Higher-rated players have lower k-factors - so their rating changes less than lower-rated players. Ratings are no longer zero-sum, upsets generate additional points and when the favorite wins the system loses points.
The theory behind ratings is that the probability of winning is determined by the difference in the two players’ ratings. For example, if the ratings differ by 200 points, the odds are 3-1 in favor of the higher rated player. (The higher rated player has a 75% chance of winning.) The key point is that it is the difference in ratings, not the absolute ratings, that determines the probability. So, whether the ratings are 1400 and 1200 or 2200 and 2000, the probability the higher rated player wins is 75%.
Tom mentioned a “K factor.” That’s a multiplier used to determine the rating change based on the player’s actual result compared to the “expected score” from the probabilistic model. Now, that’s probably clear as mud , so here’s an example. Suppose a player rated 1400 wins a game against an opponent rated 1200. Since the 1400 had a 75% chance of winning, his “expected score” is 0.75. (Of course, there’s no way to actually have a score of 0.75!) Likewise, the 1200 had a 25% chance of winning, so his “expected score” is 0.25.
To calculate the rating change, the 1400 player takes his actual score (1.0) and subtracts his expected score (0.75), which is 0.25. The 1400 player’s “K factor” is 41, so his rating change is K * (0.25), or 10.25. On the other hand, the 1200 player’s “K factor” is 50, so his rating change is K * (0.00 - 0.25), or -12.50. So, the 1400 player gains 10 points, while the 1200 player loses 12 points.
The K factor depends on both the player’s rating (a higher rating means a lower K factor) and the number of rounds in the tournament (more rounds means a lower K factor). Assigning higher rated players a lower K factor means that it is harder for higher rated players to gain points, so their ratings are more stable. On the other hand, a lower rated player who is improving will see a greater gain in his or her rating.
OK, I guess I expanded more than “a bit” on Tom’s explanation.
A player’s K-factor also depends on the number of games (up to about 50) he has played in previous tournaments. A player with just a few previous games will have (other things being equal) a higher K-factor than a player with 50 games or more.
It might be more accurate to say that assigning higher-rated players a lower K-factor is done BECAUSE their playing strengths tend to be more stable. An 1800 player is less likely to be mis-rated than a 1200 player. (Lower-rated players are more likely to improve quickly.)
The post-tournament rating is calculated as a judicious blend of the pre-tournament rating and the player’s performance in the current tournament. How much weight to give each of these two factors is a function of the confidence the ratings committee (and software) has in each.
Obviously, the confidence in the pre-tournament rating will be greater for (1) a higher-rated, more stable player than for a lower-rated player whose playing strength is fluctuating rapidly, and (2) for a player with a long tournament history than for one with a shorter history.
Thus (numbering as above):
(1) the higher the rating, the lower the K-factor.
(2) the longer the player’s tournament history (up to a point), the lower the K-factor.
Does part of the K factor relates to age in addition to # of games and rating? It seems to me kids’ ratings jump very quickly.
Here is an example.
A player with a 1219 rating played in 5 round g/30.
Rd. 1 Full point bye as lowest rated player.
Rd. 2 L vs 2484 (GM coming in with 1/2 point bye for Rd. 1)
Rd. 3 L vs 2024
Rd. 4 L vs 1753
Rd. 5 W vs 1700
Post event rating:1271
52 point rating gain for 1-3 score for the 4 rounds actually played. (Under old formula he’d gain around 29 points. -1 for each loss and 32 for the win.)
He is a junior high school student, and had over 50 rated games going into the event. So was it simply the strength of his opponents that allows for a 52 point gain for -2 score, or does age get added into the K factor?
His K factor for this tournament would be just a bit above 40. (OK, I calculate 41.36, but who’s counting? ) His expected score against those opponents would be pretty close to zero, so he would gain maybe 39 or 40 points.
There are also bonus points to consider. For a 5 round tournament, the bonus point threshhold would be 22. So, if he would have gained 40 points, he would also get (40 - 22), or 18 bonus points, for a total gain of 58 points. That’s exactly what you described.
There’s a link to the formula (10 pages of fairly complex math) on the ratings page, uschess.org/ratings.
Basically K is a combination of the number of games and the player’s current rating. Lower numbers of games means a higher K, as does a lower rating, because in both cases those increase the uncertainty as to the accuracy of one’s rating
The Ratings Committee’s reports for the last several years will be in the Delegate Call on the governance page. They’re starting to think about switching to the GLICKO2 system, which is used by Australia.
In effect it would add another component to the computation of K, activity. A player who hasn’t played much recently would have a higher K, for the same reasons as above, the lack of recent data increases the uncertainty associated with that player’s current rating.