Has anyone considered using a modified "Bayesian estimate" as the ranking formula?

It requires two quantities:

- the average percentage of (games_won / games_played) ratio for all players (games_average)

- the minimum amount of games required to consider someone eligible for ranking (games_min)


The score for each player is calculated as:


Score = ( games_won + (games_min * games_average) ) / (games_played + games_min)



So for:


games_min = 11
games_average = 0.25

and multiplying the resulting score * 1000

Games.....Wins.....Ratio.........Score
100.........100........1.................925,68
80............80...........1.................909,34
250.........125........0,5...............489,46
11..........6..........0,55..............397,73
23..........5..........0,22..............227,94
40..........6..........0,15..............171,57

2...........1..........0,5..............(288,46)
6...........4..........0,67.............(397,06)
1...........1..........1................(312,5)

[ Scores in the parentheses are below threshold of games_min. ]

This sounds like a very good idea. And the more i watch your testing table, the more i like it. Just one question: How do you set "the minimum amount of games required to consider someone eligible for ranking (games_min)". So when exactly someone should be eligible for the ranking? 20 games like in the "won in percent" table?

If there are no objections from the dev-team and the community i would like to test it.

If so we should name it "bugmenot"-system

LuisCypher wrote:
The games_min is arbitrary and another advantage of it is that it can be re-adjusted every month or so, as the games_played value rises.


1. A good approximation could be by finding the median of the games_played in pokerth. By using the median (and not the average) we isolate the players who either "live on the server" (like Alfa1 used to do ) or play 1-2 games and then they never return. We can further adjust the above approximation by eliminating players who have played under 10 games, that is: they downloaded the software, registered online, connected to the server, played a few preflop all-in games, lost and then uninstalled the software completely.


The formula could be:

games_min = median / 4

or:

games_min = median / 5

as if we used the median alone (as in "games_min = median"), then we would leave out of ranking exactly half of the players.


2. Another way (similar to the one above) could be by using a value for games_min so that it includes (let's say) 9/10 of the players of pokerth. That is: by sorting the values of game_played at the database, then excluding those under our threshold of "10" (the "preflop all-in ones that got bored and uninstalled") and then picking a number that results in having the 9/10 of the remaining players be eligible for ranking.




As it is noted, our ranking system has a "time" factor as it respects former "champions" without ignoring new ones.



As to the freshly started ones (games_played between "10" and "games_min") they could have a separate ranking on the scoring page (a "League B" compared to the main "League A"). This way they don't get disappointed nor they have to win many games in order to be promoted to "League A"; they just have to play games_min ranking games. If cheating occurs (rounds of one-hand all ins) this can be easily found and punished by the heuristics on the server.




Please don't.

It's real name is "true bayesian estimate" and is used extensively as a ranking algorithm in voting-based sites (i.e. IMDB).

Compared with ELO this system has the obvious problem that it doesn't consider the strength of opponents. Makes complete newbies the best people to play against again.

Also I would set games_average to 0. Overestimating people hurts the system more than underestimating people: It's *their* job to prove that they are good. Also prevents the whole "I'm losing points by playing" problem. Which is the best way to quickly killing motivation of your player base. Don't forget: Most of the players are bad, and you want to keep them.

And nothing beats Elo in terms of fairness, seriously. Just sayin'

Maytsh wrote:
Why should it consider it?

Players come and go. People who tend to stay longer on the server (that is: you have a greater possibility to play against them) are between the best ones of pokerth.


Why?
And how do you choose "newbies" exactly?
For how long do "newbies" stay around if they get "beaten up" by serious players?

I know I want my wins against super-players to count more but let's solve the easy part first, that is deciding on a pretty fair initial scoring method first.


Sorry, that gives:

Score = games_won / (games_played + games_min)

which after a while resorts to:

Score = games_won / games_played

and we said that we want a more accurate ranking system than that.

No, it does not. On the contrary it is tuned to poker philosophy: In poker you must pay up money and you must play in order to gain back a portion, all, or a lot more of them. Also, idle poker players lose (rising blinds method).

That might be true for commercial poker-sites where there has to be some prey for the "sharks" but not for a user community as PokerTH.

I choose to play on PokerTH because it gives me the privilege to practice against some pretty good players without spending the amount of money I would have to, if played on a commercial poker site.



Don't get me wrong, I do find the ELO idea interesting.

> you have a greater possibility to play against them

Possibility, maybe. But players can choose who they play against. And in case the ladder gets any kind of credibility, they quickly will.

> Why?

Okay, I'm a bit off -- it's actually even worse: It makes *bad players* the optimal choice to play against...

> which after a while resorts to: Score = games_won / games_played

For a large number of games, you always approach that point -- no matter what you set games_average to. Isn't that the whole idea behind the formula? To have some sort of "start hypothesis" that gets refined as we get data on the player? That's how I read it, at least.

> In poker you must pay up money and you must play in order to gain back a portion, all, or a lot more of them.

I don't understand this argument. Real-life poker is terrible, people are going broke over it. We play online and without money because we don't like that, right...?

> That might be true for commercial poker-sites

You misunderstood me. You want to keep bad players, because they are tomorrow's good players. The more bad players you keep, the more good players you eventually have (and attract).

Or another way to look at it: The validity of a good player's achievement doesn't come from how many points he has or how good he is objectively, but from how many people have *less* points than him.

That's the number we should optimize.

> Don't get me wrong, I do find the ELO idea interesting.

Sorry, I just wanted to get the message across that fairness is *hard*. If you use a system without sound mathematical model and track-record, there will be weaknesses. I have the scars to prove it