The problem is you are losing precision at the weaker levels and adding too much c h precision at the higher levels.
Might be time to learn logarithms instead.
I fixed Fargorate
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Might be time to learn logarithms instead.
The thing is the reason I understand the fargorate logarithms so well is because as a computer scientist I understand the base 16 and base 2 logarithms even better.
Also, which is a linear scale and which is a nonlinear scale is in the eye of the beholder.
If we use inches for length and plot the number of trout in a stream at each length, we get a nice bell curve
If we use grams for weight/mass and plot how many raspberries are at each weight we get a nice bell curve
If we use hours for time and plot how long each of our fully-charged cell phone batteries lasts, we probably get a bell curve
We think of these as linear scales of length, mass, and time. If we stretched out the ruler on the high end so that an "inch" at the high end is longer, we destroy the bell curve for the trout. It is reasonable to ask, what is a scale of pool "skill" such that we get the nice bell curves like above. That is, what skill scale acts like inches for length, grams for mass, and hours for time? Fargorate points is it.
Here is a challenge that is related to this failure to appreciate natural scales of things.
Look at a list of countries by land area (link below) or countries by population or stars by distance or numbers in balance sheets or FargoRate robustness numbers (anything that occurs naturally and spans several different numbers of digits). I claim that if you give me 20 numbers that either come from an actual list or are made up by you, I will be able to tell the difference--whether you made them up or took them from the list.
So the rules are your list of 20 numbers needs to span a range of number of digits and needs to be chosen randomly by you or by a criterion that doesn't use the numbers. An example here is population of countries that start with "B." If you gave me these numbers, that would be giving me actual numbers. If you just randomly make up 20 numbers a few of which have 3 digits, a few 4 digits, etc, that would be making them up.
Once again I will be able to tell if you made them up or got them from one of the lists you can find here or elsewhere. And the reason I can do that is related to the discussion here.
Largest Countries in the World by Area - Worldometer
www.worldometers.info
| Bahamas | 13,943 |
| Bahrain | 765 |
| Bangladesh | 147,570 |
| Barbados | 430 |
| Belarus | 207,600 |
| Belgium | 30,528 |
| Belize | 22,966 |
| Benin | 112,622 |
| Bermuda | 54 |
| Bhutan | 38,394 |
| Bolivia | 1,098,581 |
| Bosnia and Herzegovina | 51,209 |
| Botswana | 582,000 |
| Brazil | 8,515,767 |
| British Virgin Islands | 151 |
| Brunei Darussalam | 5,765 |
| Bulgaria | 110,879 |
| Burkina Faso | 272,967 |
| Burundi | 27,834 |
Do yourself a favor and don’t go to a casino to win money - your math does not add up. It is much simpler than you are showing by example. If I am rated at 50% of another player then I need better than 6 -4 to be a favorite to win a match - I should get 6-3 to be even money in the match and 6-2 to be the favorite.
Every tournament that I have ever played or followed when the 100 point Fargo difference is not split at 6-3 or better for the lower players- the money winners are always by far dominated by the higher Fargo rated players. By FAR - analyze this on digital pool tournament results and it is very obvious.
Half as good means just that if Fargo is to be taken seriously - is a coin flip not a 50/50 proposition? So also is a 100 point Fargo difference supposed to be rated the same way in proposition analogy- being rated half as good should result inthe need to win only half as many games to have a true 50% chance of winning - when the. Person twice as good needs to win only less than double then he becomes a favorite in true gambling odds.
You are not understanding what Bob is saying. You seem to think a 6-3 match for two players 100 points apart is a 50/50 proposition. I know it seems like it should be. But it isn't.
You're picking the wrong guy to argue math with.
I understand what he is saying - but I am saying that in reality the math can be thrown in the garbage. You walk into a pool
Room - a TRuE 500 is playing a true600 at 6 games to 4 - I am not betting on the 500 guy at even money. At 6 games to 3 I would bet even money on the 500 guy expecting a 50% chance to win or lose- at 6 games to 2 I would bet even money heavily on the 500 guy. Sorry - not trying to discredit anyone personally - I am just saying that I have seen that Bob’s math may look good on paper - but it ain’t what really happens
OKI understand what he is saying - but I am saying that in reality the math can be thrown in the garbage. You walk into a pool
Room - a TRuE 500 is playing a true600 at 6 games to 4 - I am not betting on the 500 guy at even money. At 6 games to 3 I would bet even money on the 500 guy expecting a 50% chance to win or lose- at 6 games to 2 I would bet even money heavily on the 500 guy. Sorry - not trying to discredit anyone personally - I am just saying that I have seen that Bob’s math may look good on paper - but it ain’t what really happens
According to FargoRate app
105 point difference 5-10 race
lower player and higher player each have 50% chance
105 point difference 50-100 race
lower player (going to 50) wins 42.9% to 57.1% for higher rating
???
105 point difference 5-10 race
lower player and higher player each have 50% chance
105 point difference 50-100 race
lower player (going to 50) wins 42.9% to 57.1% for higher rating
???
What is the question?
Mike answered this for me in a thread I started a few months back. I was confused at his answer. I worked it out on a piece of paper for about 1 hr while on a plane ride, trying several different scenarios, and it indeed makes sense. Based on my experience at least, you need to do what I did to convince yourself. Its not the most intuitive thing to understand for us common non-math-wiz folk
To Mike: I forgot to write back to that thread after my plane ride.
Why does a FargoRate 100 point difference not exactly equal 2-1 in games?
Is the 2-1 game score for a 100 point spread an approximation? I always thought it was the whole basis for the system and "exact". Also, why do the odds change based on the match length? See 3 screenshots below.
forums.azbilliards.com
I gave all the math for a race at 2-1 for two players 100 points apart. Did that explanation make any sense to you? For a probability problem, it is very, very simple.
Good explanation. This is what was tripping me up also for the longest time. I kept thinking its a simple ratio that you multiply all the way though. I did not understand that it's not.
As you show, you actually have to write out EVERY single way the match can go down. Then take all those scenerios, find how many times player A wins the match, and how many times player B wins the match. THAT ratio is the actual probability. A TON more work, if doing it by hand. That's what I did on the plane. Started with the exact example you gave, and expanded it to several longer races.
I didn't do well in my college probability class
I got an A in all my high school math classes though, without hardly studying.
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You can even work backwards to see a 2-1 race is not an even proposition for a 100 point gap.
The only way for the "2" to win the set is to win the 1st two games, and the chance of that happening is
(chance of winning the first game) X (chance of winning the second game).
For this to be 50% (1/2), we need the chance of winning the first game to be 1/squareroot(2), right?
Because then 1/squareroot(2) X 1/squareroot(2) = 1/2, what we want.
1/squareroot(2) is .707, i.e., 70.7%
So for the race to be even, the rating gap needs to be 127 points, as you can see from the Fargorate APP
Do your data on all players follow a normal distribution? I'm guessing no, but if you subset by some kind of logic (men & women, for example), would the subsets follow a normal distribution?
I just referred to this graph and numbers today, is amazing how different both the original numbers and "proposed adjusted" numbers present
I think I'll stick to trying to steal.