Your Scrabble Rating!

I like to play online scrabble at the internet scrabble club. Sometimes when Laurel and I have just gotten the baby down, we don't feel like taking out the scrabble board only to have to stop playing if she starts having a difficult time... but it is easy for us to nerdily whip out our laptops and get a game in.

I love the rating system. If you play against a more highly rated player, your rating goes up by more if you win, and down by less if you lose, but the effect isn't so great as to discourage differently rated players from having a contest. And they cap the score difference at 200 - if you win or lose by more than 200 points, they just call it "200" to prevent a cremation from ruining your rating.

The formula they use is a scary looking function of r1 (your rating), r2 (your foe's rating), d (the score difference at the end) and w (1 if you win, 0 if you lose, 0.5 if you tie)

The practical effects of this formula is that your rating will never change by more than 40, and that will happen rarely. What this page is about is to help you visualize the results of this formula without having to deal with the mathematics. ISC allows you to "ASSESS" your opponents, to see what your rating change will be if you win by 50, lose by 50, or tie - this page is for people who want a more visual idea of what is going on.

(1) What if my opponent and I are rated the same?

If you and your opponent have the same rating, and you win, your rating will go up between 10 and 20 points. (If you lose, it will go down by that amount) What follows is a graph of your rating change based on the difference in your scores (assuming you won)

This is a nice, straight line, with a truncation at 20 points, because the formula only allows a 200 point score difference.

(2) What if I tie my opponent?

Here is where the fun begins. If you and your opponent have the same rating, then the ratings don't change. If not, the rating change depends on your relative ratings. If you tie G.I. Joel, your rating will probably go up. If you tie a schmuck like me, your rating will probably go down. Below you is a function of two variables r1 (your rating) and r2 (your opponent's). Notice that the maximum rating change for a tie is 10 points either way.

3) What if I win or lose? How important is the rating difference?

We answer that question in two ways. First, let's pretend you win (or lose) by 50. Your rating will change by 0 to 25 points, depending on r1 and r2. We see how that works below. The first graph assumes you win, the second assumes you lose.

You win by 50	You lose by 50

These are all very nice, but what I am most curious about (and this is the question that prompted this whole page) is what it looks like from my perspective. Pretend my rating is 750. Now my rating change if I win is a function of the score difference, d, and my opponent's rating, r2. THAT is what I want to be able to visualize. The resulting function is plotted below (from two different perspectives so you get a feel for it). You will note that, as promised at the outset, your maximum rating change is 40.

If you have any questions, drop me a line, and I will try to answer them. And remember, the best way to increase your rating is to play me!

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