This article is from the Table Tennis (Ping Pong) FAQ, by ttennis@bu.edu with numerous contributions by others.

Before discussing the data, let's discuss how the rating system works. This

will make it easier to understand the data.

The tournament director of each tournament sends all the results for the

tournament to the USATT rating chairman Dan Simon. Dan processes the

tournaments in the order they were played. After processing, he sends a

report back to the tournament director that gives the new rating for each

player who played in the tournament. So, you may get your new rating from

the tournament director several weeks after the tournament.

Here is the rating chart which gives the number of rating points that the

winner of each match wins and the loser loses.

--------------------------------------- Rating | Higher rated | Lower rated difference | player wins | player wins --------------------------------------- 0- 12 | 8 | 8 13- 37 | 7 | 10 38- 62 | 6 | 13 63- 87 | 5 | 16 88-112 | 4 | 20 113-137 | 3 | 25 138-162 | 2 | 30 163-187 | 2 | 35 188-212 | 1 | 40 213-237 | 1 | 45 238- | 0 | 50 ---------------------------------------

However, the calculation of the ratings involves more than just this chart.

The first problem is unrated players. Dan looks at the results of each

unrated player (including the number of points the player scored). Using

this information, he assigns a rating to each unrated player. From now on

he treats unrated players just like rated players using the newly assigned

rating. So, you do win and lose points when you play an unrated player.

To finish calculating the post-tournament ratings, Dan makes two passes

through the results. The first pass is a screening pass to identify players

whose ratings should be adjusted. Dan uses the rating chart to calculate

how many points each player would win for the tournament. Any player who

would win at least fifty rating points has his rating adjusted up. This

means that Dan replaces his pre-tournament rating with a new adjusted

rating which is used as his rating for the second pass. In the second pass,

Dan uses the rating chart again to calculate the post-tournament rating for

each player.

So, from the point of view of the rating system, there are actually three

ratings for every player in a tournament. The first rating is the

pre-tournament rating which is the rating the player has going into the

tournament after all earlier tournaments have been processed. This is not

necessarily the same as the rating used at the tournament since Dan

processes the tournaments in the order they were played.

The second rating is the adjusted pre-tournament rating. This is different

from the pre-tournament rating for two classes of players:

1. unrated players,

2. players who have their ratings adjusted.

No one has a zero adjusted rating, since all the unrated players are given

a rating. If the player was rated and he is not being adjusted, then his

adjusted rating is the same as his pre-tournament rating. The third rating

is the post-tournament rating.

To summarize: the pre-tournament rating is the rating before the tournament

is processed. The adjusted rating is the rating after unrated players are

given ratings and after the first screening pass. The post-tournament

rating is the player's new rating that will be published in the next issue

of TT Today.

DATA

Dan graciously sent me the results from eight tournaments played in April

and May 1989. Here are some statistics of the number of players and matches

in those eight tournaments.

--------------------------------------------------------- Category | Players | Matches |------------------------------------ | Number Per cent | Number Per cent | of total | of total --------------------------------------------------------- all | 459 100.0 | 1510 100.0 unrated | 49 10.7 | 225 14.9 adjusted | 49 10.7 | 417 27.6 unrated or adjusted | 98 21.4 | 609 40.3 ---------------------------------------------------------

The row labeled "all" is all the players and all the matches. The row

labeled "unrated" is those players who were unrated going into the

tournament and those matches in which either player was unrated. The row

labeled "adjusted" is those players who had their ratings adjusted and

those matches in which either player was adjusted. The row labeled "unrated

or adjusted" is those players who were either unrated or had their ratings

adjusted and those matches in which either player was unrated or adjusted.

In case you were wondering, the number of "unrated" matches plus the number

of "adjusted" matches doesn't equal the number of "unrated or adjusted"

matches because there were 33 matches in which an unrated player played an

adjusted player. It is interesting that 40.3% of the matches involve

unrated or adjusted players. This and the fact that you don't know the

pre-tournament ratings is why you can't exactly calculate your own

post-tournament rating.

Which set of ratings should we use to construct a handicap chart? Well, in

principle we should use the pre-tournament ratings since these ratings are

closest to the ratings that are actually used at the tournaments. Rather

than make a decision, we'll construct charts using each of the three sets

of ratings.

Continue to: