Match probability calculator, given Fargo ratings

[Bob Jewett]

So you're saying that the ghost Fargo level, even though it never misses or makes a mistake, can be not much more than a B or A player if a C player plays it and gets a few games on it before losing? ...

No, the ghost made the mistake of giving up the break and ball in hand after the break. With that handicap, the ghost plays at about the 760 level on Nick's table. It would be really interesting to see how the ghost would do against a 760 player on that table. By the simple theory, it would be an even match.

If the ghost played on a tournament table with 4-inch pockets, he would have a higher Fargo rating because he's not giving up as much spot. I'd guess at least 800. For 10 ball on a 12-foot snooker table, he might be a 900.

On the other hand, I can imagine a player who has a high Fargo because he ties his opponents in knots with safety play. That doesn't work against the ghost. I can't think of any top player who does depend on safeties.

 

[Patrick Johnson]

The takeaway I get from this is that there is no “the ghost” - it’s always “your ghost for this table.”

pj
chgo

 

[hang-the-9]

No, the ghost made the mistake of giving up the break and ball in hand after the break. With that handicap, the ghost plays at about the 760 level on Nick's table. It would be really interesting to see how the ghost would do against a 760 player on that table. By the simple theory, it would be an even match.

If the ghost played on a tournament table with 4-inch pockets, he would have a higher Fargo rating because he's not giving up as much spot. I'd guess at least 800. For 10 ball on a 12-foot snooker table, he might be a 900.

On the other hand, I can imagine a player who has a high Fargo because he ties his opponents in knots with safety play. That doesn't work against the ghost. I can't think of any top player who does depend on safeties.

Right, Fargo would give you a relative rating to the player. I am taking the handicap out of it, just going by raw skill, not how well it can win, because you can game the handicap enough to make a win against the ghost easier. Ball in hand vs no ball in hand, play the 7 ball ghost, etc... It's not a match-up between gamblers looking for weight. If we look at Fargo at just a ranking for how good a player is, like the TPA scale does, would not the ghost be a perfect player, thus should be rated as basically an infinitely high Fargo since no human can match it? All of us should be in agreement that no one on the planet from Mosconi, to Reyes, to Gorst is infallible, but the ghost is. The ghost will play at a 1.000 TPA every match, correct? 0 mistakes, no matter what the opponent can do. No player, ever, has played at a 1.000 TPA in a whole tournament, never mind ALL the time. Can we, in good faith, say that a player that is always at a perfect game be an iota under the top ranked player on the planet?

If we ask "what should a Fargo rated player of X be able to do at the table", we can give some good general guidelines. We know how well a 600 player plays, and we know how well an 800 player plays, because, well, reality and looking. So if we describe a player that never misses, and wins 100% of the time if the other player makes any mistake, what rating can we possibly give that player aside from higher than anyone else except another player that wins 100% of the time.

How the Fargo system rates players ends up in a funny way with Mr Ghost. We really should have the ghost as two different players in the system, as a lazy player, that only plays good enough to try to beat someone they are playing against but no better. But at the same time we can rate the ghost as an amazing player that can never be beat over the long haul, in theory, and be one of those legends that road players talk about never missing a ball and robbing everyone.

 

[Sheldon]

All of us should be in agreement that no one on the planet from Mosconi, to Reyes, to Gorst is infallible, but the ghost is. The ghost will play at a 1.000 TPA every match, correct? 0 mistakes, no matter what the opponent can do. No player, ever, has played at a 1.000 TPA in a whole tournament, never mind ALL the time.

The Ghost scratches on the break every time. By your logic, the ghost is a horrible player with a negative fargo rating.

 

[mikepage]

[...] The ghost will play at a 1.000 TPA every match, correct?

Don't think of the ghost like that here. Think of the ghost as YOUR opponent in this particular "game." The game is YOU always go first and attempt to do something (run out or make a spot shot or whatever.) The ghost only participates when you fail.

So if Gorst runs out two thirds of the racks on a particular table, this ghost is winning one third of the games against Gorst. If a 640 player runs out one third of the time on the same table, this ghost is winning two thirds. Either way the ghost is performing like a 740.

 

[hang-the-9]

The Ghost scratches on the break every time. By your logic, the ghost is a horrible player with a negative fargo rating.

