odds of 7-10 split in bowling

[Tim923]

I'm interested to know the approximate odds of converting a 7-10 split
for a spare in bowling. I've seen different odds: 1/1000, 1/5000,
1/700000.

It has occurred 3 times on television in PBA games. That's all I
know. Has anyone gone thru the math before in this group.

[[e-mail]]

Post by Tim923
I'm interested to know the approximate odds of converting a 7-10 split
for a spare in bowling. I've seen different odds: 1/1000, 1/5000,
1/700000.
It has occurred 3 times on television in PBA games. That's all I
know.

Too bad. You also need to know out of how many attempts.

Post by Tim923
Has anyone gone thru the math before in this group.

The math is easy. If you hit the pin in exactly the right spot,
the odds of making it are 100%.

[Proginoskes]

Post by ***@aol.compost

Post by Tim923
I'm interested to know the approximate odds of converting a 7-10 split
for a spare in bowling. I've seen different odds: 1/1000, 1/5000,
1/700000.
It has occurred 3 times on television in PBA games. That's all I
know.

Too bad. You also need to know out of how many attempts.

Post by Tim923
Has anyone gone thru the math before in this group.

The math is easy. If you hit the pin in exactly the right spot,
the odds of making it are 100%.

I bet you were influenced by my contribution to Atom Totality called
"Golf Theory" which tells how to get a hole in one every time:

THE TOTAL ATOM THEORY GUIDE TO WINNING GOLF

Total Atom Theory allows you to attain a perfect score in golf (18 on
an 18-hole course)! Here's how.

(1) Find a golf club which will launch the ball at a 45 degree angle.

(2) When you get to the first tee, measure the distance to the hole and
call it D.

(3) Hit the ball so that its initial velocity is sqrt(D*k), where k is
"the magic number". (Send me $10,000 for it.)

(4) The ball will land in the hole without even bouncing.

(5) Pick up the ball and go to the next hole.

Clearly golfers have ignored this procedure, which will guarantee a
perfect score. Tiger Woods and other players clearly have wasted their
time on their "technique".

Archimedes Plutnoium
http://www.amishrakefight.org/gfy/
There is a Plutonium atom in my brain, which makes me a genius!
Send me your paycheck, Tiger Woods!

[Bob Kolker]

Post by Proginoskes
(4) The ball will land in the hole without even bouncing.

Wrong. The pin is in the hole.

And for the long holes one would have to do "Kentucky Windage", i.e.
figure the effect of wind.

Bob Kolker

[Bob Kolker]

Post by Proginoskes
THE TOTAL ATOM THEORY GUIDE TO WINNING GOLF
Total Atom Theory allows you to attain a perfect score in golf (18 on
an 18-hole course)! Here's how.
(1) Find a golf club which will launch the ball at a 45 degree angle.
(2) When you get to the first tee, measure the distance to the hole and
call it D.
(3) Hit the ball so that its initial velocity is sqrt(D*k), where k is
"the magic number". (Send me $10,000 for it.)
(4) The ball will land in the hole without even bouncing.

What about the Coriolis Effect? One has to figure in the direction of
the hole.

Bob Kolker

[David T. Ashley]

Post by Tim923
I'm interested to know the approximate odds of converting a 7-10 split
for a spare in bowling. I've seen different odds: 1/1000, 1/5000,
1/700000.
It has occurred 3 times on television in PBA games. That's all I
know. Has anyone gone thru the math before in this group.

Unlike Blackjack or [fair] dice, bowling involves skill combined with
probability rather than probability alone. Asking the probability of making
this split isn't the same type of question as asking for Blackjack what the
probability of busting by taking a hit on 16 with a fresh set of decks is.
It is player-dependent.

The other poster correctly identified that math:

(# of successes) / (# of attempts)

You could probably get more accuracy by knowing more about the person
throwing the ball and the specific circumstances: age, sex, success at this
type of split, whether making the split is important (which might affect the
level of risk the bowler is willing to carry), etc.

You state that this has occurred 3 times on television in PBA games. Could
this be because the bowler doesn't always try to make the split, or tries
half-heartedly to make it? My understanding is that if you _really_ try to
make this split, you risk striking neither pin. Could it be that the
bowlers aren't _really_ trying?--they are throwing balls guaranteed to hit
one pin or the other, and they're striking the pin off-center and they
_might_ get the other pin but they've positioned the probability
distribution to avoid a gutter ball?

Of course, I don't know how skilled these folks are. My high game bowling
is about 120 ... and in a 7-10 split I'd just aim for one pin or the other
... I'm not sure how much control the pros have.

