Fargo Ratings
Get INSTRUCTIONS on how to download and setup the Fargo app.
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FargoRate computes pocket-billiard player ratings called Fargo Ratings that rate amateur and professional players worldwide. Coupling game win/loss data across local leagues, regions, countries, and continents ensures players everywhere are rated on the same scale.
North Country CSI Pool reports to Fargo to help establish and grow amateur poolplayer ratings.
Fargo Ratings are as useful for handicapping a small-town league as they are determining top players by country. To achieve its vision of a new era for pocket billiards in which all players everywhere are connected, FargoRate has created a league management system called FargoRate LMS that is available for use by all leagues.
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Unlike high jumpers, who have height, swimmers, who have time, and javelin throwers, who have distance, pool players –pocket billiard players—have no absolute measure of performance. Skill at pool, like skill at chess, must be based on relative performance—upon who beats whom.
FargoRate rates pool players worldwide on the same scale based on games won and lost against opponents of known rating. We compute the optimum set of ratings—also known as maximum likelihood ratings—as those that best predict the outcome of all of the games amongst all of the players.
Professional players generally have ratings between 700 and 800. A random company holiday party might have many players rated between 50 and 200. Most people who play pool in leagues and tournaments are between these ranges, i.e., between 200 and 700. There is no top and no bottom to the scale.
The rating difference between two players determines the chance each will win a game.
Two players with the same rating, i.e., a 300 and another 300, or a 600 and another 600, have equal chances of winning a game between them. If the two players play multiple games, they will tend to win them in a ratio of 1:1 (one to one).
When two players are 100 points apart, say a 300 versus a 400, the ratio of game wins will be near 1:2, as in 5 games to 10 games, or 50 games to 100 games.
A 200-point gap leads to a game win ratio of 1:4
A 300-point gap leads to a game win ratio of 1:8
A 400-point gap leads to a game win ratio of 1:16
Two players with a 34-point gap, like a 530 and a 564, will win games in a 4:5 ratio. A 50-point gap predicts a 5:7 win ratio.
A new player can establish a rating by performance against an opponent of any rating. For instance, a new player who consistently wins 2 out of 3 games against a 350 is performing like a 450. That is, the two win games in a 2:1 ratio and thus are separated by about 100 points. A group of players who are well coupled to one another, like in a local league, can become coupled to the rest of the world by a few players or even a single player playing outside the group.
Games are added to our dataset every day. And a new rating optimization, coupling everybody together around the globe, is performed every day.
The result is a system that is as useful for rating two-dozen players in a small-town league as it is for rating players in a regional tournament tour as it is for rating world-class completion. And a byproduct is each of these groups knows exactly where it stands relative to the others.
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Fargo ratings are on a logarithmic scale — like the Richter scale for earthquakes. For each gap of 100 Fargo points, the higher rated player is twice as good as the lower rated player. A fair match between them would be 8-4 or 10-5, i.e., the higher rated player generally wins twice as many games as the lower rated player.
Rating players and handicapping matches are two separate things. Many people are interested only in rating players to compare performance. But ratings can also be used to generate fair matchups between players of different skill. The easiest way to do this is to have matches where the two players must win a different number of games to claim the match. To be victorious in a 9-7 race, the higher-rated player must win 9 games before the lower-rated player wins 7 games.
Charts are easily constructed that show fair matches for any rating difference (such as the ones we feature in the player guide for our SKY OPEN events). You can review recommended Fairmatch races inside your Fargo app, under the FIND ACES button.
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A starter rating—aka a starter guess—is part of an optional approach to incorporate local knowledge/prior knowledge in assigning a useful preliminary rating for players who don’t yet have a Fargo Rating. It is not part of the FargoRate system.
The FargoRate system computes a performance rating based on data. When that performance rating is based on 200 or more games, it is called a Fargo Rating. Because a performance rating based on only a few games is unreliable as a measure of skill, it can be supplemented with prior knowledge to generate a sensible guess of skill for players without a Fargo Rating.
The preliminary rating the player sees is a weighted blend of the performance rating (with influence determined by the number of games it is based upon) and the starter rating (with influence based on the remaining games to 200.)
For instance, a player with performance rating of 580 based upon 50 games and a starter rating of 540 will see a preliminary rating of 550.
Once a player has 200 games the starter rating is ignored. -
Robustness is a measure of the reliability of a player’s Fargo Rating. For now, it is simply the number of games a player has played that contribute to his or her rating. A robustness of 200 is a minimum standard for us to consider a rating “established.” In general, a rating is more reliable not only by being based on more games but also by more of those games being recent and by more of those games being against opponents with established ratings. Robustness will likely incorporate these latter two factors in the future, and that is why we don’t simply call it number of games. Players with a robustness under 200, i.e., those with an unestablished rating, have an official rating that may be influenced by a starter rating.
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There were two implementations of ELO-type schemes in the 1990s. One was by Ron Shepard, a scientist at Argonne National Laboratory outside of Chicago, who implemented the scheme for 8-ball players in the Argonne Pool League. The other was by Bob Jewett, who used an ELO-type scheme as the basis of the NPL (National Pool League) rankings for 9-ball players largely in the San Francisco area. More recently the idea of an Ab Initio Global Optimization of ELO-type ratings was described by Michael Page in a 2002 Billiards Digest article, “Sizing up with the Pros.” Fargo Ratings were later implemented without the global optimization at Fargo Billiards in Fargo ND, by Michael Page and Steve Ernst.
The basic relation between rating differences and win probability is characteristic of ELO schemes. Arpad Elo was a Hungarian-born American physicist who first applied these ideas to rate chess players several decades ago. These ideas are still core to chess ratings and also form the basis for world ratings in football (soccer), NFL football, baseball, a variety of competitive video games, the game Go, and many others. These equations even made an appearance in the movie Social Network (the facebook movie) as part of facemash, an elo-based scheme to rate the attractiveness of female university students at Harvard.
MICHAEL PAGE
After finishing a post-doctoral research fellowship with the US National Research Council, Michael spent eight years as scientist in the Laboratory for Computational Physics at the US Naval Research Laboratory. He followed this by eighteen years as Associate Professor of Chemistry at North Dakota State University, where he taught graduate and undergraduate courses in physical chemistry and ran an active research program that produced several PhD scientists. He is the author of over 40 published articles and book chapters in the areas of quantum chemistry and computational molecular physics. He quit his academic career in 2008 to become the proprietor of Fargo Billiards & Gastropub in Fargo, ND.
STEVE ERNST
Steve is a former senior software developer for Microsoft Corporation with background in electrical engineering and computer science.