Match probability calculator, given Fargo ratings

T

tomker

AzB Silver Member
Silver Member
I was trying to find a calculator for match probabilities yesterday, and failed. There are vague references to "tools" on the FargoRate web site but I couldn't find said tools.

So, I made my own calculator:


For smaller values of "race to," the calculator sums up the probabilities of all possible outcomes and the results are exact. For larger values of "race to," the page does a Monte Carlo simulation, and the results are accurate, but not 100% perfect.

I'm sure there's a clever way to use combinatorics to instantly calculate the exact probabilities, but I hate combinatorics.

Anyway, I hope people find the page useful!
 
The link doesn't work for me.

I think there was a previous thread about this. On the FargoRate website, the calculator is under the "Search for Player Ratings" button. I don't know where it is in the app. https://fairmatch.fargorate.com/

The problem with combinatorics is that the calculation involves factorials and computers choke on races longer than about 100 games.

A different technique to do the calculation is a "Markov process". It does not involve large numbers but it does require a memory array roughly equal to the match length. It gives an exact result and can be modified to have different break formats. It is much faster than doing Monte Carlo runs.
 
Bob Jewett said:
The link doesn't work for me.
...
Click to expand...
Can you try a different browser?

The page is hosted via HTTP and not HTTPS, so some picky apps and browsers consider it "insecure" and make it difficult to get to.

Thanks for the tip re: Markov process. But the Monte Carlo simulation code on my page was dead simple to implement, and running the simulation for 250 milliseconds on my laptop is pretty accurate for all the scenarios I've tried.
 
Bob Jewett said:
...
I think there was a previous thread about this. On the FargoRate website, the calculator is under the "Search for Player Ratings" button. I don't know where it is in the app. https://fairmatch.fargorate.com/
...
Click to expand...
I think I may have crashed the FargoRate web site.

After clicking around, refreshing, trying (and failing) to log in, trying to reset my password, etc. for a few minutes, some UI finally popped up that offered to calculate match odds.

It seemed to work well enough for small "race to..." numbers but I tried a race to 100 and the page barfed. Now, when I click on "Search for Player Ratings" I get a Bad Gateway error message.

If I use my web page to calculate the odds for a race-to-100 match between two players with the same Fargo rating, it does ~160,000 simulations in 250 milliseconds and the results are accurate +/- 0.2 percent or so.
 
It’s built into the app. Hidden away but it’s there. The app works much better than the website.

Within app:

Magnifying glass (the one on the bottom) > Find Race > Odds.

Note most players go by the race odds of hot, med, mild. Those odds give a big advantage to the better player, even if hot is selected. The “odds” way will get the closest to 50/50 with some trial and error.
 
iusedtoberich said:
It’s built into the app. Hidden away but it’s there. The app works much better than the website.

Within app:

Magnifying glass (the one on the bottom) > Find Race > Odds.

Note most players go by the race odds of hot, med, mild. Those odds give a big advantage to the better player, even if hot is selected. The “odds” way will get the closest to 50/50 with some trial and error.
Click to expand...
Just downloaded the app (iOS version)... it's asking for me to find my Fargo rating and won't let me past that screen. I don't have a Fargo rating (never played in a Fargo rated tournament) so this app seems like a non-starter to me. Ugh.

I'm sure that someday I'll play in a rated tournament.
 
Combinatorics.

Yeah, I googled it, guess it is an actual thing.

Can I, can we, let’s just over complicate some stuff now, can we?

So, what I thought the Fargo baseline was, is, 100 points = 2 to 1 ratio.

Obviously, a shorter set allows for more flukes.

Bottom line; if you are on the bottom look for a short set, if on the top string it out.
 
tomker said:
... It seemed to work well enough for small "race to..." numbers but I tried a race to 100 and the page barfed. Now, when I click on "Search for Player Ratings" I get a Bad Gateway error message.
...
Click to expand...
The calculation involves factorials. At about 100 games, a factorial is too large to fit in normal computer arithmetic. There are work-arounds, but they are far more complicated than simply calling factorial(100).

The calculator seems to be working again.
VarmintKong said:
... Can I, can we, let’s just over complicate some stuff now, can we? ....
Click to expand...
If you want to figure actual match probabilities on your own, the math is relatively simple. You end up calculating the chance of each possible outcome. It's only as complicated as it has to be to get the answer. "Combinatorics" basically means "all possible ways" studied in an organized manner.

Example: I'm a 500 FR giving up 2 games on the wire to a 350 in a race to 5. What's my likelyhood of winning? Answer: I'm 73% to win. Along the way, you have to calculate my chances of winning 5-0, 5-1 and 5-2 and all the combinations of wins/losses that produce those results.
 
Bob Jewett said:
"Combinatorics" basically means "all possible ways" studied in an organized manner.

Example: I'm a 500 FR giving up 2 games on the wire to a 350 in a race to 5. What's my likelyhood of winning? Answer: I'm 73% to win. Along the way, you have to calculate my chances of winning 5-0, 5-1 and 5-2 and all the combinations of wins/losses that produce those results.
Click to expand...

I’ll always listen to what you have to say, but it seems like Much Ado.

If I’m a 500 v 350 to 5, I can expect to win at a rate better than 2:1. Do you really need an overanalyzed thing or just a baseline to get ya started?
 
tomker said:
I was trying to find a calculator for match probabilities yesterday, and failed. There are vague references to "tools" on the FargoRate web site but I couldn't find said tools.

