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View Full Version : Break-and-Run Percentage - Extrapolate to Series?

SpiderMan
02-08-2007, 10:08 AM
I've recently joined an 8-Ball league that keeps statistics on several figures of merit, including break-and-runs.

On any given night, 5-man teams play five "rounds", each player matching up against a different opponent each round. Total for the night is 5 games per man, or 25 per team.

Breaking is determined solely by the lineup - it alternates, with no "break reward" for winning a game. One team gets all the breaks first round, the other team the second round, etc. In the fifth round, the breaks are alternated between teams. Any individual player will break twice in his first four rounds, and then break or not in the last round according to where he falls in the lineup. On average, any given player will therefore break 2.5 times per 5-game match. 8-on-the-break is spotted, so you still have to run out for it to be a B&amp;R.

I've played 10 weeks so far, therefore I am assumed to have had 25 breaks (out of 50 games). of these 25 games, I have had 5 break-and-runs, therefore my percentage is 20%. This means that, on average, I break and run 1 time out of 5. Assuming I make something on the break about half the time, then I must be running out 40% of these cases to wind up at 20% overall.

When I practice with friends, we play "winner breaks", so we get a chance to string together several racks if we're hot. Under this format, my best string so far is 4 B&amp;Rs in a row.

Mathematically, my B&amp;R percentage of 20% says that I'll probably string together four racks of 8-ball every 625 starts: 1/(.2)(.2)(.2)(.2)= 625

So, what if I wanted my best string to be six in a row? If I extrapolate the above data (yeah, I know it's a stretch) and say that my high series will still probably be a 1-in-625 event, then the corresponding B&amp;R percentage would be the sixth root of (1/625), or 34.2%.

So improving my B&amp;R percentage from the current 1-in-5 to about 1-in-3 would have me stringing together six about as often as I now string together four.

Assuming I still only make a ball on the break about half the time, that means I would have to run out 68% of these cases in order to maintain the 34% B&amp;R percentage.

Does this make sense? Dr Dave?

SpiderMan

02-08-2007, 10:49 AM
At your current B+R probability, you would be expected to run 6 about 1 in 15625. Increasing your B+R probability to about 1 in 3 would get you into the 1 in 625 realm for running 6 racks.

From where I stand near the bottom of the billiards food chain, running a 4 minute mile looks easier than being able to consistently B+R with that frequency. Do the pros do that well?

I am relatively new to this, but I am suprised that there is such a big disparity between your frequency of pocketing one on the break and your ability to run racks. I would think it to be far easier to increase the yield on the break, than to increase the probability of running the rack.

dr_dave
02-08-2007, 11:02 AM
<blockquote><font class="small">Quote SpiderMan:</font><hr> I've recently joined an 8-Ball league that keeps statistics on several figures of merit, including break-and-runs.

On any given night, 5-man teams play five "rounds", each player matching up against a different opponent each round. Total for the night is 5 games per man, or 25 per team.

Breaking is determined solely by the lineup - it alternates, with no "break reward" for winning a game. One team gets all the breaks first round, the other team the second round, etc. In the fifth round, the breaks are alternated between teams. Any individual player will break twice in his first four rounds, and then break or not in the last round according to where he falls in the lineup. On average, any given player will therefore break 2.5 times per 5-game match. 8-on-the-break is spotted, so you still have to run out for it to be a B&amp;R.

I've played 10 weeks so far, therefore I am assumed to have had 25 breaks (out of 50 games). of these 25 games, I have had 5 break-and-runs, therefore my percentage is 20%. This means that, on average, I break and run 1 time out of 5. Assuming I make something on the break about half the time, then I must be running out 40% of these cases to wind up at 20% overall.

When I practice with friends, we play "winner breaks", so we get a chance to string together several racks if we're hot. Under this format, my best string so far is 4 B&amp;Rs in a row.

Mathematically, my B&amp;R percentage of 20% says that I'll probably string together four racks of 8-ball every 625 starts: 1/(.2)(.2)(.2)(.2)= 625

So, what if I wanted my best string to be six in a row? If I extrapolate the above data (yeah, I know it's a stretch) and say that my high series will still probably be a 1-in-625 event, then the corresponding B&amp;R percentage would be the sixth root of (1/625), or 34.2%.

So improving my B&amp;R percentage from the current 1-in-5 to about 1-in-3 would have me stringing together six about as often as I now string together four.

Assuming I still only make a ball on the break about half the time, that means I would have to run out 68% of these cases in order to maintain the 34% B&amp;R percentage.

Does this make sense? Dr Dave?<hr /></blockquote>
Sounds reasonable to me. Although, I would think that if you were able to improve your run percentage so significantly, you might also be able to improve your ball-on-break percentage.

