Mathematics of player levels in game development

My husband is a game developer and my contributions are usually of the sort where I look at what he’s done and say “hey wouldn’t it be great if it did this”. While these are usually positive ideas, they’re mostly a pain to code in. Today however, I was able to contribute some of my maths knowledge to help balance out one of his games.

Using an open api, he’d written a simple pokemon battle game to be used on twitch by one of our favourite streamers, FederalGhosts, and needed a way of determining player level based on the number of wins, and the number of wins required to reach the next level without recursion. While this post is specifically about the win to level relationship, you could use any progression statistic by applying scaling. Here we want to determine:

  • Number of wins (w) required for a given level (l)
  • The current player level (pl) given a number of wins (pw)
  • Wins remaining to the next level (wr) for a player based on current wins (pw)

Let’s take a look at a few ways of doing this. Each section below has the equations and code examples in python1. Assume all code samples have the following at the top:

import math

database = [
{"name": "player1", "wins": 5},
{"name": "player2", "wins": 15},
{"name": "player3", "wins": 25}
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