How to calculate your chance of winning given Fargorates

[Pubo]

If you open your Fargo app and click on the "FIND RACE" button, you can calculate the odds of winning given two players Fargo, but the app doesn't tell you how this is calculated.

Here is what I found: as long as the scores difference is 332 (say 732 vs. 400), the higher-rated player has a 90.9% to 9.1% chance of winning 1 match.

If you take this a step further, and have a match between a 400+332+332 = 1064 (I know nobody on Earth has a Fargo this high, but let's assumed so) vs a 400, then the chance (of winning one match) becomes 99% to 1%.

This suggests that the chance of winning increases 10-fold as your score difference increases by 332. This is a standing assumption of the Fargo system: that if you are 10 times as likely to beat player A, and player A is 10 times as likely to beat player B, then you are 100 times as likely to beat player B. This is not true in real world, but I guess this is a good enough assmption.

So the relationship is logarithmic. If your Fargo is M and your opponent's O, then your chance of winning one rack is

I remember reading an article from FargoRate, and they said that they changed their rating system away from ELO, but this seems to be exactly the same as the ELO system, but just with a different number (400 for ELO, 332 for Fargo) which is widely used in chess.

 

[MitchAlsup]

Here is what I found: as long as the scores difference is 332 (say 732 vs. 400), the higher-rated player has a 90.9% to 9.1% chance of winning 1 match.

If you take this a step further, and have a match between a 400+332+332 = 1064 (I know nobody on Earth has a Fargo this high, but let's assumed so) vs a 400, then the chance (of winning one match) becomes 99% to 1%.

This is to be expected:

733 vs 400 = 90.9% to 9.1%
733 vs 068 = 99%

1 - 90.9% = 0.091
0.091×0.091 = 0.0083 or just less than and round up to 1%

 

[Pubo]

This is to be expected:

733 vs 400 = 90.9% to 9.1%
733 vs 068 = 99%

1 - 90.9% = 0.091
0.091×0.091 = 0.0083 or just less than and round up to 1%

right, that's what I described in the fourth paragraph. If you are 10 times stronger than B and B is 10 times stronger than C, then you are 100 times stronger than C.

 

[Bob Jewett]

If you take the win ratio between two players, say 4:1, and take the log base 2 of that ratio and multiply that by 100, you get the difference in their ratings. That pair would be 200 FR points apart exactly.

This has been described several times before. I'm pretty sure it is either in the FargoRate FAQ on the website or in one of Mike Page's videos on his YouTube channel.

The system assumes that you can simply add/subtract ratings (or the equivalent of multiplying/dividing win ratios) and the statistics seem to confirm this. I imagine that there is some error in this assumption, but it seems to be small.

For matches, the single-game probabilities go into a relatively simple multi-event probability calculation.

 

[Pubo]

If you take the win ratio between two players, say 4:1, and take the log base 2 of that ratio and multiply that by 100, you get the difference in their ratings. That pair would be 200 FR points apart exactly.

This has been described several times before. I'm pretty sure it is either in the FargoRate FAQ on the website or in one of Mike Page's videos on his YouTube channel.

The system assumes that you can simply add/subtract ratings (or the equivalent of multiplying/dividing win ratios) and the statistics seem to confirm this. I imagine that there is some error in this assumption, but it seems to be small.

Indeed! Your way of calculating and my way of calculating are basically the same haha, the ratio of your way v.s. my way is:

 

[Pubo]

If you take the win ratio between two players, say 4:1, and take the log base 2 of that ratio and multiply that by 100, you get the difference in their ratings. That pair would be 200 FR points apart exactly.

This has been described several times before. I'm pretty sure it is either in the FargoRate FAQ on the website or in one of Mike Page's videos on his YouTube channel.

The system assumes that you can simply add/subtract ratings (or the equivalent of multiplying/dividing win ratios) and the statistics seem to confirm this. I imagine that there is some error in this assumption, but it seems to be small.

For matches, the single-game probabilities go into a relatively simple multi-event probability calculation.

I found it!