The
Elo rating system is a method for calculating
the
relative skill levels of players in twoplayer games
such as
chess and
Go.
It is named after its creator Arpad Elo, a Hungarianborn American physics professor.
The Elo system was invented as an improved chess rating system, but
today it is also used in many other games. It is also used as a
rating system for multiplayer competition in a number of
computer games, and has been adapted to team
sports including
association
football, American college football and basketball, and
Major League Baseball.
History
Arpad Elo was a masterlevel chess player and an active participant
in the
United States
Chess Federation (USCF) from its founding in 1939. The USCF
used a numerical ratings system, devised by
Kenneth Harkness, to allow members to track
their individual progress in terms other than tournament wins and
losses. The Harkness system was reasonably fair, but in some
circumstances gave rise to ratings which many observers considered
inaccurate. On behalf of the USCF, Elo devised a new system with a
more
statistical basis.
Elo's system replaced earlier systems of competitive rewards with a
system based on statistical estimation. Rating systems for many
sports award points in accordance with subjective evaluations of
the 'greatness' of certain achievements. For example, winning an
important
golf tournament might be worth an
arbitrarily chosen five times as many points as winning a lesser
tournament.
A statistical endeavor, by contrast, uses a model that relates the
game results to underlying variables representing the ability of
each player.
Elo's central assumption was that the chess performance of each
player in each game is a
normally
distributed random variable.
Although a player might perform significantly better or worse from
one game to the next, Elo assumed that the mean value of the
performances of any given player changes only slowly over time. Elo
thought of a player's true skill as the mean of that player's
performance random variable.
A further assumption is necessary, because chess performance in the
above sense is still not measurable. One cannot look at a sequence
of moves and say, "That performance is 2039." Performance can only
be inferred from wins, draws and losses. Therefore, if a player
wins a game, he is assumed to have performed at a higher level than
his opponent for that game. Conversely if he loses, he is assumed
to have performed at a lower level. If the game is a draw, the two
players are assumed to have performed at nearly the same
level.
Elo did not specify exactly how close two performances ought to be
to result in a draw as opposed to a win or loss. And while he
thought it is likely that each player might have a different
standard deviation to his
performance, he made a simplifying assumption to the
contrary.
To simplify computation even further, Elo proposed a
straightforward method of estimating the variables in his model
(
i.e., the true skill of each player). One could calculate
relatively easily, from tables, how many games a player is expected
to win based on a comparison of his rating to the ratings of his
opponents. If a player won more games than he was expected to win,
his rating would be adjusted upward, while if he won fewer games
than expected his rating would be adjusted downward. Moreover, that
adjustment was to be in exact linear proportion to the number of
wins by which the player had exceeded or fallen short of his
expected number of wins.
From a modern perspective, Elo's simplifying assumptions are not
necessary because computing power is inexpensive and widely
available. Moreover, even within the simplified model, more
efficient estimation techniques are well known. Several people,
most notably
Mark Glickman, have
proposed using more sophisticated statistical machinery to estimate
the same variables. On the other hand, the computational simplicity
of the Elo system has proven to be one of its greatest assets. With
the aid of a pocket calculator, an informed chess competitor can
calculate to within one point what his next officially published
rating will be, which helps promote a perception that the ratings
are fair.
Implementing Elo's scheme
The USCF implemented Elo's suggestions in 1960, and the system
quickly gained recognition as being both more fair and more
accurate than the Harkness system. Elo's system was adopted by
FIDE in
1970. Elo described his work in some detail in the book
The
Rating of Chessplayers, Past and Present, published in
1978.
Subsequent statistical tests have shown that chess performance is
almost certainly not normally distributed. Weaker players have
significantly greater winning chances than Elo's model predicts.
Therefore, both the USCF and FIDE have switched to formulas based
on the
logistic distribution.
However, in deference to Elo's contribution, both organizations are
still commonly said to use "the Elo system".
