# About

#### What is this?

This is an Elo rating system designed specifically for handball. The purpose of this list is to act a measuring stick for the relative ability of all the world's men's national teams using a method that, in general, awards points to teams when they win and deducts them when they lose. The database this system uses consists of about 7000 competitive matches since 1994, in all competitive tournaments and qualifiers associated with the IHF or any of its continental federations.

The Elo rating system was invented in the 1960s specifically to rate competitive chess players, but has since found use in a variety of different competitive venues, notably in many competitive video games and perhaps most famously by FIFA in their FIFA World Ranking.

The International Handball Federation has not seen fit to develop an official list comparable to FIFA's, hence why this website was created.

Neither this website nor its creator is affiliated with the IHF or any related organization.

# Methodology

#### The basis

Lesser known than the FIFA World Ranking is the World Football Elo Ratings, which generally is considered the better of the two. A detailed description the system this list deploys can be found on Wikipedia, and this is where the basis of this handball ranking comes from.

#### The formula

The core system is described on Wikipedia quite elegantly. A team's new rating after playing a match is equal to its rating before the match plus a value "P" (for Points), where P is the product of a tournament weight constant, a goal-difference factor, and the actual result subtracted by the expected result. These two formulas remain the same for this list, but not all of the variables are exact copies in terms of how they are calculated.

#### The Expected Result

This formula looks at the rating difference between the two competing teams, and outputs a probability value that represent which outcome the system expects. An output of 0.25 would represent a somewhat confident expectation of a loss, 0.5 would represent an expected draw, and 0.75 would represent a somewhat confident expectation of a win. This aspect of the system remains unchanged.

Not shown in this formula is that this system considers a team playing on home soil to have an additional 100 points, as does the handball rating. This means a team playing at home is deducted a greater number of points by losing compared to on neutral grounds, and wins fewer by winning.

#### The Weight Constant K

Pictured above is this system's weighting regime, which essentially says that a World Championship win is worth twice as many points
as a win in a qualifying match to the same tournament.
Worth noting is that the football system has five tiers where the top has a K of 60, and this is where the real differences between these rating systems begin.
The reason for this change lies in the purpose of these weight tiers.

In a perfect statistical utopia where any given pair of teams are equally
likely to meet, this system could simply weight all competitive matches equally.

However, handball competitions are highly geographically
compartmentalized, meaning the top teams from weaker continents would be consistently overrated as they lack teams that can challenge them.

The weighting system keeps this effect in check by facilitating the flow of points between continents more effectively when cross-continental matchups do happen.
That being said, the top-tier competitions in handball are much more frequent than in football, so the weighting regime has been appropriately narrowed.

The fourth tier, worth 10 points, currently contains only the South-Central American and North American-Caribbean qualification tournaments to the Emerging Nations Cup.

Friendly matches and tournaments that do not qualify for any of the tournaments that eventually lead to the World Championship or the Olympic Games are not considered.

#### Goal Difference

The Football Elo system grants a multiplying factor based on goal difference shown in the table above, where a 5-goal win reaps twice as many points as a single-goal win. This consideration is also necessary in handball, but requires a different approach.

Pictured above is the comparison of the goal difference distributions of handball and football. The football graph is based on numbers taken from footystats.org,
while the handball graph is based on data from this website's database of ~7000 competitive matches played between roughly 1994 and the end of 2022.

The football results are a textbook example of an exponential distribution (draws aside), but the handball results are much closer to being linear.
This is presumably explained by the rules of handball, where teams are punished for passive play while no such penalty exists in football,
making it easier for better teams to run up the score while not necessarily representing the relative strength of the teams.
This means one can't simply match the proportions to figure out which goal difference in handball is worth a G-factor of 2.

To avoid very large wins having an outsized effect on the calculation, this relatively steep Sigmoid curve was chosen. A goal-difference of 8 here is worth twice as many points as a goal-difference of 1, with the factor having a maximum value of 3 rather than 2.65 to further increase the reward for a larger win.

#### Other

Note that teams with less than 10 matches are filtered out of the list, as their ratings are not considered valid.