Mathematical analysis of Predator format (sets)

T

tomker

AzB Silver Member
Silver Member
Out of curiosity, I wrote a program that enumerates all possible outcomes of a Predator Pro Billiards Series match and collected some stats that I thought might be interesting to people.

Assuming:
- Player A is rated 50 Fargo points higher than Player B (odds of him winning any particular rack: 58.58%)
- The odds of Player A winning a shootout are the same as his odds of winning a rack

Here are the stats I've calculated:
- The odds of Player A winning a Predator match against player B: 76.12%
- The odds of Player A winning the match but NOT winning more racks: 3.07%
- The odds of the match going to a shootout: 7.25%
- The odds of Player A winning 9 racks but losing the match: 5.17%
- The average number of racks played for a Predator match between these two players: 13.93

Ultimately, the odds of player A winning such a match are the same as if the players just played a regular race-to-9 match.

Disclaimer: I'm not trying to say that either format is better, I just wanted to have a better understanding of how the formats compare to each other.
 
tomker said:
Out of curiosity, I wrote a program that enumerates all possible outcomes of a Predator Pro Billiards Series match and collected some stats that I thought might be interesting to people.

Assuming:
- Player A is rated 50 Fargo points higher than Player B (odds of him winning any particular rack: 58.58%)
- The odds of Player A winning a shootout are the same as his odds of winning a rack

Here are the stats I've calculated:
- The odds of Player A winning a Predator match against player B: 76.12%
- The odds of Player A winning the match but NOT winning more racks: 3.07%
- The odds of the match going to a shootout: 7.25%
- The odds of Player A winning 9 racks but losing the match: 5.17%
- The average number of racks played for a Predator match between these two players: 13.93

Ultimately, the odds of player A winning such a match are the same as if the players just played a regular race-to-9 match.

Disclaimer: I'm not trying to say that either format is better, I just wanted to have a better understanding of how the formats compare to each other.
Click to expand...
World 10ball Stage 1 is best of three sets. World 10ball Stage 2 is best of five sets. Which type of match have you analyzed?
 
sjm said:
World 10ball Stage 1 is best of three sets. World 10ball Stage 2 is best of five sets. Which type of match have you analyzed?
Click to expand...
Didn't realize that. I was doing best of 3 sets.

For best of 5:

- The odds of Player A winning against player B: 81.26%
- The odds of Player A winning the match but NOT winning more racks: 2.75%
- The odds of the match going to a shootout: 4.71%
- The average number of racks played: 22.52

So that falls right between a race-to-13 and a race-to-14.
 
it feels like the odds of a 650 beating a 600 is different than of joshua filler (864) beating aleksa pecelj (814). kledio, pijus, chang yu lung are also in that 50 point lower than filler range.

the gap between 600 and 650 i know from experience is huge. but from what i have observed in watching the pro scene, i wouldn't say it's an identical difference. doesn't mean those odds are wrong, though i think they may be, but that they wouldn't be the same.

(i would fire at pecelj 18.74% / 5.3)
 
Interestingly, I think this analysis might show the sets format gives the weaker player a better chance (depending on assumptions).

With three sets being equivalent to a single race to 9, if we count the shootout as one rack (consistent with the original assumptions), then the three-sets format has a maximum rack total of 21, whereas a race to 9 is capped at 17.

Similarly, a five-set match has a 35-game max, and a race to 14 has a 27-game max.

In general, a weaker player has a better chance with fewer racks played. Therefore, for any given number of maximum racks, the weaker player should prefer sets. A race to 11 (21 racks max) is "harder" than three races to 4 (also 21 racks max), which is only the same difficulty as a race to 9.

The only caveat is the probability of any given race length. A straight race to 11 is more likely to go 21 racks than the three sets, if for no other reason than a 4-0, 4-1, or 4-2 start means the sets match can't go the maximum number of racks.

I'm guessing Predator knows all this. I think the sets format is designed to keep probabilities close, and expected time close (so, three sets the same as a race to 9 by both measures) while making drama/interest higher than in a straight race. Every rack seems more important to the viewer in sets, and the periodic reset to 0-0 seems to keep the trailing player in the match more.
 
skogstokig said:
it feels like the odds of a 650 beating a 600 is different than of joshua filler (864) beating aleksa pecelj (814). kledio, pijus, chang yu lung are also in that 50 point lower than filler range.

the gap between 600 and 650 i know from experience is huge. but from what i have observed in watching the pro scene, i wouldn't say it's an identical difference. doesn't mean those odds are wrong, though i think they may be, but that they wouldn't be the same.

(i would fire at pecelj 18.74% / 5.3)
Click to expand...
Mathematically, the way Fargo ratings are calculated, the difference is the same.

I think the difference you're seeing is that, at very high ratings, both players have high likelihood of a clearance. So the difference for any given rack is harder to notice. You probably have to zoom out to the match level to see the same difference that you see for lower-rated players. But, ultimately, the difference is the same.
 
skogstokig said:
it feels like the odds of a 650 beating a 600 is different than of joshua filler (864) beating aleksa pecelj (814). kledio, pijus, chang yu lung are also in that 50 point lower than filler range.

the gap between 600 and 650 i know from experience is huge. but from what i have observed in watching the pro scene, i wouldn't say it's an identical difference. doesn't mean those odds are wrong, though i think they may be, but that they wouldn't be the same.

(i would fire at pecelj 18.74% / 5.3)
Click to expand...
From my understanding, they should be the same. An x-point difference is meant to correspond to a y-percent chance, regardless of where on the scale folks are.

This aligns with my experiences, both playing at my very modest ability, and watching top pros. There's a lot (over 70) of 800+ players now, but it's still quite disproportionately the handful of 830+ guys who are taking down the titles.
 
