winner vs alternate break, computer simulated

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poolscholar

AzB Silver Member
Silver Member
I've always been curious about the difference and if it matters. So, I wrote a software program which runs random simulated races in both formats. I thought that winner break should obviously favor the better breaker. Well the effect is very small, so effectively it doesn't matter when the players have an even race. A lot more hill hill matches in alternate. The lesser player will win more games in alternate break. I'd think you want to adjust for this when creating a spot in gambling or handicapping a match. Also alternate should be more exciting for fans because more hill hill matches =]

I based the simulations off of percentage chance of winning when the player is breaking. No doubt there are more complicated ways to model this, but this seemed good enough to test a theory.

Here is a typical result (I ran a LOT of variations). The main result is a lot more hill hill matches, but the race outcome is oddly the same.

Chance to win when breaking
p1 65%
p2 55%

races to 5
Winner break
p1 races won: 12473483 62.367415%
p2 races won: 7526517 37.632585%
hill hill matches: 21.318485%

Alternate break
p1 races won: 12474201 62.371005%
p2 races wons: 7525799 37.628995%
hill hill matches: 26.86128%


So then I decided to track games won and try to find a difference. Here p1 scores a handful more games in alternate but not much difference.

Chance to win when breaking
p1 20%
p2 80%
race to 15

Winner break
p1 races won: 47 0.01175%
p1 games won: 1470557
p2 races won: 399953 99.98825%
p2 games won: 5999878
hill hill matches: 0.02625%

Alternate break
p1 races won: 44 0.011%
p1 games won: 1473704
p2 races won: 399956 99.989%
p2 games won: 5999901
hill hill matches: 0.0275%


Now I tried a simulation where both players can break and run racks. Perhaps this is good local player vs a top pro in bar table 8 ball. The lesser player P1 scores almost 30% more games in alternate compared to winner break, but as with the other trials, the winner of the race is the same.

Chance to win when breaking
p1 55%
p2 80%
race to 15

Winner break
p1 races won: 26995 6.74875%
p1 games won: 2718290
p2 races won: 373005 93.25125%
p2 games won: 5883089
hill hill matches: 3.436%

Alternate break
p1 races won: 26590 6.6475%
p1 games won: 3520262
p2 races won: 373410 93.3525%
p2 games won: 5925346
hill hill matches: 5.4835%

The caveat here is that I made up these numbers on chance of winning while breaking. I know there are some break stats geeks out there. If you have real world numbers from big events, let me know and I can run a simulation and post the results.
 
P

poolscholar

AzB Silver Member
Silver Member
One more example. Here is a race to 9 with p1 getting 2 games on the wire. Even match when playing winner break, but alternate break gives the edge to the lesser player.

Chance to win when breaking
p1 55%
p2 65%

Winner break
p1 races won: 504267 50.4267%
p1 games: 7400908
p2 races won: 495733 49.5733%
p2 games: 6965942
hill hill matches: 17.1451%

Alternate break
p1 races won: 547769 54.7769%
p1 games: 7773891
p2 races won: 452231 45.2231%
p2 games: 7065062

hill hill matches: 21.3734%
 
Bob Jewett

Bob Jewett

AZB Osmium Member
Staff member
Gold Member
Silver Member
poolscholar said:
I've always been curious about the difference and if it matters. So, I wrote a software program which runs random simulated races in both formats. ...
Click to expand...
It is possible to find the answer without random trials by using a Markov process which is a standard technique used to study complicated random situations. The expected probabilities for winner/alternate breaks are identical. I've posted about this before and written a column on it (BD, Sept. 2016). If anyone wants a spreadsheet to do the calculations, send me a PM or email to jewett@sfbilliards.com

I haven't worked out a proof yet, but I'm sure one's in there.

For the first case you list above, the chance for p1 to win the race to five is 0.623599363 regardless of the break assignment.
 
C

Ched

"Hey ... I'm back"!
Silver Member
poolscholar said:
I've always been curious about the difference and if it matters. So, I wrote a software program which runs random simulated races in both formats. I thought that winner break should obviously favor the better breaker. Well the effect is very small, so effectively it doesn't matter when the players have an even race. A lot more hill hill matches in alternate. The lesser player will win more games in alternate break. I'd think you want to adjust for this when creating a spot in gambling or handicapping a match. Also alternate should be more exciting for fans because more hill hill matches =]

I based the simulations off of percentage chance of winning when the player is breaking. No doubt there are more complicated ways to model this, but this seemed good enough to test a theory.