I can't help but thinking that you have a follow-on conclusion that will put the above logic into question. Is that the case?

Dave

SpiderMan
02-08-2007, 11:36 AM
<blockquote><font class="small">Quote dr_dave:</font><hr>
Sounds reasonable to me. Although, I would think that if you were able to improve your run percentage so significantly, you might also be able to improve your ball-on-break percentage.

I can't help but thinking that you have a follow-on conclusion that will put the above logic into question. Is that the case?

Dave <hr /></blockquote>

Actually I don't - the ball-on-the-break percentage is pretty much an unknown for me. I feel like it's around 50%, but have never made any controlled observations.

Scott Lee once told me that he had information from Accu-stats to indicate that the percentage was less than 50% for pros - but that's for nine-ball, and I feel that it's better for 8-ball. I watched one of Deeman's pro 8-ball tapes, and those guys were dropping a ball close to 75% of the time. Of course, that was one match and it may not be typical.

This whole line of thought started when I realized that my "best effort" was only 4 racks, and it seems like everyone I know claims to have run 5 or 10.

So I started wondering if I could relate a "lifetime best" back to a B&amp;R percentage. The missing constant is, of course, the likelihood of achieving your "lifetime best" for any particular start. Since we know the real answer is "once in a lifetime", the problem is assigning a practical number for sake of calculation. Since I had data for percentage and lifetime best on myself, I was able to solve for the probability of 1 in 625.
<font color="blue">
Here's my summary: if ball-on-break is really around 50%, and 1-in-625 is reasonable for a "best series", then that series would be <font color="red"> INTRINSICALLY LIMITED TO A MAX OF 9 OR 10. </font color> This number is forced by assuming a B&amp;R percentage of 50%, meaning you always run out once you make that first ball. Of course this doesn't happen, but really good players come closer than the rest of us, and also probably have a better break percentage (as you suggested).

But I find it very interesting that any set of reasonable assumptions for a pro's ball-on-break percentage and conversion percentage all seem to point to "best series" totals in the range of 8 to 13. The common factor between all of these calculations is the 1-in-625 probability assumed for the best-effort result.
</font color>
Again, this is 8-ball.

SpiderMan

SpiderMan
02-08-2007, 11:45 AM
<blockquote><font class="small">Quote DeadCrab:</font><hr> At your current B+R probability, you would be expected to run 6 about 1 in 15625. Increasing your B+R probability to about 1 in 3 would get you into the 1 in 625 realm for running 6 racks.

From where I stand near the bottom of the billiards food chain, running a 4 minute mile looks easier than being able to consistently B+R with that frequency. Do the pros do that well?
<hr /></blockquote>
I wish I knew. With everyone focused on 9-ball performance as a benchmark of ability, 8-ball data may be a little scarce.
I am relatively new to this, but I am suprised that there is such a big disparity between your frequency of pocketing one on the break and your ability to run racks. I would think it to be far easier to increase the yield on the break, than to increase the probability of running the rack. <hr /></blockquote>

That's a very good point, made also by Dr Dave, and I don't really know my break-yield percentage. I doubt it's much over 50%, and certainly no one considers me a strong breaker. We play on regular-size tables. Balls would drop more often on bar tables, but the clutter might also make runouts harder.

SpiderMan

jondrums
02-08-2007, 01:46 PM
I think your logic may be severely limited by two issues.

One assumtion you are making is that your lifetime best should occur once in 625 starts. This sounds very low to me! If you only were to play for 10 more years, twice a month, and got 10 starts on each of those nights, you'd still get almost 2500 starts. I would consider this a fairly conservative estimate, but perhaps you don't play this much. If you're given 2500 starts you should be able to string 8 games together once with a 20% BandR percentage! (versus only 4 games at 625 starts)

The other assumption of 50% ball on break could surely use more study (as others have pointed out). Here's why: at 50% balls on a break and shooting 100%, you're limited statistically to 9 games in a row over 625 starts. Improve to 56% and you'll make that 11 games. 61% -&gt; 13 games.

The point is that a little change in the balls on break percentage or number of starts has a large change in the games in a row probability.

Is this making sense?
Jon

Deeman3
02-08-2007, 02:47 PM
Not that I'm a statistical type person but a couple of things seem to stand out here. First, it is not the success in break percentage that is important here and, no, I know Spidermen is not a particularily strong breaker but the rest of his game is VERY strong. The important point is the percentage of breaks where a ball is made AND a reasonable shot is available, admittedly less a factor in 8 ball but still important. The second thing is the breakability factor (did I say that?) of certain tables. While tight pockets limit success in runouts, they seem, to me, to have more impact on break success. You can, and good players do, adjust to the tighter pockets with more care, better shot selection, etc. However, it seems tight pockets, slow cloth and poor cushion response are much less under a player's control.