Rocket354 said:
Interestingly, I think this analysis might show the sets format gives the weaker player a better chance (depending on assumptions).
...
Click to expand...
I modified my Fargo match odds calculator to display the likely number of racks played in a match:


For a race to 9, Fargo difference of 50, the odds of the stronger player winning are 76.52 percent, and the average match length is 14.23 racks.

Compare to a Predator best-of-3-sets match, the odds of the stronger player winning are 76.12 percent, and the average match length is 13.93 racks.

So there's basically no difference in it. The formats might as well be the same from the perspective of either player.
 
This reminds me of poker solvers. People can get really in the weeds with this stuff. Nerd Fodder more than anything. That's not meant to be an insult at all, more just to say that these numbers are not particularly predictive/reliable in ONE MATCH or even ONE EVENT. Over the course of 1000 matches or 100 events I'm sure the number bare out to some degree and are reliable but if you were to try to use them to bet individual matches, I Believe you'd have some rude awakenings.
 
tomker said:
Mathematically, the way Fargo ratings are calculated, the difference is the same.

I think the difference you're seeing is that, at very high ratings, both players have high likelihood of a clearance. So the difference for any given rack is harder to notice. You probably have to zoom out to the match level to see the same difference that you see for lower-rated players. But, ultimately, the difference is the same.
Click to expand...

could there be fargo creep at the top? is filler that much better than some year ago when he was at 825? i have no doubt filler is a better player than pecelj/kledio/chang, i'm just saying few people would set the odds for pecelj at 5.3 (that's euro odds, so 5.3x the money) whereas at the other example it seems like reasonable odds
 
tomker said:
Out of curiosity, I wrote a program that enumerates all possible outcomes of a Predator Pro Billiards Series match and collected some stats that I thought might be interesting to people.

Assuming:
- Player A is rated 50 Fargo points higher than Player B (odds of him winning any particular rack: 58.58%)
- The odds of Player A winning a shootout are the same as his odds of winning a rack

Here are the stats I've calculated:
- The odds of Player A winning a Predator match against player B: 76.12%
- The odds of Player A winning the match but NOT winning more racks: 3.07%
- The odds of the match going to a shootout: 7.25%
- The odds of Player A winning 9 racks but losing the match: 5.17%
- The average number of racks played for a Predator match between these two players: 13.93

Ultimately, the odds of player A winning such a match are the same as if the players just played a regular race-to-9 match.

Disclaimer: I'm not trying to say that either format is better, I just wanted to have a better understanding of how the formats compare to each other.
Click to expand...
The pressure gradients - which probably don't affect math, will be different than in a straight ahead set. (people are dumm)
Also the numbers don't add the same as in a straight ahead set.
Lastly, I have no idea if I'm talking nonsense or not.
 
It would be interesting to run down the data whether it is easier to win a match race to 9 after down 4-0 than with a Predator BO3 format after losing the first set 4-0. With Fargo ratings of course.
 
InsertCleverNameHere said:
This reminds me of poker solvers. People can get really in the weeds with this stuff. Nerd Fodder more than anything. That's not meant to be an insult at all, more just to say that these numbers are not particularly predictive/reliable in ONE MATCH or even ONE EVENT. Over the course of 1000 matches or 100 events I'm sure the number bare out to some degree and are reliable but if you were to try to use them to bet individual matches, I Believe you'd have some rude awakenings.
Click to expand...
As stated in the original post, I only did this to see how the formats compare to each other. Nothing about betting.
 
skogstokig said:
could there be fargo creep at the top? is filler that much better than some year ago when he was at 825? i have no doubt filler is a better player than pecelj/kledio/chang, i'm just saying few people would set the odds for pecelj at 5.3 (that's euro odds, so 5.3x the money) whereas at the other example it seems like reasonable odds
Click to expand...
The way Fargo is calculated, it only ensures that the relative relationships between players are as accurate as possible.

As far as I know, no effort is made to ensure that a particular Fargo rating translates to a certain level of play. There is no reason to believe that e.g. 800 today means the same thing that it did a few years ago.
 
mjantti said:
It would be interesting to run down the data whether it is easier to win a match race to 9 after down 4-0 than with a Predator BO3 format after losing the first set 4-0. With Fargo ratings of course.
Click to expand...
Assuming two players, Player A is +50 Fargo vs. Player B.

In a race to 9, if Player A is down 0-4, his odds of winning are 31.47%.

In the Predator BO3 format, if player A loses the first set 0-4, his odds of winning are still 46.54%.
 
tomker said:
Assuming two players, Player A is +50 Fargo vs. Player B.

In a race to 9, if Player A is down 0-4, his odds of winning are 31.47%.

In the Predator BO3 format, if player A loses the first set 0-4, his odds of winning are still 46.54%.
Click to expand...
Doesn't this run counter to your hypothesis that the odds are the same between the two formats?
 
nmh2008 said:
Doesn't this run counter to your hypothesis that the odds are the same between the two formats?
Click to expand...
The odds could be similar overall, but different in particular settings conditional on what has happened so far.

The question at hand isn’t “are the formats the same after one player wins the first 4 games in a row?” Clearly they are not, as a traditional format banks those wins while predator consolidates them into a single set. In a traditional format, being down 4-3 is better than being down 4-0. In a set format, they are the same.
 
tomker said:
Assuming two players, Player A is +50 Fargo vs. Player B.

In a race to 9, if Player A is down 0-4, his odds of winning are 31.47%.

In the Predator BO3 format, if player A loses the first set 0-4, his odds of winning are still 46.54%.
Click to expand...
And that's the crux of it. The sets format keeps the drama high throughout the match.

I really like the sets format. Other than the shootout, of course.
 
You must log in or register to reply here.
Back
Top