The Non-League Ranking has now been fully adapted to the ELO Rating system in order to rank the clubs at step 1 to 4 in the Non-League pyramid (Currently 310 clubs and 320 clubs when the restructuring has been fully completed from beginning of the 2022/23 season).
The ELO Rating system is in general very simple. All clubs will at any given point in time have a single value measuring their strength at which they are ranked against the other clubs included in the ranking, the ELO value.
Clubs will then either gain or loose ELO points based on each game they play in the League, FA Cup or FA Trophy. The amount of points won or lost will be based on the strength of the opposition they are playing. Winning against a stronger opponent (higher ranked with a higher ELO value) will give more points than winning against a weaker opponent. The same will happen when loosing. Higher ranked teams loosing to a lower ranked team, will loose more points than if the opposite was the case. Draws will simply mean that the higher ranked loose some ELO points and the lower ranked team wins some ELO points, again based on their relative strength.
Teams can never gain or loose ELO points from matches not played or finished due to the match being cancelled, abandoned or forfeited. These matches will simply be excluded from the rating.
The ELO rating explained
In order to determine the amount of points lost and won (which is always the same amount) between the two teams playing each other, a win probability is calculated.
The formula is like this:
Win Probability = 1 / (10(-diffRating/400)+1)
diffRating is the difference between the 2 teams ELO rating point.
This means, that a team that has 100 ELO rating points more than the other team, will have a win probability of 0.64 (on a scale between 0 and 1). The lower ranked team will in this case have a Win probability of 0.36.
The actual result of the game between the 2 teams will then decide how many ELO points both teams will either win or loose by comparing the expected win probability and the actual result. A win is given the value 1, a draw 0.5 (half win and half defeat) and a defeat 0.
The difference between the win probability and the actual result is then multiplied with the so called K factor. The higher the K factor the more points are exchanged. In the example below the K-factor is set to 20.
If the team with 100 ELO points more than the opponent wins, the calculation of ELO points exchanged will look like this:
Team A: 1500 ELO points
Team B: 1400 ELO points
Team A has a Win probability of 0.64 and Team B has a win probability of 0.36
If Team A wins:
Team A: 1 - 0.64 = 0.36. With a K-factor 20, the ELO points gained for Team A will be 0.36 x 20 = 7.2 ~ 7 point, taking them to a new ELO score of 1507
Team B: 0 - 0.36 = -0.36 => -0.36 x 20 = -7.2 ~ -7 ELO points, taking them to a new ELO score of 1393
If Team B wins:
Team A: 0 - 0.64 = - 0.64. With a K-factor 20, the ELO points lost by Team A will be -0.64 x 20 = -12.8 ~ -13 point, taking them to a new ELO score of 1487
Team B: 1 - 0.36 = 0.64 => 0.64 x 20 = 12.8 ~ 13 ELO points, taking them to a new ELO score of 1413
If Team A and B draws:
Team A: 0.5 - 0.64 = - 0.14. With a K-factor 20, the ELO points lost by Team A will be -0.14 x 20 = -2.8 ~ -3 point, taking them to a new ELO score of 1497
Team B: 0.5 - 0.36 = 0.14 => 0.14 x 20 = 2.8 ~ 3 ELO points, taking them to a new ELO score of 1403
In this way 2 teams will either get closer to each other or move away from each other in terms of ELO points but always relative to their strength.
The Non-League Rankings implementation of the ELO rating
The initial ranking
The initial ELO rating was based on the league the club was in from the formation of the Non-League Ranking (Beginning of Season 2014/15):
Clubs at Step 1 was given the ELO score 1800
Clubs at Step 2 was given the ELO score 1600
Clubs at Step 3 was given the ELO score 1400
Clubs at Step 4 was given the ELO score 1200
The ELO points allocated will result in an initial average difference between each step of 200 ELO points (Win probability of 0.76)
As it is well known, the home team has an advantage against the travelling opposition in most cases. As the rating should not be affected by this, the home advantage most be taken into account when calculating the win probability
As shown earlier the win probability is based on the difference between the ELO points of the 2 teams. The home team will therefore be allocated some extra ELO points (only when calculating the win probability) in order to increase the win probability for the home side.
