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Stat question about the break off

Postby acesinc

WARNING! Long, boring, dull, drab post ahead! (Unless you are a numbers nerd.) You have been warned.
_____________________________

In my regular Friday night match with my kid, a question came up that I have a gut feeling about, but really, I have no evidence at all either way and maybe there is not even an answer to be had.

Let me start by saying that this is a "numbers" questions, probably boring to nearly everyone on the planet except us few nerds that get a kick out of this sort of thing. So I am looking for an actual answer with some sort of statistical reference, NOT looking for everybody and anybody's own personal opinion. If you feel you want to chime in with your own opinion about the answer, that is fine, but please give some sort of support information as to why that is your opinion.

On to the actual question, it is about the break off. Playing English Billiards, we string for the break off and playing Snooker, we flip a coin per custom. Now, I have always been of the opinion that if you win the coin flip, you should take the break off. When it comes to a re-spotted Black, if you win the coin flip, you should pass the first shot.

My kid is a fantastic "numbers guy". He can spout off numbers and statistics for all kinds of things, especially sports, even on occasion some sport I may have never even heard of. So to tie this all in, for us, the coin flip is completely irrelevant because when I win the flip, I take the break off. When he wins the flip, he passes the break off to me. Even so, he does insist that we conduct the pleasantries of the coin flip in homage to tradition. It used to be that he would pass the break off to me simply because he was not good at it so he didn't want to do it. But now he takes the break off as well as anyone, but he will still pass it to me when he wins the flip. So I asked why?

He said he noticed that whenever he takes the break off, then I am nearly always the first to score. So by the psychological benefit of being "first on the board", he is statistically better off to let me break off. Huh.........makes sense, I guess. That doesn't mean that he is always first to score when I break off, but statistically, he has a better chance of scoring first.

So this led us to a deeper overall discussion. In some sports, certain actions are obvious benefits to one player or the other. Tennis is probably most obvious. The longest tennis match in history (which, for anyone who may not be in the know, cannot be won by a margin of a single point or a single game) went to a final set and astoundingly to a game score in that final set of 70-68. The reason is because the server is always at an advantage to win the game (or in fact, any individual point, statistically speaking), so in that case, it just kept going back and forth for THREE DAYS with the server winning virtually every single game until someone finally slipped up, the server finally lost the critical game, hence, set and match was finally over.

So are there any serious Snooker statisticians in the audience? Does the record show a relationship between breaking off and winning/losing the frame? Another thing (correctly) pointed out by my kid is that (except in exhibition play; see here: https://www.youtube.com/watch?v=1vCYf_Z ... dded#at=18) a professional will NEVER take the break off and run the table for the win. The odds are simply too great that a Red will not fall in on the break off so of course, a safety break is the wise move. But time and again, it is not all that unusual that (again, professionally,) the second shot of the frame is a cracker of a pot on Red and the player may go on to win the frame in a single visit. By the same token then, a good opening safety break may well lead to a mistake on the second shot which may then lead to the "breaker" winning the frame in a single visit during his next turn at the table.

Does anyone have access to these stats? Truthfully, I don't even know where or how to even begin looking. Of course, back in the day, we old timers didn't pay very close attention to these type of things except anecdotally, but with today's computational powers, unusual stats seem to creep out of the woodwork so maybe someone can look up that ratio for, say, all professional tournaments for the last five years or something.

By my gut feeling, my assumption is that it is probably a wash, 50/50, doesn't matter whether one breaks off or not, chances of winning or losing any individual frame is probably about the same. But maybe the numbers will prove me wrong. Anyone any good at deciphering this sort of information?



EDIT: I suppose this should be in "General Snooker Discussion" but somehow, I ended up with it here in "Rules and Referees" and I can't figure out if and how it's possible to edit which Forum so I guess I will leave it here...

Re: Stat question about the break off

Postby Dan-cat

hehe. Love it.

My mate did the worse break off ever (since we began playing together about two years ago) in our last session. He missed the reds entirely. I broke from where the white came to rest of course, we are sticklers for the rules.

Re: Stat question about the break off

Postby PLtheRef

Just playing around with some figures here while I have Statman's Crucible Almanac in front of me.

In the last ten Crucible finals 304 frames have been played the person breaking has won 152 of those. - The person not breaking has won 152 of those.

Re: Stat question about the break off

Postby PLtheRef

acesinc wrote:WARNING! Long, boring, dull, drab post ahead! (Unless you are a numbers nerd.) You have been warned.
_____________________________

In my regular Friday night match with my kid, a question came up that I have a gut feeling about, but really, I have no evidence at all either way and maybe there is not even an answer to be had.

