## The Rating Principle

The rating principle is easy to understand if it is compared to dealing with money. Even though none of us has enough money, most of us have some idea about what is fair when dealing with money.

Let's say Smith and Brown agree to play a series of head-to-head games for money (the actual sport is irrelevant). They each have a special bank account (say \$2000) set aside for the purpose. Each game is played for a \$40 kitty made up from a contribution from each player's bank account. The winner of each game takes the kitty and adds it to his account. Say that after a few games it is obvious that Smith is a better player than Brown. It would only be a matter of time before Smith would win all of Brown's money. Brown demands some kind of a handicap to give him a fair go. They decide that they will still play for a \$40 kitty, but that the better player is to put in more than \$20 and the lesser player is to put in less than \$20. This seems a reasonably fair and simple idea.

Rather than just guessing how much each is to put into the kitty, they agree to use their current winning percentages (or fractions) to proportion out how much each is to contribute. For example: if Smith is currently winning 5 games out of each 8 they play, then this means that Smith must put in 5/8 of the kitty or \$25 and Brown must put in 3/8 of the kitty or \$15. This is the whole principle of odds and chance and the actual values can be found in statistical tables (Table Z).

Using this method for each game will cause their bank accounts to gradually settle down. The amounts in their bank accounts will give some kind of a measure of their relative skill as players.

There are direct relationships between these 3 factors:
(1)           winning percentages
(2)           inputs to the kitty
(3)           difference in banks

When their winning percentages vary, their inputs to the kitty will vary, and the difference between their banks accounts will also vary.

The principle outlined here appears to be fair to both players in monetary terms. All the Glind Rating System does is cross out the \$ signs and call a player's bank account his RATING.

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