Probability in bowling question

[Daliman]

I'm about a 195 average bowler and often after league is over i bowl pot games(everyone throws in $5, High game takes all)with some of the other guys in the league, most of whom are within 10 pins of my average in one direction or the other, so I don't sweat the difference either way.
2 weeks ago, however, I didn't get in the pots when a pro who averages 230 got in the pot games, saying that he's win 2 out of 3, to which I heard a chorus of pshaws and "don't be such a wuss"'s. I said i don't mind bowling someone who's better than me if it's within 10 pins or so, but that i'm not going to throw my money away essentially bowling headsup against a guy who's thrown 33 perfect games and 30 consecutive strikes. 3 games later, said pro had shot 225, 226 and 277, and won 2 out of 3 pot games,(came in 2nd the first game).... Said pro decided only to bowl doubles the fourth game, so i rejoined singles(of course, i beat him that game, 225-208, and won the high game pot too,lol), and he completely agreed with my position that he had too much of an overlay on the field. I was thinking that he should put in more money, say 3 to 1($15) to even out the disparity in skill somewhat.

My question is twofold:
1. Is there a way to properly "handicap" him vs. multiple opponents without taking pins off his score(or adding to ours?). Good bowlers are always loath to give pins outside of league, and always want to take them away if they give them and lose.

2. How about against a single opponent? Can some type of poisson-style accurate odds be set up? Kind of like if a team is a 4 point favorite in football, the dog gets 1.6 to 1 on bets. It seems to me someone who averages 20 pins higher than someone else would much rather give 2-1 odds than the 20 pins.

I'm going to see if the poisson spreadsheet on sharpsportsbetting.com seems to shed any light, but any expert input would be greatly appreciated.

[Bozeman]

Do you have your history? I'd sure like to see your variance.

As a crappy bowler, I was wondering what bowling score distributions look like. I would imagine that poissonian distributions don't match scores well, but that normal distribution is close. Unfortunately, then you need to know standard deviations, which may vary by bowler. For example, a bowler who is better at strikes than picking up spares should have a slightly higher sd than a great spare bowler. In addition, the non-linear scoring of bowling might skew the distribution, or at least make sd an unusual function of average.

Not any help I realize,
Craig

[RocketManJames]

As Bozeman said, maybe a Normal distribution is a better random variable for your bowling scores. Again, as Bozeman said, you will need to have the SD's of the bowlers involved.

I'm no expert on this stuff, I can barely remember a probability class I took long, long ago. I believe what you're looking for is a new probability function resulting from the sum of two random variables, namely Normal RV #1 for Bowler A and #2 for Bowler B. Normal RVs being defined by mean and variance.

Now, when you get the new RV as a result of (RV #1 - RV #2) you have some probability distribution with which you can produce fair odds, I think. Ultimately, you're looking for the area under the curve that is greater than 0 and area under the curve that is less than 0. With this, you have a fair way (I think) to set up the proper odds for your bet w/o having to add/subtract pins.

Now, I said I haven't thought about this in years, but from what I remember, you can come up with a new random variable resulting from the difference of two RV's using something called a convolution. It's some funky star symbol and is defined by some whacked integral that I really want to have no part of. Perhaps the more mathematically educated could elaborate. Or, perhaps they'd like to tell me that my proposed method is wrong altogether. Either way, I'm all ears.

-RMJ

[Bozeman]

The convolution of two normal distributions in another normal distribution. In this case, it will have mean of mean1-mean2, and sd of sqrt(sd1^2+sd2^2). Thus for bowlers with aves of 220 and 195 and sd's of 40 and 30 pins, mean=25, sd=50, so bowler 2 should win about 31% of the time.

Craig

[Daliman]

I'd guess that SD for most bowlers would be about 15% of their average. For me, that would be about 29 pins. That would mean,(If i'm getting this right), that about 68% of my games are between 166 and 224 and that 95% are between 137 and 253 and 99.7% are between 108 and 282, which wouldn't really be right(it's been YEARS since i've shot below 118, about 1500 games in between. I'd say that 68% of my games are 175-215, 90% 155-235, 99.7% 135-255, so 10% seems about right, however, that must be too low an SD for lower average bowlers. A 150 bowler would bowl over 195 more than 3 games out of every 1000, so that's somewhat skewed,(mainly by the fact that he would get better), but, using the figures I just gave for myself, which I believe to be very accurate(I don't have exact scores, however), can something be figured?

P.S. This was also posted on Sharpssportsbetting.com

[Ray Zee]

the only way is to give pins. that way you can handicap fairly.

if you must do it with odds on the money, then you have to know each persons chances of beating what his average score would be. and how could you know that unless you had full records on those type of conditions.
he is so much better its foolish to play against him. ask him to spot pins or sit out. the others will get the messge soon after they have no money left.

[Dynasty]

Spotting pins sounds good to me. When my mother and I go bowling, I usually spot her about 100 pins and we have a competetive game.

[Clarkmeister]

Your Mom only shoots a 14?

[chaos]

Not that I'm much of a bowler but I don't think the distribution is evenly centered around the mean. I think for a decent bowler it is more likely that they will have a game much higher than their average than much lower than their average.

Just my gut feeling based on the way the game is scored.

[KUBowler99]

I have to agree with Ray on this one. There is a huge difference between a guy who averages 190 and one who averages 230 (not just 40 pins a game). If I were you, I'd try to convince him to give you 75-80% of the difference in 'handicap'. That will even things out a bit.

Is the guy an actual pro, or is he a guy that can bowl really well on one type of shot? If he's the latter, you may try to get him to bowl in a different center in addition to giving you pins.

Just a thought