NEW USCF RATING SYSTEM

Calculations for Established Players



A Guide for Non-mathematicians



By: Michael Aigner

Alternate Delegate, CA-N

May 15, 2001



This is a crash course in the new rating system. What follows applies only to established players, which are defined as those with 50 or more USCF rated games. There are some minor changes for players who have a published rating but have less than 50 rated games. The content within is derived from Approximating Formulas for the USCF Rating System by Professor Mark Glickman (see http://math.bu.edu/people/mg/ratings/approx/approx.html).

In order to understand this document, you need to only read three tables and add, subtract, multiply, and divide. No complicated math formulas!

You need certain data for each tournament before you can proceed.

The more accurate all this information is, the better. Make sure to include all games you played in the tournament, even those where you beat someone rated much lower or lose to someone much higher. While those won't change your rating much, the new rating system depends on the total number of games played.



STEP #1

Calculate your expected score (We) for the tournament. This is actually the same as under the old USCF rating system. Basically, there's a formula which states that if you are rated x points higher/lower than someone else, then you are expected to score y points in each game (y is between 0 and 1). Two equally rated players are expected to score 0.50 each game. Someone much higher rated is expected to score close to 1.00 in each game. Conversely, the lower rated player is expected to score close to 0.00. Here's an approximate table for the expected score for the higher and lower rated players as a function of rating difference.

Table 1: We probability for USCF rating system

rating difference higher rated player lower rated player
0 0.50 0.50
30 0.55 0.45
70 0.60 0.40
100 0.65 0.35
150 0.70 0.30
200 0.75 0.25
300 0.85 0.15
400 0.90 0.10
500 0.95 0.05
800 0.99 0.01

When I go to tournaments, I remember these numbers to assist me in figuring out how many points I gained or lost without using a calculator. Note that the two probabilities for each rating add up to 1.00, meaning you only need to remember the expected score for the higher rated player. You can easily interpolate between the ratings given to obtain a rough estimate of your expected score. For example, a rating difference of 250 points is halfway between the rows for 200 and 300 in Table 1. Consequently, the higher rated player has an expected score of 0.80 and the lower rated has 0.20.

Now add up the expected scores for each game in the tournament. This gives you We, your expected score for the tournament. If you play mostly people rated way above you, the expected score will be comparatively low. If your opponents are much lower rated, it will be high.

How do you calculate my expected score for an opponent who is playing his first or second USCF rated tournament and doesn't have a published rating? This is rather tricky, and will introduce some error into your calculations (especially if many opponents are unrated). I recommend using, as an approximation, the old algorithm for estimating the first ratings of someone with no published. For each game they play, take the opponent's rating and add 400 for a win or subtract 400 for a loss. Add up these adjusted ratings for each game, and divide by the number of games played. You can do likewise for someone who is highly provisional (i.e., has only a small number of games rated). There is no easy way to compute these ratings, so a crude approximation must suffice.



STEP #2

Take your score (W) in the tournament (excluding byes and forfeits) and subtract your expected score (We, calculated in Step #1).

Delta = W - We

If this quantity (Delta) is positive, you did better than expected. If negative, you didn't do so well. For those with experience using the old USCF rating system, you should have noticed nothing new yet (although you may have done the calculations differently).



STEP #3

Now take the difference Delta and multiply by a K factor. Under the old USCF rating system, K was fixed at 32 for players under 2100 (and 24 for 2100-2400, and 16 for over 2400). Under the new system, K varies both with rating and the number of games played in the tournament. See the table below.

Table 2: K factor for new USCF rating system

# games 3 4 5 6 7 8 9
rating
600 63 59 54 51 48 46 43
800 57 53 50 47 44 42 40
1000 51 48 45 43 41 39 37
1200 44 42 40 38 36 35 33
1400 37 36 34 33 32 30 29
1600 30 29 28 27 26 26 25
1800 24 23 22 22 21 21 20
2000 18 17 17 17 16 16 16
2200+ 15 15 15 14 14 14 14

For example, a 2000 player would have a K of 18 for a 3 round tournament, a K of 17 for 4-6 rounds, and a K of 16 for 7-9 rounds. Note that this K is smaller than the old rating system for players above about 1500, and significantly higher for lower rated players. This means that ratings change less rapidly than before for ratings above about 1500 and more rapidly for ratings below 1500.

After you found your K from Table 2, you multiply the result from Step #2 by it to obtain your rating change for the tournament.

RatingChange = K * Delta

While most tournaments in the U.S. are "full K", some are specified as "half K". Without burdening with undue formulas and calculations, if an event is rated as "half K", I recommend dividing the above RatingChange by 2. Please note that if a tournament doesn't explicitly state "half K", then by default it is "full K" and you have nothing to worry about.



STEP #4

This would be your final answer, yet USCF has now implemented bonus points for exceptional performances. If the number of points you gain at the end of Step #3 exceeds a certain value, you obtain a bonus equal to the difference between this cutoff value and the result from Step #3. First, what is this cutoff value? It depends only on the number of rounds played in the tournament. See this table.

Table 3: Cutoff rating change needed to trigger bonus points

# games 3 4 5 6 7 8 9
CutoffValue 20 20 22 24 26 28 30

So for a 4 round tournament, you must gain more than 20 rating points in order to trigger bonus points. Suppose for a moment that you are rated 1900. Since the K factor for a 1900 in a 4 round tournament is also 20 (average between 1800 and 2000 in Table 2), you would need to score 1.0 higher than your expected score to barely trigger bonus points. If you don't meet this threshold, nothing happens (bonus points are only added, and never subtracted).

if RatingChange > CutoffValue,

Bonus = RatingChange - CutoffValue

if RatingChange < CutoffValue,

Bonus = 0

How do you know that you have triggered bonus points? Essentially, you need to perform considerably better than your rating would predict. For a 1900 player in a 4 round event, that means scoring more than 1.0 higher than your expected score for the tournament. Generally, it becomes easier to score bonus points for lower rated players, and harder as you approach master level, because of how the K factor varies with rating. Also, it becomes easier to score bonus points in longer tournaments (more games played).

The data in Table 3 will change in December 2002 to make obtaining bonus points somewhat more difficult. The current system parameters are designed to slowly reverse the deflation of USCF ratings which has been observed over the past decade. Starting in 2003, the system is intended to be neutral with respect to inflation/deflation of the rating pool.



STEP #5

Now you can compute your new rating from your old (pre-tournament) rating, the rating change calculated in Step #3 and the bonus points (if any) calculated in Step #4.

NewRating = OldRating + RatingChange + Bonus



This is an estimate of your new rating after the tournament. Although activity points (2 points per rated game) were once considered by the USCF, they have since been scrapped in favor of the bonus point system described in Step #4.



EXAMPLE

pre-rating = 1235

rounds = 6

score = 6.0

opponents' ratings = 600 (estimated), 950 (estimated), 1458, 1144, 1263, 1121



STEP #1: Use Table 1 to compute the expected score for each game and add up.

opponent #1 = 600 -> rating difference = -635 (you are higher rated) -> 0.97

opponent #2 = 950 -> rating difference = -285 (you are higher rated) -> 0.84

opponent #3 = 1458 -> rating difference = 233 (you are lower rated) -> 0.21

opponent #4 = 1144 -> rating difference = -91 (you are higher rated) -> 0.63

opponent #5 = 1263 -> rating difference = 28 (you are lower rated) -> 0.45

opponent #6 = 1121 -> rating difference = 114 (you are higher rated) -> 0.66

sum: We = 3.76



STEP #2: Compute Delta = W - We.

W = 6.0

We = 3.76

W - We = 2.24



STEP #3: Find K from Table 2 and compute RatingChange.

pre-rating = 1235 and 6 games -> K = 37

RatingChange = 37 * 2.24 = 82.9



STEP #4: Determine bonus points, if any.

6 games -> CutoffValue = 24

since RatingChange > CutoffValue, Bonus = 82.9 - 24 = 58.9



STEP #5: Calculate the new rating.

NewRating = 1235 + 82.9 + 58.9 = 1377



ONLINE RATINGS CALCULATOR

To assist you in actually doing these calculations, check out the ratings calculator (thanks George John!) at http://www.uschess.org/ratings/calculator.html. All you need to do is fill in the ratings of your opponents in the top 3 rows of boxes (leave extra boxes blank). Then enter your score in the tournament, excluding byes and forfeits. Also enter your best estimate of your rating prior to this event. As long as you have played at least 50 rated games with the USCF, you can leave the number of prior games box at 50. Now click on Show K, Performance (your performance rating for the tournament), New Rating, and Bonus.

Of course, all this is approximate. However, as long as all of the ratings are reasonably close to accurate, then the approximation will be quite good.