Compete in at least 10 matches for a particular arm (5 for women) and have competed at least once within the last year. Based on your weight you are given an initial rating and everytime you have a match your rating is recalculated. If you win a match you gain points and if you lose a match you lose points. Your rating then determines where you a ranked against your competitors.
In any ranking system you will get guys above you that you can beat, and guys below you that can beat you. A ranking system is based on a set of rules for how points are allocated to try and give a good estimate of someone's ability, but no system is perfect. The ranking system should be used as a guide as opposed to a definitive answer as to who is better than who.
Compete. The rankings system rewards match wins, but also activity. The more tournaments you enter the more chances you will have to gain more rating points. Anytime you beat someone with a higher rating than you, you will gain more points than if you beat someone with a lower rating than you. There are more points on offer in higher weight classes so you can potentially can gain a lot more points, but the competition will be tougher!
The rankings are split up into several weight ranges: 165lbs and below, 195lbs-165lbs, 225lbs-195lbs, 225+lbs and overalls. You will be ranked in a weight range if a weight class you competed in within the last year falls within one of the ranges or if your bodyweight falls within a ranking range within the last year.
To sensibly compare guys who compete in different weight classes the initial ratings are set so that heavier guys start out with a higher rating value than lighter guys, as typically a heavier guy will beat a lighter guy. Then based on a competitor's match results a rating is calculated for them (described below). Their rating determines their rank compared to other competitors.
For a competitor to have an official ranking for a particular arm they must have had at least 10 matches (5 for women) with that arm. Their rating is considered to be provisional otherwise, and they will not be listed in the rankings page. A competitor must also have had a match in the last year to be considered active. If over a year has gone by without them competiting they are removed from the ranking listing, but their rating remains the same and if they compete again they will once again be on the ranking list.
The ratings are calculated using the elo rating system where the rating of a player depends on the ratings of their opponents and the results of matches against them. Given the difference in rating between two players the elo system calculates an estimate for the expected result. In the context of arm wrestling, where there can be no draws, this value represents the probability of one player beating their opponent i.e. an expected score of 0.75 represents a 75% chance of winning.
The new ratings are then calculated with the following formulas
The initial rating of a new competitor is calculated from the strench curve, shown below:
Where the y-axis shows the initial rating and the x-axis the weight of the competitor in kilograms. Note for competitors above 242lbs the elo rating is fixed for weight 242lbs and for competitors below 110lbs the elo rating is fixed for 110lbs.
A new rating is calculated after an event. For example, if a competitor with a rating of 1425 faces 4 opponents with ratings of 1378, 1670, 1450 and 1326. The result of which is a win, win, loss and a win respectively. To compute the competitor's new ranking involves the following: