 | 7-10 split |
What are the odds of an amateur bowler hitting a 7-10 split?
While reading about the Pepsi promotion last week, I became interested in SCA Promotions, one of the companies behind the billion dollar promotion. SCA offers a whole range of "promotions" which are basically legal bets with big-dollar prizes attached to them that companies can sign up for.
I was really curious about their odds on some of these things, so I requested a quote for their 7-10 split promotion. For a 50-person company bowling event, where none of the players play in a bowling league, and where everyone gets one shot to hit a 7-10 split, and a max of 1 winner, they quoted me $6,250 for a $25,000 grand prize.
This puts the straight odds for a single bowler hitting the 7-10 at 374:1.
In some threads on alt.sport.bowling about the 7-10 split, opinions differ greatly about what the real odds are of hitting a 7-10. The numbers that players came up with ranged from 1 in 2 to 1 in 200 for pro or semi-pro bowlers.
On the PBA website, they state the 7-10 split has only been converted on TV three times. Apparently it's been shown on TV somewhere around 400 times, which puts the odds (for a professional) at around 130 to 1. Based on that, I'd say the real odds for a Joe Schmoe are longer than 374:1. I would think a pro could hit a 7-10 at least 5-20 times more often than your average amateur, which puts the odds at 750:1 to 2600:1.
SCA Promotions is in a great business. They're a legal bookie, and their vig is enormous.
Update: Thanks to Howard for pointing out below that my math was flawed on the single-bowler odds. Not sure what I did, but 374:1 is way off. A 1 in 4 shot for 1 or more bowlers in 50 hitting a 7-10 split implies odds of 173.3:1 for a single bowler hitting the 7-10.
The math here is fairly simple. The 1 in 4 shot means that they expect that over 75% of the time, 0 bowlers will make the split. That's how they make their money. So 0.75 ^ (1/50) results in a probability of 99.426% that a single bowler will miss the 7-10 split, or a 0.574% chance (173.3:1) that they will hit the 7-10 split.
The odds are better than the 1 in 200 that Howard mentions below because SCA does not have to pay more than one prize if more than 1 in 50 people hit the split.
Interestingly, the "real" odds of the promotion, assuming the real odds of an amateur hitting the 7-10 split are 1 in 1000, are 19.49:1, meaning it should cost $1,219 for a $25,000 prize. That yields SCA a profit of $5,030 per bowling promotion!
Thanks for the article, although the maths is somewhat flawed.
Ignoring any profit SCA might make, the prices quoted assume that for a 50 person bowling party the prize will be won 1 in 4 times. 50 bowlers * 4 = 1 in 200, which seems too high. I agree with about 1 in 1000.
Very interesting article, especially from the perspective of a risk assessor at SCA Promotions.
I wish in our case history of 7-10 split contests, the contestants converted at a rate of 1 time in 1000.
Unfortunately for us, the contestants win more often than that.
An amateur will hit a single pin less frequently than a pro, but once the pin is hit, the relatively random process of the pin richocheting of the back wall and into the other pin is less skill dependant.
For what it is worth, our 300 game rates for amateurs vs pros are exponentially different.
I would gladly take on 1,000 rank amateurs on a 300 game vs a single pro. The same does not hold true for a 7-10 split.
What are the odds of a bowler with a 200 or better avg. bowling a 300 compared with a 150 avg.? Thanks David
Posted by: David on January 7, 2005 05:08 PMIs there anyone who can help me compute the answer to the following questions?
What is the probability of a PBA bowler bowling a 300? What is the probability of an amateur bowler bowling a 300 on regular lanes? What is the probability of a person sitting at home bowling a 300 in the Yahoo featured game '10-pin bowling'? What is the probability of it happening to each of them ( individually) more than once? What is the probability of it happening to each of them (individually) more than once within a month?
What is the the significance and probability of me bowling 7 '300' games in Yahoo '10 pin bowling' over a period of 3210 games within the time frame of ~ a few times before 7/15/2005 to 8/19/2005?
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