The Sportcompass __custom-made team rankings__ are similar to the
__Elo rating system__, in which
every team gets a rating based on past results. Our team ratings are a true estimation of the
teams' strength, because the calculation is optimised for predicting future results.

When two teams play against each other, we compare the actual result to the expected result. The team that exceeds the expectation, gains points in the ranking, while the other team loses the same amount of points.

The result is evaluated by goal difference, taking into account that goals are more
significant for close results. The evaluation of the actual result follows this
formula:

**R = 1 / (1 + p ^ (away goals - home goals))**

R ... Result rating (between 0 and 1)

p ... custom result parameter

The formula for the expected result is similar and uses the rating difference instead of
goal difference. 100 points difference correspond to one goal difference. If a team has home
field advantage, its rating is increased.

**E = 1 / (1 + p ^ ((away team rating - home team rating - h) / 100))**

E ... Expected result (between 0 and 1)

p ... custom result parameter (same as for actual result)

h ... rating adjustment for home field advantage

For both formulas above, p is the custom result parameter, which is optimised for predicting future results, just like the home field advantage in the expected result. The optimisation is done by experimenting with different parameter values and simulating predictions of past matches using only the results of earlier matches to assess the teams' strength. This mechanism makes the Sportcompass ratings especially effective in predicting the probability of future results. It also means the team ratings are as close as possible to the actual ability of the teams.

To calculate the points a team gains or loses after a match, we compare the actual result to
the expected result using the two formulas above. The difference is multiplicated with a
weighting (w), which determines the impact new results have on the rating and is also optimised
for predicting future results.

**P = (R - E) * w**

P ... Points gained/lost

R ... Actual result

E ... Expected result

w ... Match weighting

New teams get an initial rating of 1500.

Sportcompass calculates result probabilities and simulations of whole tournaments with the team rankings explained above.

To predict the outcome of a single match, we simply use all past results with a similar rating difference between the two teams and use the frequency of goal results as probabilities.

For simulations of tournaments, such as
__EURO 2021__, we simulate all matches randomly according to those
probabilities and show the frequency of various outcomes. The actual rules of the competition
and home field advantage are all taken into account correctly.