Different ratings systems
The phrase "Elo rating" is often used to mean a player's chess
rating as calculated by FIDE. However, this usage is confusing and
often misleading, because Elo's general ideas have been adopted by
many different organizations, including the USCF (before FIDE), the
Internet Chess Club (ICC),
Yahoo! Games, and the now defunct
Professional Chess
Association (PCA). Each organization has a unique
implementation, and none of them precisely follows Elo's original
suggestions. It would be more accurate to refer to all of the above
ratings as Elo ratings, and none of them as
the Elo
rating.
Instead one may refer to the organization granting the rating, e.g.
"As of August 2002,
Gregory
Kaidanov had a FIDE rating of 2638 and a USCF rating of 2742."
It should be noted that the Elo ratings of these various
organizations are not always directly comparable. For example,
someone with a FIDE rating of 2500 will generally have a USCF
rating near 2600 and an ICC rating in the range of 2500 to
3100.
FIDE ratings
For top players, the most important rating is their
FIDE rating. Since July 2009, FIDE issues a ratings
list once every two months.
The following analysis of the January 2006 FIDE rating list gives a
rough impression of what a given FIDE rating means:
The highest ever FIDE rating was 2851, which Garry Kasparov had on
the July 1999 and January 2000 lists. A list of highest ever rated
players is at
Methods
for comparing top chess players throughout history.
Performance rating
Performance Rating is a hypothetical rating that would result from
the games of a single event only. Some chess organizations use the
"algorithm of 400" to calculate performance rating. According to
this algorithm, performance rating for an event is calculated by
taking (1) the rating of each player beaten and adding 400, (2) the
rating of each player lost to and subtracting 400, (3) the rating
of each player drawn, and (4) summing these figures and dividing by
the number of games played.
FIDE, however, calculates performance rating by
means of the formula: Opponents' Rating Average + Rating
Difference. Rating Difference d_p is based on a player's tournament
percentage score p, which is then used as the key in a lookup
table. p is simply the number of points scored divided by the
number of games played. Note that, in case of a perfect or no score
d_p is indeterminate. The full table can be found in the
FIDE handbook online. A simplified version of
this table looks like this:
! p !! d_p

 0.99  +677

 0.9  +366

 0.8  +240

 0.7  +149

 0.6  +72

 0.5  0

 0.4  72

 0.3  149

 0.2  240

 0.1  366

 0.01  677
}
FIDE tournament categories
FIDEclassifies tournaments into categories
according to the average rating of the players. Each category is 25
rating points wide. Category 1 is for an average rating of 2251 to
2275, category 2 is 2276 to 2300, etc. The highest rated
tournaments have been Category 21, with an average from 2751 to
2775. The top categories are as follows:

Category 
Average rating 
10 
2476 to 2500 
11 
2501 to 2525 
12 
2526 to 2550 
13 
2551 to 2575 
14 
2576 to 2600 
15 
2601 to 2625 
16 
2626 to 2650 
17 
2651 to 2675 
18 
2676 to 2700 
19 
2701 to 2725 
20 
2726 to 2750 
21 
2751 to 2775 
Live ratings
FIDE updates its ratings list every two months.
In contrast, the unofficial "Live ratings" calculate the change in
players' ratings after every game. These Live ratings are based on
the previously published FIDE ratings, so a player's Live rating is
intended to correspond to what the FIDE rating would be if FIDE
were to issue a new list that day.
Although Live ratings are unofficial, interest arose in Live
ratings in August/September 2008 when five different players took
the "Live" #1 ranking.
The unofficial live ratings are published and maintained by Hans
Arild Runde at
the Live Rating website. Only players over 2700 are
covered.
United States Chess Federation ratings
The
United States Chess
Federation (USCF) uses its own classification of players:
 2400 and above: Senior Master
 2200–2399: Master
 2000–2199: Expert
 1800–1999: Class A
 1600–1799: Class B
 1400–1599: Class C
 1200–1399: Class D
 1000–1199: Class E
In general, 1000 is considered a bright beginner. In 2007, the
median rating of all USCF members was 657, according to
http://www.evanstonchess.org/Histogram2007.html. Class B and higher
is generally considered extremely competitive and the USCF
establishes a rating floor. A floor is your current rating minus
200 rating points. For instance, once someone has reached a rating
of 1600, they can never fall below 1400 for rating and competition
purposes. This is to protect the integrity of big tournaments and
prevent sandbagging.
