Fargorate match odds puzzle

JC

JC

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Player A has a 59.8 chance of winning a set against Player B who is at 40.2%

What then is the probability of Player A winning a match that consists of a race to five of the sets described above?

All we know is Fargo considers player A a 59.8% favorite in each of the sets.

Does it matter the individual's relative fargos? Or how long the race is in each set?

Fargo is supposed to take all this into consideration right?

So does Player B have a chance in hell to grab the cheese or not in the five set match?


JC
 
Bob Jewett

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JC said:
Player A has a 59.8 chance of winning a set against Player B who is at 40.2%

What then is the probability of Player A winning a match that consists of a race to five of the sets described above?

All we know is Fargo considers player A a 59.8% favorite in each of the sets.

Does it matter the individual's relative fargos? Or how long the race is in each set?

Fargo is supposed to take all this into consideration right?

So does Player B have a chance in hell to grab the cheese or not in the five set match?


JC
Click to expand...
You can simply treat the matches as games and use the tools on Fargorate to calculate the odds for you. First you need to find the rating difference that gives a single-game odds of 59.8%. That would be 57 points apart. Then you set the match length to 5 and get 72% for the better player.

The individual ratings make no difference, but you could find the rating difference between the players if you knew the match length that gave 59.8%. The way Fargo works, it is only rating difference that is important and not actual rating. An 820 playing a 700 has the same chance as a 620 playing a 500 if they are playing the same length of match.
 
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Masayoshi

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Look up binomial probability on google, find the binomial probablility of winning 3 sets, 4 sets, and 5 sets, and then add them up.
 
JC

JC

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Bob Jewett said:
You can simply treat the matches as games and use the tools on Fargorate to calculate the odds for you. First you need to find the rating difference that gives a single-game odds of 59.8%. That would be 57 points apart. Then you set the match length to 5 and get 72% for the better player.

The individual ratings make no difference, but you could find the rating difference between the players if you knew the match length that gave 59.8%. The way Fargo works, it is only rating difference that is important and not actual rating. An 820 playing a 700 has the same chance as a 620 playing a 500 if they are playing the same length of match.
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Let's say player B is 85 points higher than player A.

Does this matter at all compared to if Player A were the better player?

I know it's not supposed to but I'm not convinced.

JC
 
Bob Jewett

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Masayoshi said:
Look up binomial probability on google, find the binomial probablility of winning 3 sets, 4 sets, and 5 sets, and then add them up.
Click to expand...
The possible winning scores are 5-0, 5-1, 5-2, 5-3, and 5-4. If you are going to do it with binomials, I think you have to sum the chances of each of those outcomes. It's easier to just use the tools on Fargorate.
 
M

Masayoshi

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Bob Jewett said:
The possible winning scores are 5-0, 5-1, 5-2, 5-3, and 5-4. If you are going to do it with binomials, I think you have to sum the chances of each of those outcomes. It's easier to just use the tools on Fargorate.
Click to expand...

Ah, correct. For some reason, I thought he said a best out of 5 sets
 
Bob Jewett

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JC said:
Let's say player B is 85 points higher than player A.

Does this matter at all compared to if Player A were the better player?

I know it's not supposed to but I'm not convinced.

JC
Click to expand...
Maybe I don't understand the question. If two players are 85 points apart, the better player is expected to win 64.32% of the games that they play by the way that the FargoRate system is defined. It makes no difference to the system if you call the better player Mr. A or Joe Mooch.

If you mean that Billy Bob is a 600 player and he is playing Andy Ace who is a 685 player and then plays Sammy Spastic who is a 515 and you expect the odds to be different, then no, the odds are not different. The better player is 64.32% on each game. The ratings are assigned specifically to make the odds the same. The way the system is defined the odds have to come out the same.

That having been said, the system predicts that if an 800 plays a 600, the weaker player will win 20% of the games, and if a 600 plays a 400, the 400 will win 20% of the games. That is probably quite accurate on average for both cases. Where things can get dicey is when the 800 plays the 400 and is expected to win 94.11764706% (16/17ths) of the games. That is really hard to check because you would need a lot of games between players with that large a difference which doesn't normally happen.

Maybe Mike Page has some data on win ratio accuracy across wide ranges of rating difference. Or maybe he has already posted on the topic.:)
 
JC

JC

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Bob Jewett said:
Maybe I don't understand the question. If two players are 85 points apart, the better player is expected to win 64.32% of the games that they play by the way that the FargoRate system is defined. It makes no difference to the system if you call the better player Mr. A or Joe Mooch.

If you mean that Billy Bob is a 600 player and he is playing Andy Ace who is a 685 player and then plays Sammy Spastic who is a 515 and you expect the odds to be different, then no, the odds are not different. The better player is 64.32% on each game. The ratings are assigned specifically to make the odds the same. The way the system is defined the odds have to come out the same.

That having been said, the system predicts that if an 800 plays a 600, the weaker player will win 20% of the games, and if a 600 plays a 400, the 400 will win 20% of the games. That is probably quite accurate on average for both cases. Where things can get dicey is when the 800 plays the 400 and is expected to win 94.11764706% (16/17ths) of the games. That is really hard to check because you would need a lot of games between players with that large a difference which doesn't normally happen.

Maybe Mike Page has some data on win ratio accuracy across wide ranges of rating difference. Or maybe he has already posted on the topic.:)
Click to expand...

What I was saying is that in one scenario the match odds could be 60-40 because player A is better and they are playing an even race where another 60-40 scenario player B could be better and giving up games on the wire to make himself the dog.

IMO player B has a better chance to win the match I described if it's the second scenario than the first. I don't see this as an even proposition even though Fargo does. My lying eyes have told me otherwise. The math gets jinky when you add in variables.