Let me start by saying that this is a "numbers" questions, probably boring to nearly everyone on the planet except us few nerds that get a kick out of this sort of thing. So I am looking for an actual answer with some sort of statistical reference, NOT looking for everybody and anybody's own personal opinion. If you feel you want to chime in with your own opinion about the answer, that is fine, but please give some sort of support information as to why that is your opinion.

On to the actual question, it is about the break off. Playing English Billiards, we string for the break off and playing Snooker, we flip a coin per custom. Now, I have always been of the opinion that if you win the coin flip, you should take the break off. When it comes to a re-spotted Black, if you win the coin flip, you should pass the first shot.

My kid is a fantastic "numbers guy". He can spout off numbers and statistics for all kinds of things, especially sports, even on occasion some sport I may have never even heard of. So to tie this all in, for us, the coin flip is completely irrelevant because when I win the flip, I take the break off. When he wins the flip, he passes the break off to me. Even so, he does insist that we conduct the pleasantries of the coin flip in homage to tradition. It used to be that he would pass the break off to me simply because he was not good at it so he didn't want to do it. But now he takes the break off as well as anyone, but he will still pass it to me when he wins the flip. So I asked why?

He said he noticed that whenever he takes the break off, then I am nearly always the first to score. So by the psychological benefit of being "first on the board", he is statistically better off to let me break off. Huh.........makes sense, I guess. That doesn't mean that he is always first to score when I break off, but statistically, he has a better chance of scoring first.

So this led us to a deeper overall discussion. In some sports, certain actions are obvious benefits to one player or the other. Tennis is probably most obvious. The longest tennis match in history (which, for anyone who may not be in the know, cannot be won by a margin of a single point or a single game) went to a final set and astoundingly to a game score in that final set of 70-68. The reason is because the server is always at an advantage to win the game (or in fact, any individual point, statistically speaking), so in that case, it just kept going back and forth for THREE DAYS with the server winning virtually every single game until someone finally slipped up, the server finally lost the critical game, hence, set and match was finally over.

So are there any serious Snooker statisticians in the audience? Does the record show a relationship between breaking off and winning/losing the frame? Another thing (correctly) pointed out by my kid is that (except in exhibition play; see here: https://www.youtube.com/watch?v=1vCYf_Z ... dded#at=18) a professional will NEVER take the break off and run the table for the win. The odds are simply too great that a Red will not fall in on the break off so of course, a safety break is the wise move. But time and again, it is not all that unusual that (again, professionally,) the second shot of the frame is a cracker of a pot on Red and the player may go on to win the frame in a single visit. By the same token then, a good opening safety break may well lead to a mistake on the second shot which may then lead to the "breaker" winning the frame in a single visit during his next turn at the table.

Does anyone have access to these stats? Truthfully, I don't even know where or how to even begin looking. Of course, back in the day, we old timers didn't pay very close attention to these type of things except anecdotally, but with today's computational powers, unusual stats seem to creep out of the woodwork so maybe someone can look up that ratio for, say, all professional tournaments for the last five years or something.

By my gut feeling, my assumption is that it is probably a wash, 50/50, doesn't matter whether one breaks off or not, chances of winning or losing any individual frame is probably about the same. But maybe the numbers will prove me wrong. Anyone any good at deciphering this sort of information?



EDIT: I suppose this should be in "General Snooker Discussion" but somehow, I ended up with it here in "Rules and Referees" and I can't figure out if and how it's possible to edit which Forum so I guess I will leave it here...


I'll admit to being one of those who enjoys all the facts and statistics :-)

The gut feeling is that the break-off shouldn't be of a huge advantagein snooker compared to pool where you are able to break off, and clear up (and in some cases for several frames or racks in a row). Like you said that unless it's an exhibition scenario there isn't going to be an attempt to try and fluke a red of the break-off. Later on in a match or if a match goes to a decider then you could argue that having the break is an advnatage if you are able to break off and leave the cueball tight on the baulk cushion. Then again, there's been more than a few deciding frames when someone has broken-off, the other player has produced a great long pot off the break and made a match-winning break

I'm not sure how easy it would be to trace the records of break-offs from different events given that few (if any records are likely to exist) - The World Championships may well be easier to trace than the others. Given that you can find a lot of old clips on YouTube etc. Likewise its going to be easier to trace more recent Championships than older campaigns,

Through looking through the Crucible Almanac by Statman and at old clips of previous World Finals it's possible to trace the breaking records of the different finals. - Since 1984 the only final where its not possible to trace who broke first is the Hendry v Doherty final of 1997.

