Stats Question for Bob or Dr. Dave

[Dan White]

My stats was too long ago and I'm to lazy to look it up, so I'm hoping I can get spoon fed by Bob or Dave or someone else with a math background. (How's that for a motivating introduction?)

Anyway, I know this has been discussed before: Let's say I play every day and my daily high run is 50 balls, so it's safe to say I'm a 50 ball runner. How many days does a 50 ball runner have to play before he can be, say, 95% sure that he will run 100 balls? I may not be phrasing the question exactly the way a statistician might want, but you get the idea. What if I run 40 or 30 a day (vs running 100)?

I'm ignoring other factors such as nerves in reaching 100, or fatigue and so on.

Just curious,

 

[Bob Jewett]

My stats was too long ago and I'm to lazy to look it up, so I'm hoping I can get spoon fed by Bob or Dave or someone else with a math background. (How's that for a motivating introduction?)

Anyway, I know this has been discussed before: Let's say I play every day and my daily high run is 50 balls, so it's safe to say I'm a 50 ball runner. How many days does a 50 ball runner have to play before he can be, say, 95% sure that he will run 100 balls? I may not be phrasing the question exactly the way a statistician might want, but you get the idea. What if I run 40 or 30 a day (vs running 100)?

I'm ignoring other factors such as nerves in reaching 100, or fatigue and so on.

Just curious,

It depends on how many innings you take to run your 50. Suppose you take on average 30 shooting innings to run 50. That would mean that you are 1/30 to run 50 from any particular position. To have two 50s back-to-back would be the square of that probability, or 1/900. That would be one time in 30 days, more or less.

That's a very rough treatment. A better treatment would state exactly what was being assumed and go through more detailed analysis and such, maybe tailored to your particular situation. The usual assumption which makes the calculations a lot easier is that each shot is equally likely to be missed, as you hinted above. Some people have more trouble with break shots. For most calculations, it is "close enough" to take a single-shot probability somewhere between the break shot and the usual in-rack shots.

A discussion of 14.1 statistics is here: http://www.sfbilliards.com/articles/2006-06.pdf

 

[Dan White]

Thanks, Bob. That makes perfect sense. Kind of interesting, and gives people a ballpark of what to expect, I think.

 

[alphadog]

It depends on how many innings you take to run your 50. Suppose you take on average 30 shooting innings to run 50. That would mean that you are 1/30 to run 50 from any particular position. To have two 50s back-to-back would be the square of that probability, or 1/900. That would be one time in 30 days, more or less.

That's a very rough treatment. A better treatment would state exactly what was being assumed and go through more detailed analysis and such, maybe tailored to your particular situation. The usual assumption which makes the calculations a lot easier is that each shot is equally likely to be missed, as you hinted above. Some people have more trouble with break shots. For most calculations, it is "close enough" to take a single-shot probability somewhere between the break shot and the usual in-rack shots.

A discussion of 14.1 statistics is here: http://www.sfbilliards.com/articles/2006-06.pdf

STATITISTICS.DAMN STATISTICS! Now I think I can run a 100:angry:

 

[Bob Jewett]

STATITISTICS.DAMN STATISTICS! Now I think I can run a 100:angry:

Well, sure you can. The question is how long it will take. If you're 1 in 10 to clear a rack and you want to run 7 racks (more or less) it will just take (roughly) 10 to the 7th power innings. Start early each evening.

On the other hand, if with all that practice you work you way up to a 33% rack-clearance percentage, you will only need about 2000 tries.

 

[bdorman]

My stats was too long ago and I'm to lazy to look it up, so I'm hoping I can get spoon fed by Bob or Dave or someone else with a math background. (How's that for a motivating introduction?)

Anyway, I know this has been discussed before: Let's say I play every day and my daily high run is 50 balls, so it's safe to say I'm a 50 ball runner. How many days does a 50 ball runner have to play before he can be, say, 95% sure that he will run 100 balls? I may not be phrasing the question exactly the way a statistician might want, but you get the idea. What if I run 40 or 30 a day (vs running 100)?

I'm ignoring other factors such as nerves in reaching 100, or fatigue and so on.

Just curious,

If you're consistently running a max of 50 balls there is no calculation that will give you "days until you reach 100" regardless of the confidence factor. There has to be either: 1) a data point (day/inning) in which you ran 100 balls, or 2) a progression like "day 1 - 20 balls, day 2 - 40 balls, day 3 - 60 balls" and so on.

Keep records of the next 100 innings you play. It will tell you a lot about your probabilities.

 

[Bob Jewett]

If you're consistently running a max of 50 balls there is no calculation that will give you "days until you reach 100" regardless of the confidence factor. ...

It's true that simply saying "I often run 50" doesn't get you very far. I think saying "I run 50 or more about once every 300 points" is sufficient info given the assumptions Dan seems willing to tolerate.

 

[Dan White]

Bob - I read your pdf article in the link you provided. Interesting, thanks. You mentioned Mosconi and estimated a 25% chance of running 100 during a match. What do you think of his exhibition performance and how that jives with the pocketing percentages you estimate? For instance, I know my father saw numerous Mosconi exhibitions in which he ran 100 balls on the first try. He also saw Caras in an exhibition. The announcer says, "Mr. Caras will now run 100 balls," which of course he proceeded to do. Does this seeming ability to run 100 on command make sense given the shot percentages you estimate?