Not so, the Ghost just gives you ball in hand and all the breaks because it's better than anyone. You are assuming you get the ball in hand because of the scratch, but it does not need to mean that. I have seen many pros play matches with that handicap.

 

[hang-the-9]

Don't think of the ghost like that here. Think of the ghost as YOUR opponent in this particular "game." The game is YOU always go first and attempt to do something (run out or make a spot shot or whatever.) The ghost only participates when you fail.

So if Gorst runs out two thirds of the racks on a particular table, this ghost is winning one third of the games against Gorst. If a 640 player runs out one third of the time on the same table, this ghost is winning two thirds. Either way the ghost is performing like a 740.

Why can't I (we) think of the ghost like that? That would make the answer not fully correct if we put restrictions on our thinking. It would like like "well we got this faulty result, but if we remove the fact that gravity exists, we will get the predicted answer" LOL.

Is there a reasonable way to refute this logic: If the ghost never makes a mistake, it has a 1.000 TPA all the time. A player with a 1.000 TPA is a perfect player. A perfect player can't possibly be a 740 because players that are 800 are not perfect. Pretend this is a scientific / logic paper I am putting forth to a professor. Where is the flaw in this thinking? Math is solid here. You can't get a better player that never makes a mistake, technically or mentally. It will never rattle a ball, it will never shake on a shot because a cute girl is watching, a crashing plane won't disturb it's stance.

I am not saying the Fargo ratings are wrong, or bad, I am saying the Ghost player is not well suited to the way it measures ratings and performances and exists in a sort of Schrodinger's Cat / Pandora's Box / Speed of Light thing, where how we rank the Ghost depends on the observer and logic used to describe it. The Ghost is a perfect player when using the TPA system, but is not a perfect player using the Fargo system. They are both technically correct, but I think the TPA system, using my logic about a perfect player, would describe the skill of Ghost better.

I love the Fargo system, I also think it's a fun mental thing to look at the ghost player skill level in it and present my side of what it should be. And I stick by my thinking that a perfect player like the Ghost, would have a basically infinite Fargo as it will always be past the best human. And that we may need to have TWO Ghost players in the system, one that is tied to every player based on the relative skill, and one that is #1 no matter how high the Fargo Babel's Tower gets.

I don't know about anyone else, but I am really enjoying this mental game thinking about how we would rate the Ghost in different ways LOL And it seems if we look at it from different ratings, that would rank a human player very well, the ratings break down when talking about theoretical perfection.

 

[mikepage]

[...]

Is there a reasonable way to refute this logic: If the ghost never makes a mistake, it has a 1.000 TPA all the time. [...]

Nobody is refuting that. It's just that a hypothetical "rating" for a pretend player who never misses is not, unless somebody can convince me otherwise, a particularly useful or interesting thing.

Here is something different that I DO find interesting. Suppose I'm a 530 and I play for a few hours in my basement every Tuesday and Thursday.
On Tuesday, I always play 8-Ball games against my friend Harry, also a 530. After many Tuesdays we're dead even, 150 to 150, consistent with us both playing at the same speed, likely around 530.

Harry works Thursdays, so I play by myself. I always do the same thing. I break, remove all the stripes, take ball in hand, and try to run out the solids and 8-Ball. After many Thursdays, I'm at 150 successes and 150 failures. I have the same success rate at this task as I have playing games against Harry.

Moving forward, a GOOD Tuesday outcome is one where I beat Harry--win more games than I lose.
and a GOOD Thursday outcome is one where I win more than I lose against Victor, the name I've given to the opponent of success on the Thursday task.

So Victor is already interesting to ME. He acts like a worthy opponent. If I'm distracted I'll probably lose to Victor. If I don't stay down on the shots, I'll probably lose to Victor. If I can bring my A game, I'll probably beat Victor.

What would make it even more interesting is whether Victor generalizes as playing the role of a 530 opponent. For instance, a 630-rated friend would win about 200 to 100 against Harry. And a 430-rated friend would win about 100 to 200 against Harry. Would these players fare similarly playing "games" against Victor? If so, the idea of assigning a rating to a task is, imo, even more interesting and useful.

The preliminary evidence is it does work out. That suggests "9-ball ghost on an average 9-foot table" has a rating, and "9-Ball ghost on a Valley bar table" has a different rating, etc. These are all defined with a task and the human player attempting the task first.