Of the past 17 World Championship finals since Williams v Stevens in 2000 - 14 (82.3%) of them have been won by the player who broke off in the opening frame, It's only 2006, 2014 and 2016 when the eventual winner broke off in the second frame.

532 frames have been played in the 17 World Finals since 2000. - The player who broke off has won 267 (50.19%) of these frames - compared to 265 where the non-breaker won the frame.

In the 278 frames which have been played on the Sunday of World Final - 138 (49.64%) have been won by the player who broke off. Of the 254 which have been played on the Bank Holiday Monday 129 (50.79%) have been won by the player who broke off.

10 (58.8%) out of 17 winners broke off in the World Championship clinching frame.

And for what I said regarding the break-off being more advantageous in a decider? - Of the three Crucible Finals which went to a decider its only in 2002 when Ebdon beat Hendry that the champion broke off in the deciding frame.

Make of that what you will.

<cool>

Re: Stat question about the break off

Postby acesinc

Thank you so much, PL for taking the time to compile this information! The modern age of information is truly a marvel. On its face then, the gut feeling is correct....pretty much 50/50 even-steven chance of winning or losing an individual frame no matter who breaks off. (This statistic of course is based on the premise that the two players are for all intents and purposes equally skilled as is the general case among players of professional caliber.) One of your stats absolutely glares out at me however....

"Of the past 17 World Championship finals since Williams v Stevens in 2000 - 14 (82.3%) of them have been won by the player who broke off in the opening frame..."

That is astounding and defies explanation. When a data set is small, as in your stat about the decider frame going to the non-breaker 2 of 3 times, an anomaly can be expected but it will certainly even out over time. With an expected odds of 50/50 one would think the data would smooth out pretty well by 17 data points. Imagine flipping a coin five times and it comes out "heads" 4 out of 5. Not such a big deal. So five more flips and it comes out "heads" again 4 out of 5. Now you have to scratch your head and wonder. So the next five flips, guess what? 4 out of 5 "heads" again. This is definitely a curiosity. So you do two last flips....and they are both "heads". That almost defies logic and has no explanation I can think of.

Thanks again.

Re: Stat question about the break off

Postby acesinc

Dan-cat wrote:hehe. Love it.

My mate did the worse break off ever (since we began playing together about two years ago) in our last session. He missed the reds entirely. I broke from where the white came to rest of course, we are sticklers for the rules.


Worse break off ever? Hell, I do that all the time! I try for maximum spin just to see what I can make happen. I hope to make the white hit the second side cushion on the BLACK side of the table one day! But when a frame actually means something, like a tournament or a wager, then I will play a pretty standard break off.

By the way, you may not be aware....if the pack of Reds is completely missed like this on the break off, it actually is a "Foul and a Miss" scenario (and possibly a Free Ball, but that would need a good looking at. And (God forbid!) three misses in a row like this would be loss of frame (with warning after the second miss). We generally just take it as the FAAM so the original breaker takes the break off again and put back any balls that may have moved.

Re: Stat question about the break off

Postby Dan-cat

acesinc wrote:
Worse break off ever? Hell, I do that all the time! I try for maximum spin just to see what I can make happen. I hope to make the white hit the second side cushion on the BLACK side of the table one day! But when a frame actually means something, like a tournament or a wager, then I will play a pretty standard break off.

By the way, you may not be aware....if the pack of Reds is completely missed like this on the break off, it actually is a "Foul and a Miss" scenario (and possibly a Free Ball, but that would need a good looking at. And (God forbid!) three misses in a row like this would be loss of frame (with warning after the second miss). We generally just take it as the FAAM so the original breaker takes the break off again and put back any balls that may have moved.


hahaha :) Yes I meant in the context of our ongoing tournaments that we play. In a 'proper' frame as it were. We play best of 17s, usually over several sessions. In the current BO17 I'm 5 - 3 up. And in the series ongoing I'm 3 - 2 ahead. We have a shield that passes between us.

Of course - it should have been a foul and a miss! We didn't think about that. The white came to rest quite near the pack, I took the four points and played the next shot and tucked him up nicely on the baulk cushion. It was an easy safety shot from that position. Even with the option of a foul and a miss I would have still taken the shot, as effectively I would have been letting him have the break again and he could have put me in trouble (as you pointed out above, if you win the toss, you take the break. Apart from your son - that's just plain weird! hehe.) I have seen professionals give the break to the other player - I think the last time I saw this was Marco Fu last year - not sure who he was playing but I found it remarkable at the time. A little bit of gamesmanship perhaps, or maybe he hadn't been getting good breaks during his run at that tournament.

*It's funny, The Snooker Island spellchecker doesn't recognise the word baulk. Lolz.