Here is a typical result (I ran a LOT of variations). The main result is a lot more hill hill matches, but the race outcome is oddly the same.

Chance to win when breaking
p1 65%
p2 55%

...
Click to expand...

Ya kinda lost right there - cause that's 120%
 
Bob Jewett

Bob Jewett

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Staff member
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Silver Member
Ched said:
Ya kinda lost right there - cause that's 120%
Click to expand...

I think what that means is when Player1 breaks, he is 65% to win. When Player2 breaks, he is 55% to win. If the two numbers add up to more than 100% it simply means that the break is an advantage. An example would be in this thread: http://forums.azbilliards.com/showthread.php?t=416427
where Orcullo was 63% to win on his break while Ko was 55% to win on his break.
 
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F

fathomblue

Rusty Shackleford
Silver Member
"AtLarge" is a great board member to reach out to for stats......particularly the break, but also more.
 
lakeman77

lakeman77

AzB Silver Member
Silver Member
What game were you using? I think there is a huge advantage in 8 ball. Often, one set can be run with ease, the other is a nightmare. Thanks for doing the work, interesting.
 
Matt

Matt

AzB Silver Member
Silver Member
Bob Jewett said:
It is possible to find the answer without random trials by using a Markov process which is a standard technique used to study complicated random situations. The expected probabilities for winner/alternate breaks are identical.
Click to expand...
True, but I'm glad to see someone run the simulation to back up the analysis. Maybe it will convince some of the doubters from the previous threads.

As we've also discussed before, this doesn't take into account any psychological effects on the players based on the break format. The actual match results and a fair amount of anecdotal evidence seems to suggest that those effects can be significant, even for players that acknowledge that the format doesn't change the win probability.

Finally, there's the issue of handicaps. Each game on the wire in the alternate break format is "worth" more than it is in a winner breaks format, and any spot in alternate break means there's a possible no-win scenario for the stronger player.
 
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poolscholar

AzB Silver Member
Silver Member
lakeman77 said:
What game were you using? I think there is a huge advantage in 8 ball. Often, one set can be run with ease, the other is a nightmare. Thanks for doing the work, interesting.
Click to expand...

There's no game here, just chance to win if you're the breaker. In the real world, I believe good players win around 55% of the time when they are breaking in big table 9 or 10 ball.

You are correct, playing bar table 8 ball I'd guess its much higher. Given that 4 or 5 in a row is pretty common for pros, were looking at 80%+ to win while breaking.
 
P

poolscholar

AzB Silver Member
Silver Member
Matt said:
True, but I'm glad to see someone run the simulation to back up the analysis. Maybe it will convince some of the doubters from the previous threads.

As we've also discussed before, this doesn't take into account any psychological effects on the players based on the break format. The actual match results and a fair amount of anecdotal evidence seems to suggest that those effects can be significant, even for players that acknowledge that the format doesn't change the win probability.

Finally, there's the issue of handicaps. Each game on the wire in the alternate break format is "worth" more than it is in a winner breaks format, and any spot in alternate break means there's a possible no-win scenario for the stronger player.
Click to expand...

I find it quite weird that an even race is the same chance between winner and alternate, but if you start adding in games on the wire, alternate favors the lesser breaker.
 
Matt

Matt

AzB Silver Member
Silver Member
poolscholar said:
I find it quite weird that an even race is the same chance between winner and alternate, but if you start adding in games on the wire, alternate favors the lesser breaker.
Click to expand...
I'm not sure exactly what you mean by "lesser breaker" in this context. The player with the weaker break might still be the better overall player, in which case the "lessor breaker" would be giving up the spot.

One other scenario that this brings to mind is when the break is actually a disadvantage, e.g. a player that wins 70% of his breaks and 80% or his opponent's breaks. In such a scenario, the predicted results are actually more lopsided in the alternate break format. Crazy, huh?
 
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poolscholar

AzB Silver Member
Silver Member
Matt said:
I'm not sure exactly what you mean by "lesser breaker" in this context. The player with the weaker break might still be the better overall player, in which case the "lessor breaker" would be giving up the spot.