The initial home advantage has been calculated to 45 ELO points. The home advantage will be monitored every month and be adjusted accordingly in case of a change in the home win/draw/loose ratio.
If we add the home advantage to the previous example, the calculation will look like this
Team C: 1500 ELO points (The home team in this example)
Team D: 1400 ELO points (The away team in this example)
Team C has a Win probability of 0.70 and Team D has a win probability of 0.30 (RankDiff = 1545 - 1400 = 145)
If Team C wins:
Team C: 1 - 0.70 = 0.30. With a K-factor 20, the ELO points gained for Team A will be 0.30 x 20 = 6 point, taking them to a new ELO score of 1506
Team D: 0 - 0.30 = -0.30 => -0.30 x 20 = -6 ELO points, taking them to a new ELO score of 1394
If Team D wins:
Team C: 0 - 0.70 = - 0.70. With a K-factor 20, the ELO points lost by Team A will be -0.70 x 20 = -14 point, taking them to a new ELO score of 1486
Team D: 1 - 0.30 = 0.70 => 0.70 x 20 = 14 ELO points, taking them to a new ELO score of 1414
If Team C and D draws:
Team C: 0.5 - 0.70 = - 0.20. With a K-factor 20, the ELO points lost by Team A will be -0.20 x 20 = -4 point, taking them to a new ELO score of 1496
Team D: 0.5 - 0.30 = 0.20 => 0.20 x 20 = 4 ELO points, taking them to a new ELO score of 1404
If Team D was at home against Team C, the RankDiff would be 1500 - 1445 = 65 resulting in the following win probability: Team C = 0.59 and Team D = 0.41.
The K-factor is used to determine the amount of ELO points that are exchanged between clubs based on the difference between the actual result of the game and the calculated win probability as shown before.
The K-factor used in the Non-League ranking will be 20 in the first 3 months of the season in order to more rapidly adjust for promotion and relegation especially for the clubs coming in to the Non-League Ranking from outside Step 1 to 4, but also between the steps within the ranking. In the following 3 months it will be reduced to 19 and finally at the end of the season the K-factor used will be 18.
New clubs joining the ranking each season
Each year new clubs are joining the Non-League Ranking through either promotion from Step 5 or through Relegation from League 2. These new clubs will be getting an initial ranking based on a combination of how other promoted or relegated clubs have performed in their initial season in terms of League finishing and how well the clubs themselves have performed in their promotion or relegation season.
Clubs being promoted from Step 5 will be ranked based on both their own performance at Step 5 but also how other clubs from the same Step 5 league has performed in recent years.
FA Cup opponents outside the Non-League Ranking
When clubs in the Non-League Ranking plays FA Cup matches against clubs outside the ranking, the clubs from the Premier League, The Football League and Step 5 and 6, will be given an ELO rating to indicate their strength.
The ELO rating of the clubs outside the Non-League Ranking will be adjusted each season to ensure that it reflects the strength between the levels as seen in recent seasons. The initial average strength for the clubs at different levels for season 2014/15 was set as follows:
Premier League clubs: 2200
Championship clubs: 2100
League 1 clubs: 2000
League 2 clubs: 1900
Step 5 clubs: 1100
Step 6 clubs: 1000
Winning in extra time or from a penalty shoot-out:
In order to make it more fair for clubs who loose a cup match after holding a draw after 90 minutes, the normal 1, 0.5 and 0 for win, draw and loose in regular matches, has been tweaked a bit. A win after extra time or a penalty shoot-out will be regarded as 0.75, effectively half a win and half a draw. A loss in these conditions will then be 0.25.
The ELO System
The ELO system was originally developed to measure the strength of individual chess players, but has since been used to rank other types of sports and competitions. The current FIFA Ranking is based on a variation of this. Some other football related rankings use the ELO ratings as well. See below for references.
References to other uses and descriptions of the ELO rating system:
European club ranking using ELO: ClubElo
Ranking International football with the ELO rating: Eloratings
More on the ELO rating system: Wikipedia on ELO Rating