DeeMan
Not important but it is worth consideration or is that condemnation?

SpiderMan
02-08-2007, 02:54 PM
<blockquote><font class="small">Quote jondrums:</font><hr> I think your logic may be severely limited by two issues.

One assumtion you are making is that your lifetime best should occur once in 625 starts. This sounds very low to me! If you only were to play for 10 more years, twice a month, and got 10 starts on each of those nights, you'd still get almost 2500 starts. I would consider this a fairly conservative estimate, but perhaps you don't play this much. If you're given 2500 starts you should be able to string 8 games together once with a 20% BandR percentage! (versus only 4 games at 625 starts)

The other assumption of 50% ball on break could surely use more study (as others have pointed out). Here's why: at 50% balls on a break and shooting 100%, you're limited statistically to 9 games in a row over 625 starts. Improve to 56% and you'll make that 11 games. 61% -&gt; 13 games.

The point is that a little change in the balls on break percentage or number of starts has a large change in the games in a row probability.

Is this making sense?
Jon <hr /></blockquote>

I agreed that break percentages need real data in my response to Dave. But I also think that the important number, the product of ball-on-break and conversion efficiencies, may actually fall in a pretty tight range for highly-skilled players.

75% ball-on-the-break and 75% completion of runouts (probably an aggressive goal for most strong "A" players) only results in a nominal improvement over my admittedly haphazard example of 50% on the break and 100% completion of runouts (56% vs 50% B&amp;R percentages, and 11 vs 9 series, respectively). Most most logical combinations of balls on break and runout percentages (for a good player) still seem to converge on the same range of likely personal bests.

So maybe it's no wonder that we hear so many good players noting that their best series of B&amp;Rs is around 10. Most of them may be telling the truth! And I've bared my shortcomings by admitting my high series is only 4 /ccboard/images/graemlins/smile.gif

Also, I consider 10 years way too long for considering "best series" for most of us normal folk. Why? Because as long as you are actively improving, your "best" will probably be recent. That's my rationalization to justify a finite number (such as the 625 from my personal statistics) instead of something much larger, or really fuzzy like a career or an entire lifetime. I guess the number would have to be a lot larger for a player who has already peaked.

SpiderMan

jondrums
02-08-2007, 03:12 PM
<blockquote><font class="small">Quote SpiderMan:</font><hr> But I also think that the important number, the product of ball-on-break and conversion efficiencies, may actually fall in a pretty tight range for highly-skilled players.<hr /></blockquote>

I bet you're right. Someone else mentioned that the equipment is probably as much or more of a factor than anything for these highly-skilled players.

<blockquote><font class="small">Quote SpiderMan:</font><hr>
So maybe it's no wonder that we hear so many good players noting that their best series of B&amp;Rs is around 10. Most of them may be telling the truth!<hr /></blockquote>

It suddenly strikes me that 10 games B&amp;R must be about equal to the 100ball straight pool run.

<blockquote><font class="small">Quote SpiderMan:</font><hr>
Also, I consider 10 years way too long for considering "best series" for most of us normal folk. Why? Because as long as you are actively improving, your "best" will probably be recent. That's my rationalization to justify a finite number...<hr /></blockquote>

ok. If you assume that you are not getting less-skilled over time, then I don't see why you shouldn't count all the years you have coming to you towards calculating your "Lifetime" goal. However it seems that you're speaking of "best series" and I'm thinking about "lifetime best series". That's probably where I differ in the calculation

Jon

Jal
02-08-2007, 05:59 PM
<blockquote><font class="small">Quote SpiderMan:</font><hr> I've recently joined an 8-Ball league that keeps statistics on several figures of merit, including break-and-runs.....<hr /></blockquote>

You may have seen these, but some statistics from the IPT are here (http://www.internationalpooltour.com/ipt_content/events/06_na_8ball_open/player_stats.asp) and here (http://www.internationalpooltour.com/ipt_content/events/06_wo_8ball_open/statistics.asp).

Jim

SpiderMan
02-09-2007, 07:47 AM
<blockquote><font class="small">Quote jondrums:</font><hr> ok. If you assume that you are not getting less-skilled over time, then I don't see why you shouldn't count all the years you have coming to you towards calculating your "Lifetime" goal. However it seems that you're speaking of "best series" and I'm thinking about "lifetime best series". That's probably where I differ in the calculation

Jon <hr /></blockquote>

Actually, I too was speaking of "lifetime best series". But I believe it would only be necessary to consider the whole lifetime interval if you are neither declining nor improving, ie "on a plateau". Duffers such as I improve; former world-beaters decline.