Re: Stat question about the break off

Postby SnookerEd25

PLtheRef wrote:
Through looking through the Crucible Almanac by Statman and at old clips of previous World Finals it's possible to trace the breaking records of the different finals. - Since 1984 the only final where its not possible to trace who broke first is the Hendry v Doherty final of 1997.



Why is it not possible to trace who broke first in 1997? Even if, by some transmissional freak, no footage of the beginning of the match still exists, in Snooker we have alternate breaks, so surely just looking at who broke the even-numbered frames & who broke the odds would answer this question?

Re: Stat question about the break off

Postby PoolBoy

SnookerEd25 wrote:
PLtheRef wrote:
Through looking through the Crucible Almanac by Statman and at old clips of previous World Finals it's possible to trace the breaking records of the different finals. - Since 1984 the only final where its not possible to trace who broke first is the Hendry v Doherty final of 1997.



Why is it not possible to trace who broke first in 1997? Even if, by some transmissional freak, no footage of the beginning of the match still exists, in Snooker we have alternate breaks, so surely just looking at who broke the even-numbered frames & who broke the odds would answer this question?

There doesn't appear to be any footage on-line.... :sad:
But, as you rightly say, it wouldn't even have to be the first frame - any frame which shows either player breaking-off would solve it!

Re: Stat question about the break off

Postby TheSaviour

I suppose those bombs again took off according to timetable. For the last final time.

Re: Stat question about the break off

Postby TheSaviour

Yes, but how on earth can he believe something like this???? <doh> <doh> <doh> <doh>

There just won´t be someone who has a correct nationality and suddenly he or she is going to rout everybody. Where realistically, historically is just a one to challenge.

Obviously there always will be a kind of different "grades". The favourites (the usual suspects), the ones to challenge with a realistic chance to win, the underdogs who has it just bottled it before. But that´s the strick end of the any statistics and number wisdom. It´s all about the conditions.

There´s not much love lost between the statisctics like these and the reality, which always is a part of solution and depends on, relies heavily on what the current conditions are. The game of snooker is much about cutting the balls in from the different angles. I can´t see that would suddenly just end. That the conditions wouldn´t play that big part anymore. Even when many people have talked about that for ages..

I am personally a builder. Thinking wise. So there´s a lots of information available but I don´t do anything with that information. So perhaps it still is the thinking part which is lacking (from them) ? Not the natural talent. It´s not the best possible calling card to come to play with just a statistics on your mind. If fancing any results. Obviously there won´t be any expressions or looks if coming out like that.

Still some statistics-people are class acts. Anyone can make a mistakes, and will be making. They are just going to keep on surprising people a LOT if just solely underestimating them....

Re: Stat question about the break off

Postby Pink Ball

TheSaviour wrote:Yes, but how on earth can he believe something like this???? <doh> <doh> <doh> <doh>

There just won´t be someone who has a correct nationality and suddenly he or she is going to rout everybody. Where realistically, historically is just a one to challenge.

Obviously there always will be a kind of different "grades". The favourites (the usual suspects), the ones to challenge with a realistic chance to win, the underdogs who has it just bottled it before. But that´s the strick end of the any statistics and number wisdom. It´s all about the conditions.

There´s not much love lost between the statisctics like these and the reality, which always is a part of solution and depends on, relies heavily on what the current conditions are. The game of snooker is much about cutting the balls in from the different angles. I can´t see that would suddenly just end. That the conditions wouldn´t play that big part anymore. Even when many people have talked about that for ages..

I am personally a builder. Thinking wise. So there´s a lots of information available but I don´t do anything with that information. So perhaps it still is the thinking part which is lacking (from them) ? Not the natural talent. It´s not the best possible calling card to come to play with just a statistics on your mind. If fancing any results. Obviously there won´t be any expressions or looks if coming out like that.

Still some statistics-people are class acts. Anyone can make a mistakes, and will be making. They are just going to keep on surprising people a LOT if just solely underestimating them....


Saviour, you should be in sales.

Re: Stat question about the break off

Postby Badsnookerplayer

That is astounding and defies explanation. When a data set is small, as in your stat about the decider frame going to the non-breaker 2 of 3 times, an anomaly can be expected but it will certainly even out over time. With an expected odds of 50/50 one would think the data would smooth out pretty well by 17 data points. Imagine flipping a coin five times and it comes out "heads" 4 out of 5. Not such a big deal. So five more flips and it comes out "heads" again 4 out of 5. Now you have to scratch your head and wonder. So the next five flips, guess what? 4 out of 5 "heads" again. This is definitely a curiosity. So you do two last flips....and they are both "heads". That almost defies logic and has no explanation I can think of.

