Rn = Ro + KG (W – We)

I guess the first question would be what does Rn = Ro + KG (W – We) mean?

The first thing it means is that Brazil has found a way to be above Uruguay in the men’s football rankings which is quite fitting since every time they play, their games are displayed on my TV schedule as “The Brazilian World Tour”! I guess because Brazil have five stars above their emblem on their shirt representing 5 World Cup Wins as well as hosting the 2014 World Cup they need anything they can get and they believe they are the Harlem Globetrotters!!

The ELO (not Electric Light Orchestra) World Football Rankings is a ranking system developed by a mad scientist I’m sure. The equation goes something like this: (make sure you have your scientific calculator handy)

Rn = Ro + KG (W – We) 

Rn = The new team rating
Ro = The old team rating
K = Weight index regarding the tournament of the match
G= A number from the index of goal differences
W= The result of the match
We = The expected result

There is another formula that could be used which is:

P = KG (W – We) 

P = Points changed
K = Weight index regarding the tournament of the match
G= A number from the index of goal differences
W= The result of the match
We = The expected result

World Football Elo Ratings
World Football ELO Rankings

Status of match

The status of the match is incorporated by the use of a weight constant.

  • World Cup Finals (60)
  • Continental and Intercontinental Tournaments (50)
  • World Cup and Continental Qualifiers and major Tournaments (40)
  • All other Tournaments (30)
  • Friendly Matches (20)

Number of goals

The number of goals is taken into account by use of a goal difference index. G is increased by half if a game is won by two goals, and if the game is won by three or more goals by a number decided through the appropriate calculation shown below;

If the game is a draw or is won by one goal

G = 1

If the game is won by two goals

G = \frac{3}{2}

If the game is won by three or more goals

  • Where N is the goal difference

G = \frac{11+N}{8}

Result of match

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss).

Expected result of match

We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

W_e = \frac{1}{10^{-dr/400} + 1}

where dr equals the difference in ratings plus 100 points for a team playing at home. So dr of 0 gives 0.5, of 120 gives 0.666 to the higher ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher ranked team and 0.01 to the lower.

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2 thoughts on “Rn = Ro + KG (W – We)”

  1. Clear as mud, what happens if you win the Copa America? Does that count for many points or does it depend on how corrupt your Football Association is?

    Think this is the recipe for chimichurri loco!!!!

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