The
K factor, in the USCF rating system, can be estimated
by dividing 800 by the effective number of games a player's rating
is based on (
Ne) plus the number of games the
player completed in a tournament (
m).
 K = 800 / (Ne + m)\,
Ratings of computers
Since 2005–2006,
humancomputer chess matches
have demonstrated that
chess
computers are capable of defeating even the strongest human
players (
Deep Blue
versus Garry Kasparov). However ratings of computers are
difficult to quantify. There have been too few games under
tournament conditions to give computers or software engines an
accurate rating. Also, for
chess
engines, the rating is dependent on the machine a program runs
on.
For some ratings estimates, see
Chess Engines rating lists.
Theory
Mathematical details
Performance can't be measured absolutely; it can only be inferred
from wins and losses. Ratings therefore have meaning only relative
to other ratings. Therefore, both the average and the spread of
ratings can be arbitrarily chosen. Elo suggested scaling ratings so
that a difference of 200 rating points in chess would mean that the
stronger player has an
expected score (which basically is
an expected average score) of approximately 0.75, and the USCF
initially aimed for an average club player to have a rating of
1500.
A player's
expected score is his probability of winning
plus half his probability of drawing. Thus an expected score of
0.75 could represent a 75% chance of winning, 25% chance of losing,
and 0% chance of drawing. On the other extreme it could represent a
50% chance of winning, 0% chance of losing, and 50% chance of
drawing. The probability of drawing, as opposed to having a
decisive result, is not specified in the Elo system. Instead a draw
is considered half a win and half a loss.
If Player A has true strength R_A and Player B has true strength
R_B, the exact formula (using the
logistic curve) for the expected score of
Player A is
 E_A = \frac 1 {1 + 10^{(R_B  R_A)/400}}.
Similarly the expected score for Player B is
 E_B = \frac 1 {1 + 10^{(R_A  R_B)/400}}.
This could also be expressed by
 E_A = \frac{Q_A}{Q_A + Q_B}
and
 E_B = \frac{Q_B}{Q_A + Q_B}
where Q_A = 10^{R_A/400} and Q_B = 10^{R_B/400}. Note that in the
latter case, the same denominator applies to both expressions. This
means that by studying only the numerators, we find out that the
expected score for player A is Q_A/Q_B times greater than the
expected score for player B. It then follows that for each 400
rating points of advantage over the opponent, the chance of winning
is magnified ten times in comparison to the opponent's chance of
winning.
Also note that E_A + E_B = 1. In practice, since the true strength
of each player is unknown, the expected scores are calculated using
the player's current ratings.
When a player's actual tournament scores exceed his expected
scores, the Elo system takes this as evidence that player's rating
is too low, and needs to be adjusted upward. Similarly when a
player's actual tournament scores fall short of his expected
scores, that player's rating is adjusted downward. Elo's original
suggestion, which is still widely used, was a simple linear
adjustment proportional to the amount by which a player
overperformed or underperformed his expected score. The maximum
possible adjustment per game (sometimes called the
Kvalue) was set at
K = 16 for masters and
K = 32 for weaker players.
Supposing Player A was expected to score E_A points but actually
scored S_A points. The formula for updating his rating is
 R_A^\prime = R_A + K(S_A  E_A).
This update can be performed after each game or each tournament, or
after any suitable rating period. An example may help clarify.
Suppose Player A has a rating of 1613, and plays in a fiveround
tournament. He loses to a player rated 1609, draws with a player
rated 1477, defeats a player rated 1388, defeats a player rated
1586, and loses to a player rated 1720. His actual score is (0 +
0.5 + 1 + 1 + 0) = 2.5. His expected score, calculated according to
the formula above, was (0.506 + 0.686 + 0.785 + 0.539 + 0.351) =
2.867. Therefore his new rating is (1613 + 32· (2.5 − 2.867)) =
1601.
Note that while two wins, two losses, and one draw may seem like a
par score, it is worse than expected for Player A because his
opponents were lower rated on average. Therefore he is slightly
penalized. If he had scored two wins, one loss, and two draws, for
a total score of three points, that would have been slightly better
than expected, and his new rating would have been (1613 + 32· (3 −
2.867)) = 1617.
This updating procedure is at the core of the ratings used by FIDE,
USCF, Yahoo! Games, the ICC, and FICS. However, each organization
has taken a different route to deal with the uncertainty inherent
in the ratings, particularly the ratings of newcomers, and to deal
with the problem of ratings inflation/deflation. New players are
assigned provisional ratings, which are adjusted more drastically
than established ratings, and various methods (none completely
successful) have been devised to inject points into the rating
system so that ratings from different eras are roughly
comparable.
The principles used in these rating systems can be used for rating
other competitions—for instance, international
football matches.
Elo ratings have also been applied to games without the possibility
of
draw, and to games in which the
result can also have a quantity (small/big margin) in addition to
the quality (win/loss). See
go rating with
Elo for more.
Mathematical issues
There are three main mathematical concerns relating to the original
work of Professor Elo, namely the correct curve, the correct
Kfactor, and the provisional period crude calculations.
Most accurate distribution model
The first major mathematical concern addressed by both FIDE and the
USCF was the use of the
normal
distribution. They found that this did not accurately represent
the actual results achieved by particularly the lower rated
players. Instead they switched to a
logistical distribution model, which
provides a better fit for the actual results achieved.
Most accurate Kfactor
The second major concern is the correct "Kfactor" used. The chess
statistician
Jeff Sonas reckons that the
original K=10 value (for players rated above 2400) is inaccurate in
Elo's work. If the Kfactor coefficient is set too large, there
will be too much sensitivity to winning, losing or drawing, in
terms of the large number of points exchanged. Too low a Kvalue,
and the sensitivity will be minimal, and it would be hard to
achieve a significant number of points for winning, etc.
Elo's original Kfactor estimation was made without the benefit of
huge databases and statistical evidence. Sonas indicates that a
Kfactor of 24 (for players rated above 2400) may be more accurate
both as a predictive tool of future performance, and also more
sensitive to performance.
Certain Internet chess sites seem to avoid a threelevel Kfactor
staggering based on rating range. For example the ICC seems to
adopt a global K=32 except when playing against provisionally rated
players. The USCF (which makes use of a logistic distribution as
opposed to a normal distribution) have staggered the Kfactor
according to three main rating ranges of:
 Players below 2100 > K factor of 32 used
 Players between 2100 and 2400 > K factor of 24 used
 Players above 2400 > K factor of 16 used
FIDE uses the following ranges:
 K = 25 for a player new to the rating list until he has
completed events with a total of at least 30 games.
 K = 15 as long as a player's rating remains under 2400.
 K = 10 once a player's published rating has reached 2400, and
he has also completed events with a total of at least 30 games.
Thereafter it remains permanently at 10.
In overtheboard chess, the staggering of Kfactor is important to
ensure minimal inflation at the top end of the rating spectrum.
This assumption might in theory apply equally to an online chess
server, as well as a standard overtheboard chess organisation
such as FIDE or USCF. In theory, it would make it harder for
players to get the much higher ratings, if their Kfactor
sensitivity was lessened from 32 to 16 for example, when they get
over 2400 rating. However, the ICC's help on Kfactors indicates
that it may simply be the choosing of opponents that enables 2800+
players to further increase their rating quite easily. This would
seem to hold true, for example, if one analysed the games of a GM
on the ICC: one can find a string of games of opponents who are all
over 3100. In overtheboard chess, it would only be in very high
level allplayall events that this player would be able to find a
steady stream of 2700+ opponents – in at least a category 15+ FIDE
event. A category 10 FIDE event would mean players are restricted
in rating between 2476 to 2500. However, if the player entered
normal Swisspaired open overtheboard chess tournaments, he would
likely meet many opponents less than 2500 FIDE on a regular basis.
