# Frequency-based ELO rating

To replace the context, you probably heard of the recent new game Apex Legends. If not, it's a battle-royal game where 20 squads of 3 players compete to be the last team standing. So in the end of a game, your squad placement is between 1st and 20th.

Currently, there is no in-game ranking system. My goal is to have my own ranking system, waiting for the official one.

For that, I am searching a way to have a quiet efficient frequency-based ELO rating. A "normal" ELO will not be efficient - I think - because we could not know the ELO of the other 19 teams.

Assuming this ELO formula:

$$elo_{new}=elo_{current} + K \times (R - E)$$

$$K = \left \{ \begin{array}{a b} 200 , & 0 \le games < 10\\ 100, & 10 \le games < 15\\ 80, & 15 \le games < 20\\ 50, & 20 \le games\\ \end{array} \right .$$

$$R = (position * f_{position})$$

$$E = (best * f_{best})$$

$$f_X = \frac{X}{games}$$

with:

• $$\elo_{current}\$$ ; the current player ELO rating

• $$\position\$$ ; the player' squad position in the last game

• $$\games\$$ ; the player's total number of played games

• $$\f_{position}\$$ , the player's $$\position\$$ frequency

• $$\f_{best}\$$ , the most frequent player's $$\position\$$ frequency

If the player has been 5th and 8th 5 times each, and all other positions less than 5, the most chosen frequent position will be the "worst", so 8th in this example.

My current problem is about $$\E\$$ - and maybe $$\R\$$? -, I think that my estimation formula is bad, because my ELO mainly decreases.

I tried many different solutions, with and without frequencies into $$\E\$$ and $$\R\$$, or only into $$\E\$$...

A possible solution may be to add an influence on the estimation and/or the result by the difference between the most probable position ($$\best\$$) and the position got on the last game ($$\position\$$).

But I suppose I am just not very good in making formula and that I don't know how to properly use frequencies, or divisions...

I thank in advance all of you who can lead me to the right way!

• Welcome to GDSE. Could you edit this to better indicate what exactly your question is? Are you asking us if your E & R formulas are bad? If so, can you provide a concise example that demonstrates the problem your having with the current formulas? It's highly unlikely that others are going to generate their own test cases to trouble shoot something like this. – Pikalek Feb 12 at 21:50