[Tim923]

Here's a video of one.

I've read you just hit the pin hard and hope for some lucky bounces.
Maybe similar to making a full-court shot in basketball. If anyone
has estimated the odds I'd be interested to see the math, not
necessarily for PBA televised games.

[David T. Ashley]

Post by Tim923
Here's a video of one.
http://youtu.be/XtDDG5MrxAs
I've read you just hit the pin hard and hope for some lucky bounces.
Maybe similar to making a full-court shot in basketball. If anyone
has estimated the odds I'd be interested to see the math, not
necessarily for PBA televised games.

Thanks for the video. The video destroyed my mental model.

It looks to me like there isn't enough room on the outside of the pin to hit
the pin at an angle to propel it into the other pin (not enough room between
the pin and the gutter).

So, the strategies for reliably hitting one pin and actually trying for the
split ... are not mutually exclusive. A professional bowler would always
get one pin or the other, even when trying "hard" for the split.

Shows how much I bowl.

[Nick]

Post by David T. Ashley

Post by Tim923
I'm interested to know the approximate odds of converting a 7-10 split
for a spare in bowling. I've seen different odds: 1/1000, 1/5000,
1/700000.
It has occurred 3 times on television in PBA games. That's all I
know. Has anyone gone thru the math before in this group.

Unlike Blackjack or [fair] dice, bowling involves skill combined with
probability rather than probability alone. Asking the probability of
making this split isn't the same type of question as asking for Blackjack
what the probability of busting by taking a hit on 16 with a fresh set of
decks is. It is player-dependent.

Presumably this is like racing form, then or betting on the outcome of
soccer matches.

When I was at university some friends of mine who were doing Maths with
Electronics did as their final year project predicting the outcome of soccer
matches. No doubt they put the previous week's results in as new data to
predict the next week's results.

Nick

[Tim923]

To make this question more specific, how about for an average
professional bowler or average league bowler. I'm aware we can't get
an exact odds without specific stats, but we just have to estimate a
number of stats for the rough odds.

I suppose a start would be to come up with the average number of 7-10
split opportunities that occur in a game for one person. I'm not a
bowling expert so I have no idea.

[Big Crunch]

Mark Miller of USBC gave me an estimate of one 7-10 split converted
for every 150,000 games in the 2005/2006 season according.

1:150,000

1:300,000 (for 2 7/10 split opps per game both players)

[Michael Press]

In article

Post by Tim923
I'm interested to know the approximate odds of converting a 7-10 split
for a spare in bowling. I've seen different odds: 1/1000, 1/5000,
1/700000.
It has occurred 3 times on television in PBA games. That's all I
know. Has anyone gone thru the math before in this group.

Professional bowlers convert this split all the time.
The probability it has happened on television fewer
than four times in PBA games is less than 1/10000.

[Brian]

Post by Michael Press
In article

Post by Tim923
I'm interested to know the approximate odds of converting a 7-10 split
for a spare in bowling. I've seen different odds: 1/1000, 1/5000,
1/700000.
It has occurred 3 times on television in PBA games. That's all I
know. Has anyone gone thru the math before in this group.

Professional bowlers convert this split all the time.
The probability it has happened on television fewer
than four times in PBA games is less than 1/10000.
--
Michael Press

How about the 5-7-10 split, also known as the Lilly or Sour Apple?
Easier to convert, but I'll bet you'll NEVER see one in a PBA game.

http://www.utahbowling.com/Masters/week22.htm

[Big Crunch]

For televised PBA games since 1961:

7-10 conversions: 3
number of televised PBA games: 4000-8000 (guess)
7-10 occurences per game both players: 1 (guess)

So my order of magnitude guess is between
1:1000 and 1:10000 but closer to 1:1000.

[Richard Henry]

Post by Big Crunch
7-10 conversions: 3
number of televised PBA games: 4000-8000 (guess)
7-10 occurences per game both players: 1 (guess)

Bad guess.

Post by Big Crunch
So my order of magnitude guess is between
1:1000 and 1:10000 but closer to 1:1000.

[Big Crunch]

Post by Big Crunch
7-10 conversions: 3
number of televised PBA games: 4000-8000 (guess)
7-10 occurences per game both players: 1 (guess)
So my order of magnitude guess is between
1:1000 and 1:10000 but closer to 1:1000.

Heard back from PBA.com. They gave me an estimate of 5300 televised
games since 1961, about 120 matches per season.

So the last piece is how often a PBA bowler throws a 7-10 opportunity.
It is more common for amateur players that throw the ball straight,
but less common for pros who throw hooks. My guess of 1 per game may
be too high.