A single loss or draw against a player rated less than 2500 would
knock the GM's FIDE rating down significantly.
Even if the Kfactor was 16, and the player defeated a 3100+ player
several games in a row, his rating would still rise quite
significantly in a short period of time, due to the speed of blitz
games, and hence the ability to play many games within a few days.
The Kfactor would arguably only slow down the increases that the
player achieves after each win. The evidence given in the ICC
Kfactor article relates to the autopairing system, where the
maximum ratings achieved are seen to be only about 2500. So it
seems that randompairing as opposed to selective pairing is the
key for combatting rating inflation at the top end of the rating
spectrum, and possibly only to a much lesser extent, a slightly
lower Kfactor for a player >2400 rating.
Practical issues
Game activity versus protecting one's rating
In general the Elo system has increased the competitive climate for
chess and inspired players for further study and improvement of
their game. However, in some cases ratings can discourage game
activity for players who wish to "protect their rating".
Examples:
 They may choose their events or opponents more carefully where
possible.
 If a player is in a Swiss
tournament, and loses a couple of games in a row, they may feel
the need to abandon the tournament in order to avoid any further
rating "damage".
 Junior players, who may have high provisional ratings might
play less than they would, because of rating concerns.
In these examples, the rating "agenda" can sometimes conflict with
the agenda of promoting chess activity and rated games.
Interesting from the perspective of preserving high Elo ratings
versus promoting rated game activity is a recent proposal by
British Grandmaster
John Nunn regarding
qualifiers based on Elo rating for a World championship model.Nunn
highlights in the section on "Selection of players", that players
not only be selected by high Elo ratings, but also their rated game
activity. Nunn clearly separates the "activity bonus" from the Elo
rating, and only implies using it as a tiebreaking
mechanism.
Selective pairing
A more subtle issue is related to pairing. When players can choose
their own opponents, they can choose opponents with minimal risk of
losing, and maximum reward for winning. Such a luxury of being able
to handpick your opponents is not present in OvertheBoard Elo
type calculations, and therefore this may account strongly for the
ratings on the ICC using Elo which are well over 2800.
Particular examples of 2800+ rated players choosing opponents with
minimal risk and maximum possibility of rating gain include:
choosing computers that they know they can beat with a certain
strategy; choosing opponents that they think are overrated; or
avoiding playing strong players who are rated several hundred
points below them, but may hold chess titles such as IM or GM. In
the category of choosing overrated opponents, newentrants to the
rating system who have played less than 50 games are in theory a
convenient target as they may be overrated in their provisional
rating. The ICC compensates for this issue by assigning a lower
Kfactor to the established player if they do win against a new
rating entrant. The Kfactor is actually a function of the number
of rated games played by the new entrant.
Elo therefore must be treated as a bit of fun when applied in the
context of online server ratings. Indeed the ability to choose
one's own opponents can have great fun value also for spectators
watching the very highest rated players. For example they can watch
very strong GM's challenge other very strong GMs who are also rated
over 3100. Such opposition, which the highest level players online
would play in order to maintain their rating, would often be much
stronger opponents than if they did play in an Open tournament
which is run by Swiss pairings. Additionally it does help ensure
that the game histories of those with very high ratings will often
be with opponents of similarly high level ratings.
Therefore, Elo ratings online still provide a useful mechanism for
providing a rating based on the opponent's rating. Its overall
credibility, however, needs to be seen in the context of at least
the above two major issues described — engine abuse, and selective
pairing of opponents.