 

[Bob Jewett]

Bob - I read your pdf article in the link you provided. Interesting, thanks. You mentioned Mosconi and estimated a 25% chance of running 100 during a match. What do you think of his exhibition performance and how that jives with the pocketing percentages you estimate? For instance, I know my father saw numerous Mosconi exhibitions in which he ran 100 balls on the first try. He also saw Caras in an exhibition. The announcer says, "Mr. Caras will now run 100 balls," which of course he proceeded to do. Does this seeming ability to run 100 on command make sense given the shot percentages you estimate?

Well, if you assume either was 90% to run a hundred, then one would have been odds-on for a career high of 1000 or 1200. Or maybe even 2000.

 

[TSW]

Well, if you assume either was 90% to run a hundred, then one would have been odds-on for a career high of 1000 or 1200. Or maybe even 2000.

Assuming they didn't stop unfinished.

When Mosconi ran 526, IIRC he ran out whatever the exhibition number was and the crowd encouraged him to keep going. In these exhibitions, does anyone know how often those players would keep going until they missed?

 

[alphadog]

Assuming they didn't stop unfinished.

When Mosconi ran 526, IIRC he ran out whatever the exhibition number was and the crowd encouraged him to keep going. In these exhibitions, does anyone know how often those players would keep going until they missed?

Fast Eddie as Vincent's mngr in TCOM would ask, "Well, does anybody know?",

 

[Marop]

Here's some stats that everyone can try to draw a conclusion from.

In the Last 5 years I have 324 runs on video where I have run over 50. Here is the breakdown.

50 - 59 --- 176 times
60 - 69 --- 72
70 - 79 --- 39
80 - 89 --- 21
90 - 99 --- 11
100-120 --- 5

-Bill

 

[alphadog]

Here's some stats that everyone can try to draw a conclusion from.

Last 5 years, 324 runs on video above 50:

50 - 59 --- 176 times
60 - 69 --- 72
70 - 79 --- 39
80 - 89 --- 21
90 - 99 --- 11
100-120 --- 5

-Bill

Ok I looked at the last years worth of posts to az 14.1 and there are more videos over a 100 then you say in 5 yrs of video.
Is this like a double rainbow? What does it mean:wink:

 

[Marop]

Ok I looked at the last years worth of posts to az 14.1 and there are more videos over a 100 then you say in 5 yrs of video.
Is this like a double rainbow? What does it mean:wink:

Those are just my pesonal stats in the last 5 years, not all runs on AZ. My point is how much more difficult it is to run a 100 vs running 50.

 

[dmgwalsh]

Here's some stats that everyone can try to draw a conclusion from.

In the Last 5 years I have 324 runs on video where I have run over 50. Here is the breakdown.

50 - 59 --- 176 times
60 - 69 --- 72
70 - 79 --- 39
80 - 89 --- 21
90 - 99 --- 11
100-120 --- 5

-Bill

Jesus, Eddy! Those are some monster numbers.

And your most recent addition yesterday: https://vimeo.com/77934625

 

[alphadog]

Those are just my pesonal stats in the last 5 years, not all runs on AZ. My point is how much more difficult it is to run a 100 vs running 50.

SOLID! Thanks for the reply.
Since I have hit 50-but not a 100 I would concur!:smile:

 

[Rich93]

Here's some stats that everyone can try to draw a conclusion from.

In the Last 5 years I have 324 runs on video where I have run over 50. Here is the breakdown.

50 - 59 --- 176 times
60 - 69 --- 72
70 - 79 --- 39
80 - 89 --- 21
90 - 99 --- 11
100-120 --- 5

-Bill

Although Bill is just one person and your mileage may vary, etc. etc., I think his carefully compiled stats is the best indicator I've ever seen about what kind of skill it takes to run a hundred. Only 5 out of 324 runs over 50 go over 100? Unbelievable, but you have to believe it because there it is. Same shooter and same table, so those variables are eliminated.

So what are my chances of running over 100 tonight? I'd say my chances of running 50 on any given night are at most 1%. So, being generous, they are .01 x 5/324 = .00015, or 15 out of 100,000. Let's be generous again and say it's 2 out of 10,000, or 1 out of 5,000. So if I play 5,000 nights I can expect to run 100 once. I play twice a week, so say 100 times per year. 5,000 nights will take me 50 years. I'm 65. Thanks a lot Bill!!

I guess I'll just have to improve!

 

[Marop]

Although Bill is just one person and your mileage may vary, etc. etc., I think his carefully compiled stats is the best indicator I've ever seen about what kind of skill it takes to run a hundred. Only 5 out of 324 runs over 50 go over 100? Unbelievable, but you have to believe it because there it is. Same shooter and same table, so those variables are eliminated.

So what are my chances of running over 100 tonight? I'd say my chances of running 50 on any given night are at most 1%. So, being generous, they are .01 x 5/324 = .00015, or 15 out of 100,000. Let's be generous again and say it's 2 out of 10,000, or 1 out of 5,000. So if I play 5,000 nights I can expect to run 100 once. I play twice a week, so say 100 times per year. 5,000 nights will take me 50 years. I'm 65. Thanks a lot Bill!!

I guess I'll just have to improve!

Just trying to be helpful Rich, lol...

See you at Derby.

-Bill