## Elo vs Bradley-Terry model

One of those drafts I should expand…

# Elo rating system

A few days ago, a chess tournament took place. In the quarter of finals, MVL, rated 2860, played against Wesley So, rated 2741. Who should win ?

The Elo rating system answers this question, and gives a probability:

```
wesley_so = 2741
mvl = 2860
D = mvl - wesley_so
probability_mvl_wins = 1/(1+10 ** (-D/400))
probability_so_wins = 1 - probability_mvl_wins
print(probability_mvl_wins)
```

```
$ python mvl-wesley-so.py
0.6648579785547648
```

MVL should win a game with a probability of 66%. This is not what happened though, So won

## Monte carlo

There are many interesting applications. One I liked is how to estimate the winner of a tournament.

# The Bradley-Terry model

I came across a very interesting article about ranking chocolates. They compared 2 chocolates, and choose a winner. After many pairwise comparisons, it is possible to use the Bradley-Terry Model in order to assign each chocolate a score. This is well explained in the wikipedia page, here is an example with numbers about how to compute the scores

See a typo ? You can suggest a modification on Github.