The ICC has also recently introduced "autopairing" ratings which
are based on random pairings, but with each win in a row ensuring a
statistically much harder opponent who has also won x games in a
row. With potentially hundreds of players involved, this creates
some of the challenges of a major large Swiss event which is being
fiercely contested, with round winners meeting round winners. This
approach to pairing certainly maximizes the rating risk of the
higherrated participants, who may face very stiff opposition from
players below 3000 for example. This is a separate rating in
itself, and is under "1minute" and "5minute" rating categories.
Maximum ratings achieved over 2500 are exceptionally rare.
Ratings inflation and deflation
An increase or decrease in the average rating over all players in
the rating system is often referred to as
rating inflation
or
rating deflation respectively. For example, if there is
inflation, a modern rating of 2500 means less than a historical
rating of 2500, while the reverse is true if there is deflation.
Using ratings to compare players between different eras is made
more difficult when inflation and deflation is present. (See also
Greatest chess player
of all time.)
It is commonly believed that, at least at the top level, modern
ratings are inflated. For instance
Nigel
Short said in September 2009, "
The recent ChessBase article
on rating inflation by Jeff Sonas would suggest that my rating in
the late 1980s would be approximately equivalent to 2750 in today's
much debauched currency". (Short's highest rating in the 1980s
was 2665 in July 1988, which was equal third in the world. When he
made this comment, 2665 would have ranked him 65th, while 2750
would have ranked him equal 10th).
It has been suggested that an overall increase in ratings reflects
greater skill. The advent of strong chess computers allows a
somewhat objective evaluation of the absolute playing skill of past
chess masters, based on their recorded games, but this is also a
measure of how computerlike the players' moves are, not merely a
measure of how strongly they have played.
The number of people with ratings over 2700 has increased. Around
1979 there was only one active player (
Anatoly Karpov) with a rating this high. This
increased to 15 players in 1994, while 33 players have this rating
in 2009, which has made this top echelon of chess mastery less
exclusive. One possible cause for this inflation was the rating
floor, which for a long time was at 2200, and if a player dropped
below this they were stricken from the rating list. As a
consequence, players at a skill level just below the floor would
only be on the rating list if they were overrated, and this would
cause them to feed points into the rating pool.
In a pure Elosystem, each game ends in an equal transaction of
rating points. If the winner gains N rating points, the loser
should drop by N rating points. While this prevents points from
entering or leaving the system through when games are played and
rated, it typically results in rating deflation.
In 1995, the United Chess Federation experienced that several young
scholastic players were improving faster than what the rating
system was able to track. As a result, established players with
stable ratings started to lose rating points to the young and
underrated players. Several of the older established players were
frustrated over what they considered an unfair rating decline, and
some even quit chess over it.
Combating deflation
Because of the significant difference in timing of when inflation
and deflation occur, and in order to combat deflation, most
implementations of Elo ratings have a mechanism for injecting
points into the system in order to maintain relative ratings over
time. FIDE has two inflationary mechanisms. First, performances
below a "ratings floor" are not tracked, so a player with true
skill below the floor can only be unrated or overrated, never
correctly rated. Second, established and higherrated players have
a lower Kfactor. New players have a K=25, which drops to K=15
after 30 played games, and to K=10 when the player reaches
2400.
The current system in the United States (
Glicko) includes a bonus point scheme
which feeds rating points into the system in order to track
improving players, and different Kvalues for different players.
Some methods, used in Norway for example, differentiate between
juniors and seniors, and use a larger K factor for the young
players, even boosting the rating progress by 100% for when they
score well above their predicted performance.
Rating floors in the USA work by guaranteeing that a player will
never drop below a certain limit. This also combats deflation, but
the chairman of the USCF Ratings Committee has been critical of
this method because it does not feed the extra points to the
improving players. (A possible motive for these rating floors is to
combat sandbagging, i.e. deliberate lowering of ratings to be
eligible for lower rating class sections and prizes.)
Other chess rating systems
Elo ratings in other games
American Collegiate Football uses
the Elo method as a portion of its
Bowl Championship Series rating
systems.
Jeff Sagarin of
USA Today publishes team rankings for most
American sports, including Elo system ratings for College Football.