 

[Pete H]

Fargo rating for a perfect player: infinite.

The percentage of people who don't have a clue about statistics and probabilities: 99 and change.

 

[iusedtoberich]

I asked in the 2025 AZB ghost thread if any members would be willing to post “all” of their set scores for a period of time, even if they got blanked. I’ll do the same again. It will be interesting what the ghost ends up at for whomever keeps stats.

I do think my ghost of 762 was a bit high. I personally think it would end up about 720. A lot of people over the years put the ghost at about 650. I’d empty out betting against a 650 winning on a 9’ Gold Crown with factory 5” pockets.

9’ Diamond with pro cut pockets I’d put about 750.

 

[ShortBusRuss]

I asked in the 2025 AZB ghost thread if any members would be willing to post “all” of their set scores for a period of time, even if they got blanked. I’ll do the same again. It will be interesting what the ghost ends up at for whomever keeps stats.

I do think my ghost of 762 was a bit high. I personally think it would end up about 720. A lot of people over the years put the ghost at about 650. I’d empty out betting against a 650 winning on a 9’ Gold Crown with factory 5” pockets.

9’ Diamond with pro cut pockets I’d put about 750.

Rly? You put me at about 610 (which I think is about right for how I was playing when you saw me), and you've seen me on video beating the ghost 7-3 on a Diamond Pro/Am 4 3/8" table..

I realize that was a single set, and I am likely not a favorite to do that 100% of the time.. But on a Brunswick with 5" pockets, I like my chances...

I think a 650 FR player plays a lot better than you think...

 

[iusedtoberich]

Rly? You put me at about 610 (which I think is about right for how I was playing when you saw me), and you've seen me on video beating the ghost 7-3 on a Diamond Pro/Am 4 3/8" table..

I realize that was a single set, and I am likely not a favorite to do that 100% of the time.. But on a Brunswick with 5" pockets, I like my chances...

I think a 650 FR player plays a lot better than you think...

You can bet all you like you’re not beating the ghost on a factory pocket GC. Assuming you are betting every set.

 

[tomker]

...
Is there a reasonable way to refute this logic: If the ghost never makes a mistake ...

The ghost makes a pretty bad mistake literally every single rack, resulting in the opponent getting ball in hand.

 

[slyfox3]

Is there any way to get the calculator to work for high numbers? I'm trying to figure out the performance rating of the ghost on my home table vs me. 98-366 is my aggregate 9 ball ghost score for all of 2024. I'm a 572. It does not give results for high race to numbers.

View attachment 799963

I actually wrote a calculator using dynamic programming instead of combinatorics that can calculate odds of a race to few hundreds, in fact, a few hundred of those races, in a split second, in your browser.

For example, a 572 has 51.11% chance of winning a 98 to 366 race against a 762 ghost, as computed here (hover at the bottom of the chart):
https://slyfox3.github.io/FargoRateRaceChartViz/?p1=572&p2=762&race=245

-Arnie

 

[Oikawa]

Why can't I (we) think of the ghost like that? That would make the answer not fully correct if we put restrictions on our thinking. It would like like "well we got this faulty result, but if we remove the fact that gravity exists, we will get the predicted answer" LOL.

Is there a reasonable way to refute this logic: If the ghost never makes a mistake, it has a 1.000 TPA all the time. A player with a 1.000 TPA is a perfect player. A perfect player can't possibly be a 740 because players that are 800 are not perfect.

The issue with your logic is that you are saying the ghost can't possibly be perfect (1.000 TPA) with only 740 fargo, which would indeed be faulty if the rules were that the ghost always broke and therefore had an infinite series of break-and-runs. But the definition of the ghost is that the opponent of the ghost always breaks and gets BIH after the break. With this taken into account, having a 1.000 TPA with 740 fargo is no longer a logical impossibility.

Imagine Joshua Filler giving odds against someone such that his opponent always gets the break, and BIH after the break. The effective fargo of Filler playing with these rules would be much less than his normal rating of 850ish. He would play worse than the ghost, since both him and the ghost would give up the break and BIH, but Filler would sometimes miss, whereas the ghost wouldn't. The ghost would still have a TPA of 1.000, and Filler would still have (almost) his normal TPA (a bit less because he'd get worse positions to shoot at on average due to never continuing off his own break), without any logic being broken.

