatic approach like yours with just the limited information we have listed here.

[Kolotoure]

Don't we need the distribution of their scores and not just their averages?

[Miz]

You'd have to know more I'm afraid. You'd need to do something like the bill james approach in baseball, but you'd likely need to fit your own exponent using data from bowling.

[Waterstpub87]

Without knowing deviation, could perhaps you use Pythagorean?

210^2/210^2+190^2~55%

-122/+122

[Fall778899]

Gut feeling... I'm glad I'm on the high side