The Elo rating system was devised by Arpad Elo, a master-level chess player and physics professor, as a way to calculate the relative skill levels of players. A modified system is used in FIDE ratings, as well as many online competitive video games.

> The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to score an equal number of wins. A player whose rating is 100 points greater than their opponent's is expected to score 64%; if the difference is 200 points, then the expected score for the stronger player is 76%.

The winner predictor formula is:

Prob. of Victory for Home Team = (1/(1+10^-((rating_home - rating_away + HGA)/n)))

After the result the ratings are updated by:

New Rating = Old Rating + k*(R - Prob. of Victory for Home Team)

The original method does not account for a home ground advantage (HGA) however this is a massive factor is finding win probabilities in cricket. The 'k' value reflects importance of each game on the overall rating; higher values means ratings fluctuate rapidly and lower ones means teams can't overtake others. Via the method of least squares^1 I found optimal values of k and HGA to be 22.2 and 64 respectively. R would be 1 for a home team victory, 0 for a loss and 0.5 for draws or losses. All teams begin on a rating of 1200.

Below is the graph of Elo Ratings beginning for 1946.

Elo Rating Graph Plotly- No Annotations for each game: https://plot.ly/~thespacetimelord/1.embed

# Interesting Observations

* Quite unsurprisingly the highest rating was achieved by Australia in 2008, after beating India in the *infamous* Sydney game. The win at Perth by India was a result one of the biggest upsets in history. But not the biggest one, that goes to the 1990 test win by England at Kingston.

* The West Indies, post 80s, team didn't have the absolute high that Australia managed but they managed to remain the top ranked team, uninterrupted, for longer.

* South Africa manged to attain the top rank for a short amount of time despite having been banned.

* Sri Lanka, Pakistan, Bangladesh, Zimbabwe and New Zealand have never managed to attain the top rank in these ratings.

* The early 2000s SA should be talked about as one of the absolute best. Their peak rating is second after 2008 Australia.

* Despite losses across 2018 India remains the top ranked team, mostly on the back on *excellent* home season. Where they achieve their highest rating ever.

More detailed discussion: https://old.reddit.com/r/Cricket/comments/cq5xbb/an_elo_rating_system_for_test_cricket_post1946/