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InfoRugby's ratings are based on an application that attributes
points to each team depending on the results of the matches. The
heuristic method used is based on the principle that the points
attributed depend on several criteria, the most important being:
the quality of the opposing team. If we consider that "all teams
are created equal" - indeed, nothing says that the Blacks are inherently
better than the Andorrans - we attribute points to each team depending
on the matches played. Once all of the matches have been taken into
consideration, we rank the teams. To do this, we process all of
the matches once again, this time including the opponent's value,
which comes directly from the previous ranking. We continue this
process until each team's score has stabilized. In this way, the
order in which the matches are played has no importance whatsoever,
and each match can be taken into account over 1000 times, depending
on the desired accuracy. Therefore, we must run the whole application
in its entirety each time a match is played. This is an automatic
ranking system that is often used in image processing algorithms,
for instance. The objective of this system is to rank elements in
a n-dimensional space (one single dimension in the case of InfoRugby),
based on a differentiating criterion, without knowing the elements'
positioning.
For
the ranking by nation, all of the matches played in the last 64
months are taken into consideration, which comes out to more than
700 matches for more than 70 teams. We establish our ranking from
this information. The following nations are thus deleted:
- Those nations that have not participated
in at least three matches against at least two different teams;
their rank is not really pertinent.
- Those nations belonging to an isolated group; in other words,
nations that cannot rejoin by transitivity the rest of the nations
(no isolated groups have been identified yet).
- Those nations that are ranked below the 50th position.
InfoRugby periodically carries out this filtering process so as
to offer the 50 best teams out of all the teams at the international
level at any given moment, which prevents us from being confined
to the 50 same nations.
Points are calculated according to
the five following criteria:
The Value of the Opposing Team: This stems directly from
the results. All teams have 1 point to begin with. The "value" of
each team is determined according to four other criteria of the
first pass. Then, the values are calculated. We continue in this
way as long as the value of each team between two loops is less
than a certain (the smallest possible) delta.
Date of the match: Each match is weighted in inverse proportion
to the date on which it took place. If M is the number of months
between the date of the match and the current month, then the match
is weighted as follows: 1-Log(M+6/7).
Importance of the match: Most matches have a weighted value
of 1. The only matches that considered more important are World
Cup matches. Indeed, nothing really states the FIRA tournament is
less challenging then the tri-nations. The principle is to add points
to the teams participating in the World Cup and not "to multiply"
the weight of the match as is done with match date. In doing so
this would penalize the teams losing World Cup matches.
Home/visitor: Given there are roughly 1.6 more wins at home
than away, a corresponding coefficient is applied to the goal average
during an away victory and a home defeat. "Compensation" is attributed
for a zero-zero away match.
Point Difference: The square root of the difference of points
per match is multiplied by the score obtained by each team.
Example of points assigned to nation A after a 20 to 10 defeat
of nation B on nation B's turf.
Pts(A) := Pts(A) + ((((1+Val(B))*1.6*Sqrt(20-10))+ (Val(B) -
5)*5 + Importance * 10) * (1 - (Log((current month-date of the match+6)/7))))
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