Elote

A python package for rating competitors based on bouts. The classical example of this would be rating chess players based on repeated head to head matches between different players. The first rating system implemented in elote, the Elo rating system, was made for just that [3]. Another well known use case would be for college football rankings.

There are a whole bunch of other use-cases for this sort of system other than sports though, including collaborative ranking from a group (for voting, prioritizing, or other similar activities).

Currently implemented rating systems are:

• Elo [3]
• Glicko-1 [1]
• ECF [4]
• DWZ [5]

Usage

There are a bunch of examples in the examples directory if you want to dive a little deeper, but Elote is pretty simple to use. The two objects we care about are Competitors and Arenas. Competitors are the things you are rating, and an Arena is a mechanism to schedule Bouts between them. First, Competitors:

Competitors

from elote import EloCompetitor

good = EloCompetitor(initial_rating=400)
better = EloCompetitor(initial_rating=500)

print('probability of better beating good: %5.2f%%' % (better.expected_score(good) * 100, ))
print('probability of good beating better: %5.2f%%' % (good.expected_score(better) * 100, ))

This creates two competitors, intilized with different starting ratings. Right away we can see how a match between them is likely to go:

probability of better beating good: 64.01%
probability of good beating better: 35.99%

If we actually held the match, and there was an upset, updating their rankings is as easy as:

good.beat(better)

or

better.lost_to(good)

We can then rerun the predictions and see updated probabilities:

    probability of better beating good: 61.25%
    probability of good beating better: 38.75%

Not a huge change using default settings.

Arenas

Arenas are a useful abstraction for scheduling large numbers of bouts or matches. The LambdaArena object takes in a lambda function with two arguments which returns a boolean for if the first argument won (None for ties). Without ever manually setting up any competitors, as long as the arguments are hash-able, the Arena object will create all of the competitors, run the matches and rank them all.

Here's a toy example which uses a lambda function that just compares two integers. With this, we've implemented the worst performing, most over complicated sorting algorithm conceivable, but it works:

from elote import LambdaArena
import json
import random


# sample bout function which just compares the two inputs
def func(a, b):
    return a > b

matchups = [(random.randint(1, 10), random.randint(1, 10)) for _ in range(1000)]

arena = LambdaArena(func)
arena.tournament(matchups)

print(json.dumps(arena.leaderboard(), indent=4))

The final leaderboard looks like:

[
    {
        "rating": 560.0,
        "competitor": 1
    },
    {
        "rating": 803.3256886926524,
        "competitor": 2
    },
    {
        "rating": 994.1660057704563,
        "competitor": 3
    },
    {
        "rating": 1096.0912814220258,
        "competitor": 4
    },
    {
        "rating": 1221.000354671287,
        "competitor": 5
    },
    {
        "rating": 1351.4243548137367,
        "competitor": 6
    },
    {
        "rating": 1401.770230395329,
        "competitor": 7
    },
    {
        "rating": 1558.934907485894,
        "competitor": 8
    },
    {
        "rating": 1607.6971796462033,
        "competitor": 9
    },
    {
        "rating": 1708.3786662956998,
        "competitor": 10
    }
]

Examples

In the examples directory there are a bunch of basic examples using generated data to show different features of elote, as well as some use cases using real data, so far all from MasseyRatings.com, but transformed into JSON [2].

Installation

    pip install elote

Supporting only python 3.4+

Contributing

This is very much still a work in progress, so if you're interested in contributing, there is lots to do. Open up an issue or a PR and we can coordinate efforts.

References

• [1] http://www.glicko.net/glicko/glicko.pdf
• [2] MasseyRatings.com
• [3] Elo, Arpad (1978). The Rating of Chessplayers, Past and Present. Arco. ISBN 0-668-04721-6.
• [4] http://www.ecfgrading.org.uk/new/help.php#elo
• [5] https://en.wikipedia.org/wiki/Deutsche_Wertungszahl