Matchmaking and skill ratings

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Fair races

Kai designs the weed race: two players clear a plot as fast as they can. A beginner against an expert is no fun for either player.

A matchmaker needs a number for skill, and a way to update it after every race.

Elo

The Elo system, used by FIDE for chess, gives each player a rating. The gap between two ratings gives each player's expected score.

FIDE's table gives a 200-point gap an expected score of 0.76 for the higher-rated player and 0.24 for the other. After a game, each rating changes by K times (actual score minus expected).

Quick check

A 1600 plays a 1400. What does 0.76 mean?

  1. The 1600 is expected to score about 0.76 points a game
  2. The 1600 wins exactly 76 games out of 76
  3. The 1400 has no chance
Show the answer

The 1600 is expected to score about 0.76 points a game

A win scores 1 and a draw 0.5. Over many games, the 1600 is expected to average 0.76 per game.

K: how fast ratings move

FIDE's K is 40 for a new player until 30 games, and for players under 18 rated below 2300. It is 20 below 2400, and 10 once a player reaches 2400.

A big K lets a new rating find its level fast. A small K keeps an established one steady.

Do the sum

race
both players new: K = 40same rating: 0.5 expectedresult: one wins

Remy tests two new players. How many points does the winner gain?

  1. 20
  2. 40
  3. 10
Show the answer

20

40 times (1 minus 0.5) is 20. The loser drops 20.

Teams and uncertainty

Microsoft Research's TrueSkill, used on Xbox Live, starts from a limit: Elo "is not designed to work" with more than two players. TrueSkill treats a team's skill as "the sum of the skills" of its players.

It also tracks how sure it is of each rating, so a new player's rating moves fast until the system is sure.

Quick check

Elo was designed for games between many players at once.

Show the answer

False

Elo compares two players. TrueSkill was built for teams and free-for-alls.

Try it

Next, rate one race between two players 200 points apart, and find the result that moves the ratings most.

Bolt says: Next: hands-on, rate a match.

Fact-checked 12 October 2026