Round robin structures

Double round-robin dictates number of games in season

Structure of football competitions by leagues aka Round robin

Most common format in football leagues is a double round-robin, r.r, tournament what basically means that each team plays against each other twice, once at home and once away!

Major leagues in Europe are played in this format
A match outcome is converted to points that reflect the value attached to each outcome
(3 points for a win, 1 for a draw and 0 for a loss).

These points accumulate during a season and the team with the highest number of points wins the league
A significant constant (in the model making) is the total number of matches within each football league, r.r(League)

Let’s find the r.r for the English Premier League which counts 20 teams
According to one well-known combinatorial principle, if we can choose one thing in m ways and another in n ways, then the total number of ways we can choose those two things at the same time is equal to: m*n
In our example first team we can choose in 20 ways, so for the second, opposite team left 20-1=19 ways

Total number of games:
r.r()=20*19=380

(if you have doubts about the result of the above calculation-google it)

England Championship has 24 teams, so the total number of games must be equal:
r.r( )=24*23=552

Now it is not difficult to determine a formula that, depending on the number of teams, return the number of all required (double!)round-robin matches in the season:
r.r(League)=n*(n-1)

And here a story about r.r is not finished
The story does not end here, for we are now in a position to calculate the number of home/away matches by the team!
Number of home/away matches for individual team: r.r(n)/[2*n]

Another example-Premier:
n=20
r.r=380
home/away by team :
r.r(n)_H= r.r(n)_A= r.r(n)/n =380/20=19
Total number of rounds in season per club :

…………………………………………………….. r.r(n)_H+ r.r(n)_A=2*r.r(n)/n=2*19=38

.

Therefore, the season includes 42 rounds because in LaLiga 2 has 22 teams
Simple as that