One other scenario that this brings to mind is when the break is actually a disadvantage, e.g. a player that wins 70% of his breaks and 80% or his opponent's breaks. In such a scenario, the predicted results are actually more lopsided in the alternate break format. Crazy, huh?
Click to expand...

I'm generally assuming a similar level of skill and one guy just breaks better, which would be shown in the stat 'chance to win when breaking'.

Breaking disadvantage case is funny. Although I think if the break and runs are very few, it will probably even out to a close match in either format.

What would be interesting is to look at top players who break and run a lot. Look at fargorate and calculate two ratings one for alternate and one for winner break format. Looking at the simulations you'd think the best breakers would have a higher rating in winner break.
 
pt109

pt109

WO double hemlock
Silver Member
The best player wins at either format.
Not being able to run racks is compensated for by stopping miracle comebacks.

But alternate break tends to make the game more pedestrian for me.
...the game would be poorer without these milestones...

IMG_4026.JPG

IMG_4027.JPG


I get tired of watching championships where the high run is a one-pack...:rolleyes:
 
Matt

Matt

AzB Silver Member
Silver Member
pt109 said:
I get tired of watching championships where the high run is a one-pack...:rolleyes:
Click to expand...
I get tired of people assuming that pointing out that there's no statistical difference between the two break formats means I advocate alternate breaks. :rolleyes:

IMO, the equivalence of the two formats means that you should choose the format that best suits the situation. For pros, I think that means winner breaks because it's generally more exciting for the audience to see packages than close scores. For amateur tournaments where you're concerned with players feeling like they get their money's worth even when they lose, I can understand playing alternate breaks.
 
I

ineedaspot

AzB Silver Member
Silver Member
Bob Jewett said:
It is possible to find the answer without random trials by using a Markov process which is a standard technique used to study complicated random situations. The expected probabilities for winner/alternate breaks are identical. I've posted about this before and written a column on it (BD, Sept. 2016). If anyone wants a spreadsheet to do the calculations, send me a PM or email to jewett@sfbilliards.com

I haven't worked out a proof yet, but I'm sure one's in there.

For the first case you list above, the chance for p1 to win the race to five is 0.623599363 regardless of the break assignment.
Click to expand...

Here's a sketch of a proof. In a race-to-n, if it goes hill-hill, in either format, the player who breaks first gets n breaks, and the other player gets n-1 breaks. If it doesn't go hill-hill, then one or both players get less breaks than that, but it doesn't make any difference to the outcome because even with some games remaining, one player is already assured of the majority.

In fact, either format can be extended to 2n-1 games, with one player getting n breaks and the other n-1, simply by playing the unnecessary games after one player has already reached n wins. Which means that, in either format, the winning probabilities are the same as if player A breaks n times, player B breaks n-1 times, and whoever wins more racks is the winner of the set.

The only thing that changes is the order that the racks are played. You could even have player A break n times in a row and then player B break n-1 times in a row, and you'd end up with the same probabilities of each player winning the set. Or you could play loser break, and the probabilities would also be the same.

Of course, this all presumes that games are independent of each other, and there's no psychology or momentum.
 
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JB Cases

JB Cases

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Matt said:
I get tired of people assuming that pointing out that there's no statistical difference between the two break formats means I advocate alternate breaks. :rolleyes:

IMO, the equivalence of the two formats means that you should choose the format that best suits the situation. For pros, I think that means winner breaks because it's generally more exciting for the audience to see packages than close scores. For amateur tournaments where you're concerned with players feeling like they get their money's worth even when they lose, I can understand playing alternate breaks.
Click to expand...
Buddy Hall told me that he prefers alternate breaks in tournaments. He said that if he loses at least he got to break half of the time.

Sent from my SAMSUNG-SM-N920A using Tapatalk
 
JB Cases

JB Cases

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Silver Member
poolscholar said:
Thanks for opinions guys. But this is not another 'do you like winner or alternate break?' thread.
Click to expand...
Well it is destined to turn into that. Here is something you could do to see if your model correlates to actual data. Fargo Rate and one of the Wisconsin leagues tracks player performance through games win and lost. As such there have thousands of actual match results from both formats. It would be interesting to see if the actual results match up to the predictions in your model and Bob's.

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