# How can I make Elo ranking system more diversified?

As far as I know, Elo ranking system generates points between 100-2800 generally.

However lets say we have 1,000,000 players. Now this range of points is too small. Many players would get the same score

I want to prevent this happening. How should I modify the algorithm?

What I want is having a higher range of values so players would not get equal scores but rather get different scores?

• It seems from the Wikipedia article that you referenced that two players can have the same ELO ranking. Why would you want to prevent two players with equal skill to have different ranks? That doesn't make much sense to me. Theoretically you could have dozens of equally skilled players. In that case ranking them without duplicate ranks would simply be an exercise in randomization and wouldn't be of much value. If you can clarify how you would want to treat equally skilled players, we might be able to provide a better answer. – StatsStudent May 14 '16 at 3:45
• Evidently you could just show decimal places for the ratings (or multiply all scores by e.g. 10) to have more granularity, but honestly it hardly matters when people are within a few Elo. Also, whether ratings are within a certain range (say, always >0 or >100 or >1000) is an extremely arbitrary decision that is made by the organisation running the rating system. If they did not impose the restriction (there's nothing in the basic system that really requires this) some people might have negative Elo. I suppose, they feel would be bad for the motivation of people, which is the reason for that. – Björn May 14 '16 at 6:08
• To expand on showing decimal places or the like: One problem with doing so is that the precision with which you have estimated the rating (even if people were to stay at a constant skill, did not vary in form from day to day, etc.) with a lot of imprecision and you end up giving a number to a precision that is a lot higher than the uncertainty around it making the apparent extra precision pretty meaningless. – Björn May 14 '16 at 6:10
• @Björn well i am planning to have score based ranking and if many players get same score, how can i rank them? :D – MonsterMMORPG May 14 '16 at 17:52
• @StatsStudent you are right but i have to rank the people and if many people gets the same rank it causes some quite confusion – MonsterMMORPG May 14 '16 at 17:53

In Elo, the starting rating is arbitrary, it doesn't matter what number you pick. So, if you start from an higher value (e.g. $R_0 = 1500000$), use a big constant value (e.g. $K = 12000$) and a big denominator for expected score formula, e.g.
$$E_A = \frac 1 {1 + 10^{R_B - R_A \over 400000}},$$
I think there's no problem if many players would get the same score, indeed. In our ranking system rankade (here's a comparison between our ree and most known rating systems), public displayed scores have 4-digits format (e.g. $2134$), but calculation features many decimals and ranking works with real values.
• If $K=320$ and $d=4000$, I suggest you a bigger starting value, to avoid negative values. – Tomaso Neri May 15 '16 at 15:24