JC
 
Bob Jewett

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JC said:
What I was saying is that in one scenario the match odds could be 60-40 because player A is better and they are playing an even race where another 60-40 scenario player B could be better and giving up games on the wire to make himself the dog.

IMO player B has a better chance to win the match I described if it's the second scenario than the first. I don't see this as an even proposition even though Fargo does. My lying eyes have told me otherwise. The math gets jinky when you add in variables.

JC
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You still are not clear. Maybe you could give a specific example, say what FargoRate predicts and then say what you feel the actual chances are and why.

And the above post is the first time you've mentioned a spot of games on the wire. Is that what you were talking about all along?
 
JC

JC

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Bob Jewett said:
You still are not clear. Maybe you could give a specific example, say what FargoRate predicts and then say what you feel the actual chances are and why.

And the above post is the first time you've mentioned a spot of games on the wire. Is that what you were talking about all along?
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Well if player B only has a 40% probability of winning the set and he's 85 points higher fargo he has to be giving up games right? Actually 8-4. Yet player A has yet to win a match over many months of this play in the format described in the OP. So if player A is a 72% favorite to win the match and has yet to do so in many tries something isn't right.

Just not sure what.

JC
 
jasonlaus

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JC said:
Well if player B only has a 40% probability of winning the set and he's 85 points higher fargo he has to be giving up games right? Actually 8-4. Yet player A has yet to win a match over many months of this play in the format described in the OP. So if player A is a 72% favorite to win the match and has yet to do so in many tries something isn't right.

Just not sure what.

JC
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100 points difference is 2 to 1 in games.
Jason
 
Bob Jewett

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JC said:
... So if player A is a 72% favorite to win the match and has yet to do so in many tries something isn't right. ..
Click to expand...
Maybe he has a reason to play badly against the better player. Maybe his brother-in-law is betting on the other guy on the side. Maybe he has some mental block against beating the guy due to something that happened in middle school. Maybe he is trying for a larger spot. Maybe the ratings were copied down wrong. Maybe the better player has manipulated his rating to be lower and he's actually 200 points above the weaker player. Maybe the weaker player has just gotten unlucky a lot.

Without knowing more about the situation it's impossible to say what's going on. As far as Fargo itself, how it works and its expected accuracy is pretty open and clear. I think you have to look elsewhere.
 
JB Cases

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if player A is 85 points lower than player B but is actually the better player and both are established then one or both them are likely not rated correctly and I would first ask Mike to look into them to see if there were any data errors or any patterns.

If however you are referring to the players playing great for a set dogging a set - going back and forth on games and set.....that is something Fargo Ratings can never be 100% on. You can certainly stack on variables and make your own choices based on those PLUS whatever Fargo Rate says. You can know if Billy Joe has a huge plate of beans and a half gallon of ice cream and what his stomach will be doing in 45 minutes....Fargo doesn't. Fargo says I can tell you who he has played in public events and what the wins and losses were and I will use my algocalulator to spit out a number which you can use to compare him to other known players in my system. Think of Fargo as the baseline from which you can go up or down in your estimation based on all of the information you have.

Now me, I pretty much just trust Fargo if the player is established. And yes of course there are times where I will look at a person's Fargo and go no way! and then quite often when they play I realize that I never really clocked them and they don't play as good as I thought they did.
 
oneballeddie

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JC said:
Player A has a 59.8 chance of winning a set against Player B who is at 40.2%

What then is the probability of Player A winning a match that consists of a race to five of the sets described above?

72.8%

All we know is Fargo considers player A a 59.8% favorite in each of the sets.

Does it matter the individual's relative fargos? Or how long the race is in each set?

If it is known Player A has 59.8% of winning a set (presumably based on previously known Fargo ratings or results) Fargo ratings would no longer matter in calculating this probability.

But the 59.8% chance of winning a set as given in your experiment depends on both the length of the set race and the difference in Fargo ratings. All we know here is that the set odds are 59.8 and the race length and Fargo difference are unknown. This doesn't matter in the race to 5 calculation.

Fargo is supposed to take all this into consideration right?

Yes, in calculating single race (or set) odds given the single game win probability.

So does Player B have a chance in hell to grab the cheese or not in the five set match?

Yes, B has a 27.2% chance of winning.


JC
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I believe we use the same negative binomial distribution in this experiment that Fargo uses to calculate race odds (or "set" odds using your terminology) given a single game win probability. Except now the race to five has single "game" odds of 59.8%. You can verify this using the Fargo Fair Match Odds calculator with a 57 difference in Fargo ratings (which means A has 59.8% chance of winning a single "game") in an even race to 5. [/COLOR]
 
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jrctherake

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Bob Jewett said:
Maybe he has a reason to play badly against the better player. Maybe his brother-in-law is betting on the other guy on the side. Maybe he has some mental block against beating the guy due to something that happened in middle school. Maybe he is trying for a larger spot. Maybe the ratings were copied down wrong. Maybe the better player has manipulated his rating to be lower and he's actually 200 points above the weaker player. Maybe the weaker player has just gotten unlucky a lot.

Without knowing more about the situation it's impossible to say what's going on. As far as Fargo itself, how it works and its expected accuracy is pretty open and clear. I think you have to look elsewhere.
Click to expand...

Maybe he accidentally ran over a squirrel on the way to the tournament and can't get it out of his head.

I did that once. I ended up donating to "we are the squirrels"..... a home for wayward squirrels.
 
sbpoolleague

sbpoolleague

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P5.png
 
Bob Jewett

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jrctherake said:
Maybe he accidentally ran over a squirrel on the way to the tournament and can't get it out of his head.

I did that once. I ended up donating to "we are the squirrels"..... a home for wayward squirrels.
Click to expand...
D00D! That's just nuts.
 
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