I've been playing steadily since I first joined a league in Dallas, which was around 1990. I suspect my "lifetime best series" has always been within the past 5 years, but of course we never keep records on the stuff we'll eventually ponder /ccboard/images/graemlins/smile.gif

SpiderMan

SpiderMan
02-09-2007, 07:55 AM
Jal,

That's a fantastic resource. But I was about to do some calculations, and I can't find a note to tell what the format was for determining breaks. For example, if player X is listed to have a 20% B&amp;R percentage for "all games played", can I assume he broke only 50% of the time? If it's winner break, there is no way to determine how many breaks a given player had.

SpiderMan

Jal
02-09-2007, 02:29 PM
<blockquote><font class="small">Quote SpiderMan:</font><hr> Jal,

That's a fantastic resource. But I was about to do some calculations, and I can't find a note to tell what the format was for determining breaks. For example, if player X is listed to have a 20% B&amp;R percentage for "all games played", can I assume he broke only 50% of the time? If it's winner break, there is no way to determine how many breaks a given player had.

SpiderMan <hr /></blockquote>Spiderman,

I thought it would more useful to you at first, then realized that what you're really interested in is the fraction of break and runs per break opportunity. But I think you can get a pretty close figure with some assumptions.

In the official rules section, rule 4 states that the format was that the winner of a game had the option to break the next game (bummer!). But if you make the semi-safe assumption that the winner always chose to break, then you can figure out how many times a player broke by first subtracting his or her number of games lost, less the number of matches lost, from the total number of games played. (The opponent didn't break the next game if it was the final game of the match, ergo, reduce the number of games lost by the number of matches lost.)

Unfortunately, we don't know who broke the first game of each match. You can, as you please, assume the player won the lag only 50% of the time, ie, also subtract 1/2 the number of matches played from the total number of games. Whatever the actual number was, this shouldn't be too far off. Or assume both 0% and 100% by subtracting all and none to get the lower and upper bounds.

It would also be nice to know, as per your discussion, how many times balls were sunk on the break, but I can't see a way of getting at this, can you?

If it's important, I could write a program to read and process the stats in this fashion, but I'm hoping you're a programmer and would opt to do it yourself if you really want these results. /ccboard/images/graemlins/smile.gif

Jim

SpiderMan
02-13-2007, 03:04 PM
<blockquote><font class="small">Quote Jal:</font><hr> In the official rules section, rule 4 states that the format was that the winner of a game had the option to break the next game (bummer!). But if you make the semi-safe assumption that the winner always chose to break, then you can figure out how many times a player broke by first subtracting his or her number of games lost, less the number of matches lost, from the total number of games played. (The opponent didn't break the next game if it was the final game of the match, ergo, reduce the number of games lost by the number of matches lost.)

Unfortunately, we don't know who broke the first game of each match. You can, as you please, assume the player won the lag only 50% of the time, ie, also subtract 1/2 the number of matches played from the total number of games. Whatever the actual number was, this shouldn't be too far off. Or assume both 0% and 100% by subtracting all and none to get the lower and upper bounds.
Jim <hr /></blockquote>

Jim,

The approach that seems right to me for estimating the number of breaks a particular player had during the tournament would be:

BREAKS = (GAMES WON) + (MATCHES PLAYED/2) - (MATCHES WON)

The rationale is that you break once after each game won, except when it's a match-ending game, plus you first-break half of your matches played without needing a preceding win.

OPPORTUNITIES = BREAKS - EOB

This assumes that they are playing by rules that make EOB a win. It's a seldom event, anyway.

Using the above formula for Francisco Bustamante's performance at the July 2006 IPT Open, I see that he demonstrated a 40.6% probability of runout when he was breaking.

This is almost exactly equivalent to making a ball on the break 6 out of 10 times, and running out 2 of every 3 times you make a ball. Actually sounds reasonable for someone who plays 8-ball like Bustamante.

SpiderMan

Jal
02-13-2007, 06:06 PM
<blockquote><font class="small">Quote SpiderMan:</font><hr>...The approach that seems right to me for estimating the number of breaks a particular player had during the tournament would be:

BREAKS = (GAMES WON) + (MATCHES PLAYED/2) - (MATCHES WON)

The rationale is that you break once after each game won, except when it's a match-ending game, plus you first-break half of your matches played without needing a preceding win.<hr /></blockquote>Spiderman,

I completely agree. Your way is exactly equivalent to the one I mentioned, but yours involves one less arithmetic operation. (I realized this after my post, it being another case of speak first and think later).