I used to do some maths. The probability of getting fourteen heads out of seventeen flips is 1140/(2 to the power of twenty) which is about 0.1% or 'one in a thousand'.

If there is really an even chance of each break-offer winning in the final at the worlds, then this sequence (14 wins from 17) may not occur again for a long time .....but it might.

Re: Stat question about the break off

Postby acesinc

Badsnookerplayer wrote:That is astounding and defies explanation. When a data set is small, as in your stat about the decider frame going to the non-breaker 2 of 3 times, an anomaly can be expected but it will certainly even out over time. With an expected odds of 50/50 one would think the data would smooth out pretty well by 17 data points. Imagine flipping a coin five times and it comes out "heads" 4 out of 5. Not such a big deal. So five more flips and it comes out "heads" again 4 out of 5. Now you have to scratch your head and wonder. So the next five flips, guess what? 4 out of 5 "heads" again. This is definitely a curiosity. So you do two last flips....and they are both "heads". That almost defies logic and has no explanation I can think of.

I used to do some maths. The probability of getting fourteen heads out of seventeen flips is 1140/(2 to the power of twenty) which is about 0.1% or 'one in a thousand'.

If there is really an even chance of each break-offer winning in the final at the worlds, then this sequence (14 wins from 17) may not occur again for a long time .....but it might.


I am good with the maths but never studied Statistics at all. I am certain there is a method to your madness, but I have no idea how the formulae are derived. 14 of 17 coin flips coming out "heads" one in a thousand times just seems like it can't be correct though I am not willing to do the experiment myself. Gut feeling is all, I admit to nothing at all to back this up. Starting with 4 of 5 flips being heads, I can see that happening quite often....1 in 20? 1 in 50? I don't know, not a lot but quite often in the scheme of things.

So move on the the next batch of 5 flips, again, the same ratios. But it seems to me that if this second batch is going to come out 4 of 5 again, it would more likely be 4 of 5 coming up "tails" because that would follow the long term trend of a 50/50 ratio. So to come out 8 of 10 as "heads" seems very unlikely indeed even though 4 of 5 is not that big a deal. Add the third batch of 4 of 5 as "heads" and this unlikelihood would seem to multiply exponentially (and so I assume is related to the derivation of your "2^20 denominator). So a 1 in a 1000 chance just "feels" wrong. Certainly I wouldn't expect 1 in a trillion or 1 in a quintillion, but I would have guessed more like 1 in a million to 1 in 10 million.

I doubt that in the long and storied history of humanity, the actual "experiment" of flipping such a coin a million times in a row has ever occurred. Maybe recording seventeen flips a thousand times in a row has been done (17,000 coin flips total), but I wouldn't care to do it myself. How about a coin flipping "smart phone" app to avoid all the mucking about with actual coins? But that would be akin to a video Snooker game, I suppose, not the real thing. Perhaps a coin flipping robot? But surely, a robot could solve the coin flipping problem so that eventually the data would reflect a thousand "heads" of a thousand flips. Presumably this data could be considered to be corrupt. This is a dilemma.

Suffice to say that if you flip a coin 17 times and it comes up "heads" 14 times, don't bother to play the Lottery because in all likelihood, your luck has run out.

Re: Stat question about the break off

Postby Badsnookerplayer

To do the maths you need to know that there are 2 to the power of seventeen possible outcomes when you flip a coin 17 times.

There are (15x16x17)/(1x2x3) of these outcomes that have exactly fourteen heads in there.

Then just divide the two results.

I made a mistake in my calculation in that I should have divided by 2 to the power of 17 (not twenty) but that actually results in a larger probability of 14 wins from 17. It is actually about 0.52% or 1 in two hundred which I agree with you does seem counter-intuitive.

Re: Stat question about the break off

Postby acesinc

Thanks for the explanation, BSP. That does make some sense mathematically but it just seems way too frequent to work IRL (if one can legitimately call a 1 in 200 probability "frequent").

I suppose I could be a wiseacre here and make a minor correction to your calculation if my thinking is correct...it seems to me that your methodology would bring us to the conclusion of the coin flip being the same 14 of 17 flips. But that would not specify the actual state of the coin flip be it heads or tails, just that it would be the same 14 of 17. If we want to calculate the probability of it actually coming up "heads" 14 of 17, then would we need to halve the probability to 1 in 400? This would relate to the 14 of 17 times that specifically the break-offer would win, as opposed to it might be one or it might be the other 14 of 17...

EDIT: I stand corrected...it looks like you did account specifically for the state of "heads" in there, I just overlooked it, so 1 in 200 is the answer then.