The
NCAA uses his Elo ratings as part of a
formula to determine the annual participants in the College
Football
National
Championship Game.
National
Scrabble organizations compute
normallydistributed Elo ratings except in the United Kingdom, where a different system is used. The North
American
National Scrabble
Association has the largest rated population, numbering over
11,000 as of early 2006.
Lexulous also uses
the Elo system.
The popular
First
Internet Backgammon Server calculates ratings based on a
modified Elo system. New players are assigned a rating of 1500,
with the best humans and bots rating over 2000. The same formula
has been adopted by several other backgammon sites, such as
Play65,
DailyGammon,
GoldToken
and
VogClub. VogClub sets a new player's
rating at 1600.
The European Go Federation adopted an Elo based rating system
initially pioneered by the Czech Go Federation.
In other sports, individuals maintain rankings based on the Elo
algorithm. These are usually unofficial, not endorsed by the
sport's governing body. The
World Football Elo Ratings rank
national teams in men's
football .
In 2006, Elo ratings were adapted for
Major League Baseball teams by
Nate Silver of
Baseball Prospectus. Based on this
adaptation, Baseball Prospectus also makes Elobased
Monte Carlo simulations of the odds of
whether teams will make the playoffs.
One of the few
Elobased rankings endorsed by a sport's governing body is the
FIFA Women's World
Rankings, based on a simplified version of the Elo algorithm,
which FIFA uses as its
official ranking system for national teams in women's football .
Various online roleplaying games use Elo ratings for
playerversusplayer rankings. In
Guild
Wars, Elo ratings are used to record guild rating gained
and lost through Guild versus Guild battles, which are twoteam
fights. The initial Kvalue was 30, but was changed to 5 in early
2007.
Vendetta Online uses
Elo ratings to rank the flight combat skill of players when they
have agreed to a oneonone duel.
World of Warcraft used to use the Elo
Rating system when teaming up and comparing Arena players, but now
uses a system similar to Microsoft's TrueSkill. The game
Puzzle Pirates uses the Elo
rating system as well to determine the standings in the various
puzzles.
Tradingcard game manufacturers often use Elo ratings for their
organized play efforts.
The DCI (formerly Duelists'
Convocation International) uses Elo ratings for tournaments of
Magic: The Gathering
and other games of Wizards of the Coast. Pokémon USA
uses the Elo system to rank its TCG organized play competitors.
Prizes for the top players in various regions include holidays and
world championships invites. Similarly,
Decipher, Inc. used the Elo system for its
ranked games such as
Star Trek Customizable Card
Game and
Star Wars Customizable Card
Game.
See also
Notes
 World Chess Championship in Mexico reaches Category
XXI, official web site of the World Chess Championship
2007
 Anand lost #1 to Morozevich ( Chessbase, August 24 2008), then regained it, then
Carlsen took #1 ( Chessbase, September 5 2008), then Ivanchuk ( Chessbase, September 11 2008), and finally Topalov (
Chessbase, September 13 2008)
 US Chess Federation:
 "Approximating Formulas for the USCF Rating System",
United States Chess
Federation, Mark Glickman, Department of Mathematics and
Statistics at Boston University, 22 February 2001
 For instance, see the comments at ChessBase.com  Chess News  Adams vs Hydra: Man 0.5 –
Machine 5.5
 Chessbase article
 A key Sonas article is Jeff Sonas: The Sonas Rating Formula — Better than
Elo?
 FIDE Online. FIDE Handbook: Chess rules
 ICC Help: kfactor
 A Parent's Guide to Chess Skittles, Don
Heisman, Chesscafe.com, August 4, 2002
 ChessBase.com  Chess News  The Nunn Plan for the
World Chess Championship
 Nigel Short on being number one in Britain
again, Chessbase, 4 September 2009
 A conversation with Mark Glickman [1], Published in Chess Life October 2006
issue
 [2]
 Nate Silver,
"We Are Elo?" June 28, 2006.[3]
 Postseason Odds, ELO version
 World of Warcraft Europe > The Arena
References
External links