I am not saying the Fargo ratings are wrong, or bad, I am saying the Ghost player is not well suited to the way it measures ratings and performances and exists in a sort of Schrodinger's Cat / Pandora's Box / Speed of Light thing, where how we rank the Ghost depends on the observer and logic used to describe it. The Ghost is a perfect player when using the TPA system, but is not a perfect player using the Fargo system. They are both technically correct, but I think the TPA system, using my logic about a perfect player, would describe the skill of Ghost better.

I don't see how the ghost is not well suited for measuring fargo ratings at all. Perhaps you could elaborate on this point? I don't understand what you mean by the ranking of the ghost being dependant on the observer.

 

[ShortBusRuss]

I actually wrote a calculator using dynamic programming instead of combinatorics that can calculate odds of a race to few hundreds, in fact, a few hundred of those races, in a split second, in your browser.

For example, a 572 has 51.11% chance of winning a 98 to 366 race against a 762 ghost, as computed here (hover at the bottom of the chart):
https://slyfox3.github.io/FargoRateRaceChartViz/?p1=572&p2=762&race=245

-Arnie

Tried it.. Couldn't understand the results. Wanted to see what the odds of me getting to 5 in a race to 9 against Tony Chohan, given a 225 point Fargorate gap. (Which I did at DCC 2023....)

What the heck is an "R9"? Race to 9? Why do the results come back negative? I think the "expectation" is I get just under 2 games.

Why would I be interested in some color code? Seems overly complicated.

Bruhhhhh. Just give options to either set a number for both sides, and spit out a percentage for both sides... Or if only a "race to" # is given for one side, spit out the "fair match value" for the other. With maybe a bracketed readout/percentage for a few games more/less of a spot.

And I mean.... "I guess" some people might be interested in crazy long races percentages. But most people want to see tournament numbers... Race to 5... 7.....9... and 11...

Oh.. And after I put in 548/775 for the players, and put in R9... Half the time the entire page bombed out, and I had to close and reopen from your link..

 

[Oikawa]

Tried it.. Couldn't understand the results. Wanted to see what the odds of me getting to 5 in a race to 9 against Tony Chohan, given a 225 point Fargorate gap. (Which I did at DCC 2023....)

What the heck is an "R9"? Race to 9? Why do the results come back negative? I think the "expectation" is I get just under 2 games.

Why would I be interested in some color code? Seems overly complicated.

Bruhhhhh. Just give options to either set a number for both sides, and spit out a percentage for both sides... Or if only a "race to" # is given for one side, spit out the "fair match value" for the other. With maybe a bracketed readout/percentage for a few games more/less of a spot.

And I mean.... "I guess" some people might be interested in crazy long races percentages. But most people want to see tournament numbers... Race to 5... 7.....9... and 11...

Oh.. And after I put in 548/775 for the players, and put in R9... Half the time the entire page bombed out, and I had to close and reopen from your link..

On the site it says "Hover on the heatmap to see winning odds. (You can zoom in for more detail)".

The heat map is a grid containing all the possible combinations of different frame amounts you and your opponent race to, showing the likelihood of winning for each side.

For your case of 5-9 against +225 fargo, you could check the probability of winning a race with you requiring 5 frames and your opponent requiring 9, which comes off at 5.97% odds for a 225 fargo difference.

 

[ShortBusRuss]

On the site it says "Hover on the heatmap to see winning odds. (You can zoom in for more detail)".

The heat map is a grid containing all the possible combinations of different frame amounts you and your opponent race to, showing the likelihood of winning for each side.

For your case of 5-9 against +225 fargo, you could check the probability of winning a race with you requiring 5 frames and your opponent requiring 9, which comes off at 5.97% odds for a 225 fargo difference.

Good lord. I did feel that I was a bit underrated, and felt like I played "good" on Tony... But 6% odds of getting to 5??? And those were 4 1/8" pockets!

 

[slyfox3]

Tried it.. Couldn't understand the results. Wanted to see what the odds of me getting to 5 in a race to 9 against Tony Chohan, given a 225 point Fargorate gap. (Which I did at DCC 2023....)

What the heck is an "R9"? Race to 9? Why do the results come back negative? I think the "expectation" is I get just under 2 games.

Why would I be interested in some color code? Seems overly complicated.

