[Attempt at] New PBEM rating system - continued

[Mathemagician]

double posted - deleted

[Mathemagician]

Originally posted by ricketyclik


I tested the formula when I firstr saw it years ago and it seemed to work without the "^", but I never checked it against actual ladder results though.

im sure it was meant with the "^" as the formula loses some important characteristics without the "^", for example, points taken by the winner are not equal to the points lose by the loser anymore. also, for equally scored players BOTH of them would take points and that doesnt seem to make sense to me.

[Mathemagician]

Originally posted by Mathemagician

Originally posted by Solver
In this regard, you better trust me. Excel does not work good enough, and I say that as someone who has been doing that stuff with Excel.

i see that as a challenge to prove you wrong.

while i must agree with Solver that his proposed ranking system is probably superior to mine (i tested some and just cant get all desired characteristics under one hat), i must say im pretty sure i proved him wrong on the Excel issue.

ladies and gentlemen,
i present the almost completely automatic Excel sheet for ranking games (attached).
since i was using a german version, i hope the commands are auto-translated when loading the file.

please disregard the precise formulas, as i just admitted they are not as good as desired.

all the work you'll have with this sort of Excel sheet is:

for a newly started game
copy the template from above in table 2 to the end and modify player names and player numbers as well as delete the surplus fields (delete the whole lines, not just the content !).

for a finished game
add the scores from the game to the 'fix score' column in table 1 and delete the game.

for ranking updates
just change the numbers 1 - n in the power graph column of that game in table 2.

try it out !
i'll gladly program a similar excel sheet for any system we come up with to use for the PBEM rankings.

[Solver]

Mathe - yes, if the power symbol was forgotten, systems are the same. Testing your sheet out now.

And, I say, it's not as good as an automated program would be, although surely feasible. It's good, yet I see ways how a program could work better. For instance, you would have an easier time adding new games, etc. I agree though, that you have done a very good job, but I still remain confident that a program would do it even quicker.

A question... can you explain s(i) to me?

[quinns]

CtP PBEM Ratings Formulae, Oct 2000
The ratings would change using the formula: Probability of Lower Rated Player Defeating Higher Rated Player =
Prob = 1 /(2 + (player1 - player2)^2).

If the higher rated player defeats the lower rated player, then the Change in Rating = Prob./2

If the lower rated player defeats the higher rated player, then the Change in Rating = (1 - Prob.)/2.

-----

This is not a tennis formula. It was used to calculate tennis ratings but it had nothing to do with tennis. I created these formulas. Thanks for "credits" Solver!

[Mathemagician]

@Solver
sure, an automated program would always require less manual input.
just programming a real program is much more work (and requires more knowledge) than programming an excel sheet. if you want to do that, its fine with me.

the s(i) resulted from several attempts to appromixate the
1 / (10^(RD/400) + 1) part from the ELO formula for 2 player games, and thus make them fit the multiplayer requirements.
they were meant to approximate the points an average ranked player would gain in the game (since you cannot easily pack the probability for a player 'winning' the game in one value.)

i could get almost all characteristics of the original (exponential) formula in in the non-exponential one, but not all. thats why i gave up.

i had to cut back on either or several of the following:

- point change totals of all players adding up to zero
- winning player never losing points
- all participating players rankings being accounted for
- proportionality of ranking points, finishing position and gained/lost points being reasonable
- probably some more i forgot now...

@quinns
thanks for the formula
but still, i'd prefer combining the exponential ELO formula with Solver's suggestion to count a multi-player game as several 2 player games and use the ELO formula for the seperate rating adjustments instead of yours.

[Solver]

Ouch, sorry Quinns . Didn't mean to underestimate you.

Mathe - what's wrong with the Quinns formulas ?

[Mathemagician]

Originally posted by Solver
Mathe - what's wrong with the Quinns formulas ?

just that i believe the exponential attempt comes closer to the probability estimation than the quadratic attempt.

[Solver]

Well, that's just your belief . Probability isn't an exact thing, so both methods are rather close to the real amount.

Now... I'm too lazy atm to do it, but some tests should be ran with the same game results, e.g, with both the Quinns-tennis formulas, and the ELO exponential ones... and see how much do the ratings change after a game in these systems.

[Mathemagician]

Originally posted by Solver
Well, that's just your belief . Probability isn't an exact thing, so both methods are rather close to the real amount.

probability is, just not its estimation

[Solver]

But seeing how we are humans we can only estimate .

[Mathemagician]

Originally posted by Solver
But seeing how we are humans we can only estimate .

who is human ? you ?

sorry for you . didnt know that.

[Solver]

Yeah, that hurts .

[Grandpa Troll]

Originally posted by Solver
But seeing how we are humans we can only estimate .

Estimate the probability of being expotentially human?

Two types:

Version One:


How about the winner gets this:

Each game gets 100 points assigned to it. PERIOD!

whether you have 2,3,4 or more...

First place 50 points

Second Place 35 points

Third place 15 points

Fourth ya just didnt make the cut

Fifth..hmm..you need much more practice!

no having to do a bunch of math..(not the Deutche Expert herein!!)..but arithametic (?? spelling?)

I know..Im just a simple minded Troll but hey..its a simple way to keep all understanding?

Version Two

take 100 points per player in a game
(i.e. 5 players=500 points, 7 players 700 points)

First place player gets 40%

2nd place 25%

3rd place 15%

split the remaining between the rest (20%)

If only 3 people keep the above formula and no one be rewarded the rest.

Just my unsolicited $0.02 worth!!

Ya dont need a spreadsheet, a program or a degree from Apolyton University!

Ill be good now and go back in my hole!!

Peace

Grandpa Troll

[quinns]

Originally posted by Solver
Ouch, sorry Quinns . Didn't mean to underestimate you.

Mathe - what's wrong with the Quinns formulas ?

No problem, Solver. I was going to ignore it, but I just couldn't continue to see my simple-minded formulas being called "tennis formulas"!

Troll, with your system you'd still need a big old fat spread sheet, along with about 2 hours a day arguing with people that say your system is "unfair" and "doesn't reflect the true ability of the player", etc, etc, etc.!! Ratings and rankings are a pain. Ladders are easy! Join the PBEM Challenge Ladder! (I'll crawl back into MY hole now... )