No, I did not expect to ever write a column that combined the sport of bowling with the field of mathematics. Just thought I would answer that question right off the bat.
When something very unusual happened at the bowling alley last week, I was sent scurrying to find out just how rare the feat was. I found a whole lot more information than I expected to. Much of it was math-related, and though I doubt any of this will make you a better bowler, it should make you think. And not just about how goofy I am.
The unusual occurrence involved a bowler throwing the first two strikes in the 10th frame then getting just two pins on his final ball. I was quick to realize that had the fellow thrown the first nine strikes of the game, he would have rolled a 292, which just happens to be the rarest score in the game of bowling.
A 292 can only be accomplished by starting a game with 11 strikes and then getting a two count on the last ball. What are the odds of doing this? Well, let me tell you. You have just as good a chance at hitting the lottery.
Believe it or not, the score has been recorded some 20 times. Each time it was done by a professional bowler who - get this - was so unimpressed with "another" perfect game, he intentionally tried to get two pins on the last ball.
Oh, to be so bored.
Now, personally I don't know which would be more difficult. Throwing the front 11 or getting the two count. Odds are I won't ever do either. I have yet to throw the first 11 (10 is my best), and I don't ever remember getting two pins on a full rack. Then again, I have never tried to get just two.
In 2005 Kent Wagner bowled a 292 game in Florida. He intentionally tried to get two pins on the last ball so he could lay claim to being the only bowler to shoot scores of 291, 292, 293, 294, 295, 296, 297, 298 and 299. Did he ever shoot a perfect 300? Well, of course he did. That's why he was "bored" and started trying to get that elusive 292.
All right, here's where the mathematics kicks in. There is only one way to shoot the games of 291-299. It involves throwing the front 11 and getting 1 to 9 pins on the last ball. Similarly you can only get a perfect 300 by throwing 12 straight strikes. At the other end of the spectrum there is only one way to get a score of zero. You must throw 20 consecutive gutter balls.
Now let's look at a 290 game. How many ways can a bowler achieve that score? Did you guess 11? If you did, you are correct. A spare followed by 11 strikes will give you a 290 score. That spare could be accomplished in 10 different ways depending on how many pins you got on the first ball. Eleven strikes plus a last-ball channel cat also gives you 290. Though that would be a disappointing finish for those of us seeking that first perfect game, the "bored" guy probably has already shot this 290 while striving for that hard-to-get 2 count.
The math becomes even more interesting if you go to the other end of the scoring possibilities. Remember a score of 0 can only be accomplished one way. How about a score of 1 - how many ways can this be done? Try 20. One pin on any of the 20 balls you throw with gutters on the other 19. Cool, don't you think?
Well, check out these mathematical probabilities. You have 210 ways to get a score of two and 42,504 ways to get a 5. Jump to a game score of 10, and the math says 20,030,010 ways can be used to accomplish this feat. Now, allow me to ask if you are thinking someone must not have much of a life to spend time figuring out these scenarios. You were, weren't you? OK, I was too, but let me give you one more math brain buster.
Do you know which bowling score - from zero to 300 - can be accomplished the most different ways? I'll give you a minute. Need another minute? Come on, you might as well give up because I'll guarantee you cannot come up with the correct answer. So here it is:
The score is 77. Didn't guess that did you? Want to take a crack at how many different ways this can be done? I will be impressed if you can even pronounce the number I am about to reveal. The number is 172,542,309,343,731, 946! However many illions that may be.
Whew, all this math is making me dizzy (yeah I know, I didn't need that much help). I'm just glad I was not the mathematician that had to figure all this out. I think golf is easier. For example, what are the odds of getting a hole in one? It's simple. They have to be 50-50.
You hit the ball and it goes in the cup, or it doesn't.
Let's begin at the K of C Lanes, where Chris Johnson used one of those 11 ways to fashion a 290 game in the Tuesday Night League. Combine that with a 217 and 239 and you have a whopping 746 series. Steve Steinmetz Jr. added a 693, Jim Rainey 607, Jim Lord 586, Bill Lord 566, Steve Depinet 546 and Andy Hess 537. In the 55 Plus League Jim Ruess shot 621, Dick Gabel 542, John Ferstler 531, Bob Reinhart 513, Jim Ferstler 503, Jim Donaldson 469 and Steve Schafer 448. Carol Burmeister had 492, Linda Caseman 467, Deb Hoerig 435 and Marilyn Gangluff 427 in the Lady Knights League.
Robin Dickman had the maples flying with a 677 series in the Alley Cats League. Angie Puesey backed that with a 545, Carol Fry had 539, Kim Weaver 523, Carla Seibenaller 513 and Cindy Sendelbach 511. Sunday Night Rock N Roll League scores included Bob Steele 740, Steve Barnes 651, Brett Babcock 634 and Tony Riedlinger 611. For the ladies Beth Jones shot 576, Janice Young 512 and Rose Steele 499. Joyce Babcock topped the women in the Grange League with 518, while Hunda Shook had 454 and Nicole Babcock 449. For the men Jere Morlock shot 554, Gary Smith 489 and David Sauber Jr. 478.
Dave Jumper led the way in the Wednesday Morning League with 714. Kyle Peck shot 705, Tim Sturgill 667, Zach Gaietto 649, Aaron Sherman 644, Mark Huffman 629, Harry Smith 624, Ken Lofton 600 and Cindy Conger 476. In the Sportsman League, Rich Yates Jr. had 718, John Tyree 691, Ron Yentzer 663, Ken Butturff Jr. 635, Mike Kimmet 634, Chris Johnson 625 and Rich Yates Sr. 622. Steve Steinmetz Jr. rolled a 718, Brian Jakupca 568, Steve Steinmetz Sr. 552, Rhonda Fitch 502, Deb Nominee 476 and Anne Laughlin 461 in the Imperial-Majorette League.
Kathy Breyman shot 511, Tessa Shope 488, Kathy Young 485, Deb Cleveland 468, Brenda Rosier 459 and Pam Smith 458 in the Ladies Classic League. In Rocket League action Eric Vanover had 644, Tom Tiell 591, Tim Sturgill 586, Dave Coppus 577, Neil Mizen 572 and Virginia Vanover 485. Ben Williams shot 657, Zach Zoeller 619, Kevin Fitch 616, Tom Tiell 601, Robin Brownell 461 and Rhonda Fitch 442 in the Twilight League.
Al Stephenson is The A-T bowling columnist.
Read his blog at:
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