Bruhhhhh. Just give options to either set a number for both sides, and spit out a percentage for both sides... Or if only a "race to" # is given for one side, spit out the "fair match value" for the other. With maybe a bracketed readout/percentage for a few games more/less of a spot.

And I mean.... "I guess" some people might be interested in crazy long races percentages. But most people want to see tournament numbers... Race to 5... 7.....9... and 11...

Oh.. And after I put in 548/775 for the players, and put in R9... Half the time the entire page bombed out, and I had to close and reopen from your link..

R9 chart for 548F vs 775F, works totally fine:
https://slyfox3.github.io/FargoRateRaceChartViz/?p1=548&p2=775&race=9

This is a hobby project of mine, a superset of a simple calculator. I was curious to visually see how odds change at realtime, and how "HOT" handicap sits at the intersection of the segments in the chart.

If you find anything not working on your end, please report an issue.

R9 is not just race to 9, it's a set of possible races capped by 17 racks max (races to 9-9, 9-8, 10-8, .10-7, 11-7, ...), explained HERE

-Arnie

 

[hang-the-9]

The issue with your logic is that you are saying the ghost can't possibly be perfect (1.000 TPA) with only 740 fargo, which would indeed be faulty if the rules were that the ghost always broke and therefore had an infinite series of break-and-runs. But the definition of the ghost is that the opponent of the ghost always breaks and gets BIH after the break. With this taken into account, having a 1.000 TPA with 740 fargo is no longer a logical impossibility.

Imagine Joshua Filler giving odds against someone such that his opponent always gets the break, and BIH after the break. The effective fargo of Filler playing with these rules would be much less than his normal rating of 850ish. He would play worse than the ghost, since both him and the ghost would give up the break and BIH, but Filler would sometimes miss, whereas the ghost wouldn't. The ghost would still have a TPA of 1.000, and Filler would still have (almost) his normal TPA (a bit less because he'd get worse positions to shoot at on average due to never continuing off his own break), without any logic being broken.



I don't see how the ghost is not well suited for measuring fargo ratings at all. Perhaps you could elaborate on this point? I don't understand what you mean by the ranking of the ghost being dependant on the observer.

The Ghost definition is how you play against it, not it's skill level. The skill level is that it never misses or makes an error. The player is the one that gets the handicap of first break and ball in hand, or no ball in hand in the advanced version. The Ghost, as an imaginary player opponent, does not care who it's playing, it never misses against anyone.

As for measuring the Fargo rating of a player when doing the ghost play, you would of course need known Fargo skill ratings of existing players to do that. We know that to beat the 9-ball ghost in a race to say 7, a player would need to be a certain Fargo rating, about a 630-670, from existing data. Then going by that you can estimate how good a player is by how much they beat the ghost. A player winning 7-6 is a worse player than one that wins 7-3. And then you can play the 10/11/12 ball ghost which the better pros do and estimate a rating based on that.

By the rating being based on the observer, it means that in a vacuum of no players, the Ghost is an infinite Fargo since it NEVER misses. Once you start playing, how the ghost rating ends up in reality is dependent on the player, so it starts to flow and change as we observe the results. It's almost like when we had to create a new temperature scale for very low and very high temperatures, Kelvin, since the other scales we use to measure normal temps on Earth were not suitable to experimental and rare temperatures found in physics. With the Ghost being the perfect player, our human based ratings fail it, so we need a new way to measure how good that player is based on our human failures to not be perfect. Fargo still fails the Ghost, but TPA does not. The ghost has a TPA or 1.000, anytime it plays.

Fargo does not have a rating to measure a perfect player since there is theoretically no upper limit to it, since it measures human performance. Eventually, if we get the Ghost race high enough, say a 15 ball Rotation Ghost, the Ghost will beat out the highest Fargo since I don't think anyone out there can beat the Ghost in Rotation. We just need to give the Ghost a high enough game where it's skill can show, playing the 9 ball or even 10 ball Ghost is like an 800 Fargo playing a 600 Fargo a single game, the 600 has an OK chance to win that one game, especially when we give the 600 the break. We need to give the Ghost a long enough race to show its skill, much like the better players are favored in a longer race. Think of the Ghost as a race car built for top end speed vs short distances. You may have a car that can beat it to 60, or even 100, but give it a long enough track, the other cars will fall behind eventually.