### What are Elo ratings?

## What is Elo?

Very simply, Elo ratings are a method of ranking teams and predicting the outcome of a game. An average team has 1500 rating points, and gains or loses rating points depending on the match result (teams always gain rating points for winning, and lose rating points when they lose). The method can also give a more accurate indication than a ladder of how well a team is performing.## How Elo ratings are calculated

Elo ratings are calculated by giving every team a rating of 1500, which is considered an average Elo rating. Teams that joined the league after that time started at 1300. The first seasons are:- AFL: 1990
- A-League: 2005-06
- BBL: BBL01 (2001-12)
- NBL: 2009-10

A team gains rating points when they win, and lose rating points when they lose. It is a zero-sum system, meaning whatever one team gains their opponent loses. Teams gain more points for beating teams with a higher rating than theirs compared with beating a team with a lower rating than theirs. The margin is taken into account too, but is calculated using diminishing returns. This means that a team with a high rating that beats a team with a low ranking by a large margin doesn't gain many rating points.

Some examples:

- Hawthorn Hawks (1522) defeated Melbourne Demons (1516) by 67 points in round 4 2018, Hawthorn gained 17 rating points
- Sydney FC (1643) defeated Central Coast Mariners (1363) in round 6 2018, Sydney gained 2 rating points
- Sydney Swans (1625) lost to Gold Coast Suns (1301) in round 18 2018, Sydney lost 26 rating points

One last thing, at the end of each season all team ratings are adjusted towards the average rating of 1500. This can be observed in game results over time: the same team doesn't win the Grand Final every year.

## How Elo ratings can predict game outcomes

By comparing the rating of two teams through a mathematical formula, we get a percentage chance of winning. In the same Sydney v Gold Coast game mentioned above, Sydney had a 87% chance to win. This is also why Sydney's rating changed so much: if the favourite wins, the rating change is small. If the underdog wins, the change is bigger.

## What else can Elo do?

Elo ratings also give a very good indication of when a team is on the decline, or when a team is starting to win consistently. For example in the 2018 AFL Home and Away season, Port Adelaide finished round 17 with a rating of 1598, but watching the ratings over the next few rounds showed a steady decline.## What can't Elo do?

One thing Elo is not great at predicting is the margin of victory. For example, Elo ratings predicted that Richmond had a 71% chance to win vs Essendon in round 22, 2018 AFL Home and Away season yet Richmond only won by 8 points.## Show me the numbers

For those interested, these are the formulas used in our Elo calculations.- Rating change: R
_{n}= R_{o}+ KG(W - W_{e}) - R
_{o}= the team's original rating - K = constant, set to 20 for these calculations
- G (AFL & NBL) = margin of victory multiplier = ((winning team margin of victory + 3)
^{0.8}/ (7.5 + 0.006^{(winner Elo - loser Elo + home ground advantage})) - W = match result: 1 for a win, 0.5 for a draw, 0 for a loss
- W
_{e}= expected match result, calculated by this formula: 1/(1 + 10 ^ (W_{opp}- W_{o}) / 400)), where Wo is the team's rating before the game and W_{opp}is the opponent's rating before the game. - Home ground advantage is 100 if the home team wins, -100 if the away team wins.

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