So, I made my own calculator:


For smaller values of "race to," the calculator sums up the probabilities of all possible outcomes and the results are exact. For larger values of "race to," the page does a Monte Carlo simulation, and the results are accurate, but not 100% perfect.

I'm sure there's a clever way to use combinatorics to instantly calculate the exact probabilities, but I hate combinatorics.

Anyway, I hope people find the page useful!
Click to expand...
Double the probability of winning for every 100 added points of Fargo spread. Is that about the same as Fargo predicts?

pj
chgo
 
VarmintKong said:
I’ll always listen to what you have to say, but it seems like Much Ado.

If I’m a 500 v 350 to 5, I can expect to win at a rate better than 2:1. Do you really need an overanalyzed thing or just a baseline to get ya started?
Click to expand...
The reason I wanted a calculator is because I was watching a race-to-7 match between two players. The stronger player was rated 100 points higher than the weaker player. I knew that the odds of the stronger player winning any given rack were 66% but I didn't have a feel for the race-to-7 odds.

Turns out, the weaker player only has a 10.35% chance of winning a race-to-7 match. I knew it would be pretty low but I didn't know it would be that low. Did you?
 
Patrick Johnson said:
Double the probability of winning for every 100 added points of Fargo spread. Is that about the same as Fargo predicts?
...
Click to expand...
That's the probability of winning any given rack. The probability of winning a race-to-whatever match can be very different.

When you first load my page, it will show you the probability of a 600 beating a 500 in a race to 1 (i.e., for a single rack). That probability is exactly what you said, 66% = double the probability of losing.
 
I put in about 10 different scenerios on your website and on the fargo app, and they were all dead the same.

Only when I got to races of 50 range, there was a tiny disparity of about .1 on the percentage odds.

Good enough;)
 
tomker said:
Just downloaded the app (iOS version)... it's asking for me to find my Fargo rating and won't let me past that screen. I don't have a Fargo rating (never played in a Fargo rated tournament) so this app seems like a non-starter to me. Ugh.

I'm sure that someday I'll play in a rated tournament.
Click to expand...
You don't need to have a Fargo rating or anything.

Just tap the 🔎 at the bottom and then the "Find Race" button at the top.
 
tomker said:
Just downloaded the app (iOS version)... it's asking for me to find my Fargo rating and won't let me past that screen. I don't have a Fargo rating (never played in a Fargo rated tournament) so this app seems like a non-starter to me. Ugh.

I'm sure that someday I'll play in a rated tournament.
Click to expand...
Tom

If you email support@fargorate.com we will create profile for you in FargoRate
 
kingwang said:
You don't need to have a Fargo rating or anything.

Just tap the 🔎 at the bottom and then the "Find Race" button at the top.
Click to expand...
You're using a different app than I am. The iOS app requires you to find your Fargo rating before you can do literally anything else at all.
 
Bob Jewett said:
The link doesn't work for me.

I think there was a previous thread about this. On the FargoRate website, the calculator is under the "Search for Player Ratings" button. I don't know where it is in the app. https://fairmatch.fargorate.com/

The problem with combinatorics is that the calculation involves factorials and computers choke on races longer than about 100 games.

A different technique to do the calculation is a "Markov process". It does not involve large numbers but it does require a memory array roughly equal to the match length. It gives an exact result and can be modified to have different break formats. It is much faster than doing Monte Carlo runs.
Click to expand...
Bob Jewett, you are better than google.
 
tomker said:
I think I may have crashed the FargoRate web site.

After clicking around, refreshing, trying (and failing) to log in, trying to reset my password, etc. for a few minutes, some UI finally popped up that offered to calculate match odds.

It seemed to work well enough for small "race to..." numbers but I tried a race to 100 and the page barfed. Now, when I click on "Search for Player Ratings" I get a Bad Gateway error message.

If I use my web page to calculate the odds for a race-to-100 match between two players with the same Fargo rating, it does ~160,000 simulations in 250 milliseconds and the results are accurate +/- 0.2 percent or so.
Click to expand...

The differences between a race to 50 odds and a race to 100 are negligible. Going by years of experience and "seat of the pants" feel, I think any race of 20 or greater will show up the better player as well as a race to 50 most of the time. Back in the day when pro events had races to 11 and higher, the announcers say that races to 15 or 19 were good enough to bring out the better players to the top.

There is no way you can say your results are accurate without someone actually playing those 160,000 matches to get the results. "accurate" in a model is only as good as the model. It can be 100% accurate based on the numbers you feed it, but I would bet the reality will have a standard deviation of many %, not .2. If a match predicter was even 75% accurate I would call it a good model.
 
hang-the-9 said:
The differences between a race to 50 odds and a race to 100 are negligible. Going by years of experience and "seat of the pants" feel, I think any race of 20 or greater will show up the better player as well as a race to 50 most of the time. Back in the day when pro events had races to 11 and higher, the announcers say that races to 15 or 19 were good enough to bring out the better players to the top.

There is no way you can say your results are accurate without someone actually playing those 160,000 matches to get the results. "accurate" in a model is only as good as the model. It can be 100% accurate based on the numbers you feed it, but I would bet the reality will have a standard deviation of many %, not .2. If a match predicter was even 75% accurate I would call it a good model.
Click to expand...
The "model" we're talking about is Fargo ratings. My page calculates accurate numbers according to players' Fargo ratings. If you think Fargo ratings aren't accurate for longer matches, that's a different discussion.
 
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