Formula for Ranking Players

Has anyone here had to rank players playing against each other before?

Player1 plays 10 games, wins 8 out of the ten games -> so 80% win / loss ratio.
Player2 plays 100 games against the same easy opponent, wins 99 of the 100 games -> so 99% win / loss ratio
Player3 plays 1 game, wins that 1 game -> so 100% win / loss ratio
Player4 plays 50 games, wins 40 games -> so also a 80% win / loss ratio.

Player1 might play against Player2 today and tomorrow Player1 might not play at all, but Player2 might play against Player3 - so not all players will be playing at the same time, some might play many more games than other.

Which player should be ranked highest and what formula did you use to make that decision?

Also, how would your scoring system encourage weaker players to play against stronger players and stronger players to want to play against the weaker players.

I have some ideas, but would like some input from Hashnoders

Update - rating systems so far:

And in case you need to calculate these things without a computer, by hand, there's a simplified version of ELO called the Harkness Rating System, you start with a rating of 1200 and then based on the difference in rating between player1 and player2, you transfer points according to this table:

title here

Check out Elo Rating System, Jan: https://www.wikiwand.com/en/Elo_rating_system. It details methods to rate players of a competitive game in to higher/lower rank buckets, based on their skill levels. It all started with chess. A lot of online competitive games now-a-days use this sort of rating, to rank their players.

Alternatively you can also look into this: evanmiller.org/how-not-to-sort-by-average-rating.…. Evan details a way to correctly sort a product according to user ratings, using statistical sampling; and does it "correctly" even in the case when the no. of ratings between two products are disparately different. You can adapt this model for rating your players; where the no. of ratings would be analogous to the number of games played, and a positive rating is a win, a negative one, a loss.

ELO was one of the rating systems I had in mind, but it seems old compared to Glicko2. Evan Miller's How Not To Sort By Average Rating solution was something I was looking for, but couldn't remember what to search for, thanks for this!!

What distribution does the data need to be in order for the Bayes Estimator to work?

i don't know. IMDb uses this.

Maybe you could take a look at implementations of the ELO ranking method, which takes into account the rank of both players before ranking (meaning Player1 will gain less points when winning against Player3 than Player2).

https://en.wikipedia.org/wiki/Elo_rating_system

ELO was one of the rating systems I had in mind, but it seems old compared to Glicko2

(PHP / SQL)

(1 way to do this, I've never actually calculated player rank, but this came to mind)

player_stats
-- player_id
-- wins (int)

player_id    |    wins
1                8
2                99
3                1
4                40


// find who the current player should play against 
// +/- 10 wins
"select * from `player_stats` where wins Between ($current_user_wins - 10) AND ($current_user_wins + 10) limit 1"

"Also, how would your scoring system encourage weaker players to play against stronger players and stronger players to want to play against the weaker players."

// find a random opponent
// from a larger pool
// + / - 50 wins for a bigger pool
"select * from `player_stats` where wins Between ($current_user_wins - 50) AND ($current_user_wins + 50) order by RAND() limit 1"

(Be sure to mind any negative values and results with 0 rows)

For overall rank, I think I'd find the player with the most games played or store it somewhere and calculate each players rank out of that - ie: if the most games played by any given player was 100, player 2 would be at the top, player 3 at the bottom and player 4 somewhere in the middle

Your algorithm will suffer from many imbalances. The people I'm doing this for is already doing a similar handwavey technique that has not been mathematically proven and players are quick to exploit the weaknesses in the rankings if it's possible to do.

At least I tried? Everyone else just linked to other answers. Had you made it clear in your question that you / they tried something like that, my answer might have been different.

Hi Mario, I appreciate you taking the time to write an answer!

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