Elo rating system: start value when players can join the game constantly

I've implemented an Elo rating system in a game. There is no limit for the number players. Players can join the game constantly so the number of players probably rises gradually.

How the Elo values are exactly calculated isn't important because of this fact: If team A beats team B then A's Elo win equals B's Elo loss.

Hence I've got a problem concerning the starting values for my rating system:

• Should I use the starting value "0" for every player? The sum of all Elo values would be constant. But since the number of players is increasing there would be some kind of Elo deflation, wouldn't it?
• Should I use any starting value greater than 0? In this case, the sum of all Elo values would constantly increase. So there could be an Elo inflation. The problem: Elo points lose value but the starting value keeps always the same.

What should I do? Can you help me? Thanks in advance!

You can start at zero and add a fudge factor to the displayed score to keep it above zero, or you can start at 1000 - they are the same thing. Yes, with the 1000 starting point you'll have an increasing number of total ELO points in the system but it will always be the same number per player on average - 1000. The starting value for Elo is always the current average. ELO is a zero sum game, points lost by player A are gained by player B.

When you set a starting point at 1000 what you are essentially saying is that the average player = 1000 pts. With a closed group of initial players (beta testers?) this is true, within that group average = 1000. But if the game is something you improve at with time then your closed group average player becomes highly skilled compared to someone who hasn't played.

Now when you assign a 1000 to a new player you are saying new average players = existing highly skilled average player. This is not true, they are likely to be much less skilled that your original closed group. So the new player loses points and your highly skilled players gain => inflation. What you would need to do is accurately assess the skill of new players and assign them a ranking that is more in keeping with their actual skill. This could be done be assigning them a "provisional ranking" for their first x games until you get a feel for their skill. When provisionally ranked only their ELO score would change, not those of the people they play. Once they join the real system the points they bring into the scored ELO would roughly equate to their actual skill and they wouldn't move up or down dramatically => no inflation or deflation.

In short: Provisional rankings

This site used the elo rating system. They start at 1200

taken from http://gameknot.com/help-answer.pl?question=29

GameKnot rating system is based on Elo rating system with a fixed K = 20 and the following modifications:

The first 20 games are used to establish player's rating on the website. During the first 20 games, the player's rating is calculated as an average of the ratings of all his/her opponents, +400 in case of a win, -400 in case of a loss, same for a draw. +/-200 points are used when playing against a player with a provisional rating. PLayer's rating is provisional during the first 20 games, after which it becomes established. Player's rating is considered to be equal to 1200 during the first 5 rated games.

Timeouts are counted as wins only if there were at least 3 moves made in the game (losses are always counted for the timed out players, regardless of how many moves were made).

The higher of two ratings, at the beginning of the game and at the end, is used to calculate the rating adjustments after the game is over.

For example, if during your first 20 rated games, you played 3 games and you won against 1200 player with provisional rating, then against 1400 player with established rating, but lost against 1600 player with established rating, your rating will be: ( (1200 + 200) + (1400 + 400) + (1600 - 400) ) / 3 = 1467

Or, if during your first 20 rated games, you win against 1200 provisional, win against 1400 established, lose against 1600 provisional, draw against 1500, your rating will be: ( (1200 + 200) + (1400 + 400) + (1600 - 200) + 1500 ) / 4 = 1525

Elo works on the difference in the ratings of the two players or teams, the actual value is irrelevant. You can start at any number you like. I run a system for the Facebook Scrabble League with a starting value of 5000 simply to distinguish it from other Scrabble ratings systems out there.

Inflation does not result from over-rated newcomers losing points to experienced players - that all evens out in time. Inflation results from people with less than average ratings leaving the system. This is what tends to happen in online games unlike real life chess, where deflation is a problem because highly rated players retire and take their points out of the system.

But do you need to worry about inflation? The only time it is important is if you wish to compare the performance of current players with historical figures - not a problem any online gamers are likely to face. Even if you do worry about inflation, it's easy to correct. Find the mean rating of all your current players and compare it with the start figure, if it's too high, reduce everyone's rating to bring it back in line. In my experience a reduction of 1 or 2 points per ratings period does the trick and accounts for a lot of newcomers who get thrashed and don't come back.

Many systems give newcomers higher K values in order that they find their level more quickly.

Another approach is not to rate newcomers until they have played their first ratings period, at which point you calculate the rating based on what if would have to have been for Elo to predict the results correctly. This is impossible if you have all unrated players together and (I think) would involve recursion if you have multiple newcomers in a tournament. It also undermines the zero-sum principle of Elo and removes your ability to measure inflation. However, talking to people who use this system, I am told "it all evens out" in practice.

I would also add that we have one determined player who has lost all but 21 out of 732 games he's played in the last four years and his Elo is still about 4100. The ratings points he loses each round are rapidly approaching zero.

I don't know if it is useful, but Mark Glickman's Ratings Page discusses some issues with Elo ratings, their declines, etc. (see the last few paragraphs there). Also see his rating system, the Glicko system, which seems to account for playing frequency and discusses rating reliability. Finally, his research page has a lot of papers discussing ratings and their reliability.

Hope that helps.

1. Do players see this score?
2. Will the players understand Elo?
3. Will players continue to play if their score becomes negative?

I would start everyone out at some positive point value (10, 100, 1000, it doesn't matter). When two people of relatively capability play each other, the scores trade as expected. Where you need to concentrate is some sort of relative capability between two players.

Suppose, later on in the game's life, I have 25000 points, and you're a n00b with 100. I beat you, I gain nothing and you lose nothing. Why? Because I just pwned a n00b, that's why. There should be no advantage for a new player to take down a starting player. Also, even if you are in some point range, you should implement something where you can only earn so many points from a given player in a certain time range.

Obviously, this will be something that will be continually tweaked throughout your game's life time.