There would have to be a great deal of data and there would have to be data separated by winner breaks and loser breaks. Further, the breaker of each game would have to be known.
The OPs simulation had 20,000,000 games between just two players.
winner vs alternate break, computer simulated
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The OPs simulation had 20,000,000 games between just two players.
I think a lot of players prefer to play alternate break tournaments for similar reasons, and there are even some spectators that can appreciate the tension of the format. Personally, I like knowing that I still have a chance any time I step up to the table and the pressure of knowing that any miss could be my last shot of the match.
Yes that would be good, unfortunately some people see things as black and white so this may not happen.
winning chance when breaking = WCB
The effect mainly happens when both players win a lot when breaking
Let's say p2 has a WCB of 75%
Race to 9 with p1 getting 1 game on the wire
If p1 has a 30% WCB then it doesn't matter if its winner or alternate
p1 has a 40% WCB then p1 wins 1% more matches in alternate compared to winner
p1 has a 50% WCB then p1 wins 2% more..
p1 has a 60% WCB then p1 wins 4% more..
Going extreme, top pros playing each other in bar table 8 ball (although this probably won't happen with a 1 game spot, maybe gambling?)
If p1 WCB 80% and p2 WCB 85%
p1 wins 9% more matches (43% vs 52%) in alternate compared to winner
Interesting to note that if the players break only slightly better, there is still a huge difference. p1 WCB 80% and p2 WCB 81%
p1 wins 7% more matches in alternate
The effect mainly happens when both players win a lot when breaking
Let's say p2 has a WCB of 75%
Race to 9 with p1 getting 1 game on the wire
If p1 has a 30% WCB then it doesn't matter if its winner or alternate
p1 has a 40% WCB then p1 wins 1% more matches in alternate compared to winner
p1 has a 50% WCB then p1 wins 2% more..
p1 has a 60% WCB then p1 wins 4% more..
Going extreme, top pros playing each other in bar table 8 ball (although this probably won't happen with a 1 game spot, maybe gambling?)
If p1 WCB 80% and p2 WCB 85%
p1 wins 9% more matches (43% vs 52%) in alternate compared to winner
Interesting to note that if the players break only slightly better, there is still a huge difference. p1 WCB 80% and p2 WCB 81%
p1 wins 7% more matches in alternate
I would have expected the point where winner vs. alternate breaks leveled out to be at WCB(p1) = 25% (since that would give them a 25% chance of winning any given game, regardless of the breaker). Any explanation for it being at 30%?
There is a very slight effect at 30%. Looks like somewhere around 26.5% is the break even point
atlarge, do you have enough data to compare performance between alternate and winner?
Well, I've posted stats threads on many events for both winner breaks and alternate breaks. But some of the events are 8-Ball, some 9-Ball, some 10-Ball, some on 7-footers, some on 9-footers, a few on 10-footers -- and many differences among the events in the rules being used.
Spending a lot of time trying to filter out something significant and meaningful from all those events is not something I'm inclined to do. I'm satisfied with the mathematical conclusions posted by folks like Bob Jewett and ineedaspot. The rest seems to be just personal preference. For me, either way is fine if the race is long, but I prefer alternate breaks for short races. [So what's long and what's short?
]
Assuming identically distributed gameplay, the expectation of who wins is going to be identical regardless of break format. However the matches will play out differently, at least for players with a reasonable chance of putting together packages. Specifically, average margins will be much closer with alternate break than with winner breaks.
I ran some simulations on this and will post the results in a little bit.
I ran some simulations on this and will post the results in a little bit.
This is based on 20,000 simulated matches in each length.
- Winner break vs alternate breaks has no appreciable impact on the ultimate result.
- However when players with the ability to string together packages are involved, which is approximated by the likelihood of winning a game in which they are the breaker, the winning margins are quite a bit smaller in the alternate break setting.
- In a match between two players who don't have an advantage on the break the format is irrelevant to both the result and margin.
I can run other versions of this if people want.
Even race it makes no difference. However it does make a difference in the games won, which changes the result if you have a handicap involved.
Good point.
Sandbaggers and higher-rated players should support alternate break because it will help them hide their true speed in FargoRate
An interesting stat might be the 'chance of the breaker winning if they broke and ran the previous game' =]
That I could do pretty easily. Interested in any particular event(s)?
[You say the "chance," but the stat would be the actual percentage of such occurrences in the streamed matches I watched.]
That would be awesome. Any 'pro' tournament that is winner break would be good. Would be fun to see stats on the great breakers like Shaw or Van Boening playing big table 9 or 10 ball.
I've wasted an entire hour thinking about this. Easy to prove a race to 2 or 3, but to make a general proof for a race to n games is mighty tough...at least for me it is.
If you ever do work out a proof, let us know.
But since it is possible to calculate the percentages exactly in, for example, Excel, sims are not needed. If anyone else wants a copy of the spreadsheet, just ask. Here is an example match up. The number in each box is the chance that the corresponding score will occur, so a score of 0-0 is certain to happen and a score of 11-11 is impossible because in this run they are playing to 11.
It is possible to calculate the chances with a spot of games on the wire by adding up the appropriate row or column that corresponds to a win by the spotted player.
![CropperCapture[2].png](https://forums.azbilliards.com/data/attachments/337/337130-159cbbea246c9d05d225449374615da9.jpg "CropperCapture[2].png")
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That alteranate vs. winner breaks has the same match probabilities for a given pair of "wins-when-breaking" probabilities. This is found to be true (calculated over many cases) regardless of match length and WWB and lag-win probabilities.