[Slynky]

OK, we need to come to an agreement on the best way to rate a multiplayer game. I re-read the thread portion that discussed it and I don’t think there was a consensus. So…here we go again:

(1) I think everyone agreed a multiplayer game needed to result in a rating that yielded (or lost) more points than a regular 1 x 1 game.
(2) But, I think, most also agreed that the gain or loss in points shouldn’t be so great that it would discourage entry into multiplayer games.

With this in mind, I worked on a formula based on the formula we use for 1 x 1 games and added a dimension to, hopefully, reflect the fact that a winner beat more than one player and a loser lost to everyone. And those in the middle got a variation in between. It goes like this:

4 players (for simplicity sake, all rated 1000). Players A B C and D (who finished in alphabetical order).

Player A beat everyone. So, we average the scores of the people he beat, in this case, 1000. Compute points based on the formula which we all know comes out to +16 for him and –16 for the others. But, we disregard the losers. We only compute the points for player A. HERE is the adjustment: Player A beat 3 other players so we square the number of players he beat (3) to get a total of 9 and subtract the square of the number of players who beat him (0) to get 0 and add that to his score. This yields a total of 25. FINALLY, we add a point for every person he beat (3) for a final score of 28.

Player B beat everyone except one person. So, we average the scores of the people he beat, again 1000, and he gets 16 points. Then we average the points of the person who beat him (1000). He loses 16. So far, he is even. Then we do the multiplier. He beat 2 people, so 2 squared is 4 and then subtract the square of the total number who beat him (only a 1). The resulting score is 3. And we add 2 points (for the number of people he beat giving a FINAL score of 5.

Player C, without being verbose, should be a FINAL score of -2.

And player D should wind up with a loss of 25 points.

This is for Ratings of 1000 (to make it easy). Here, we can see the people in the middle of this 4 x 4 didn’t win and didn’t lose. Hence, not a lot gained or lost. Of course, this changes a bit based on Ratings that aren’t 1000. (well, DUH!)

Let’s look at 5 people and see if the person exactly in the middle comes out about even:

A B C D E (this is the shortened Version and same winning order):

A=
+16 points from rating computation (beaten players)
-0 points from rating computation (players beating him)
+16 points for the square of beaten players (4 squared)
-0 points for the square of players beating him (0 squared)
+4 (for each victory)
Total = 36

B=
+16 points from rating computation (beaten players)
-16 points from rating computation (players beating him)
+9 points for the square of beaten players (3 squared)
-1 points for the square of players beating him (1 squared)
+3 (for each victory)
Total = 11

C=
+16 points from rating computation (beaten players)
-16 points from rating computation (players beating him)
+4 points for the square of beaten players (2 squared)
-4 points for the square of players beating him (2 squared)
+2 (for each victory)
Total = 2

D=
+16 points from rating computation (beaten players)
-16 points from rating computation (players beating him)
+1 points for the square of beaten players (1 squared)
- 9 points for the square of players beating him (3 squared)
+1 (for each victory)
Total = -7

E=
+0 points from rating computation (beaten players)
-16 points from rating computation (players beating him)
+0 points for the square of beaten players (0 squared)
-16 points for the square of players beating him (4 squared)
+0 (for each victory)
Total = -32

Remember, we are using points based on everyone being at 1000. This would fluctuate with various Ratings plugged in. We all see that the winner got about as many points as if he had played in 2 and a quarter games. And the loser lost about as many points as if he had lost 2 games. The others inside are a mixture.

Though not as exact a formula as the 1 x 1 rating, remember, rating a multiplayer game is not ever going to be perfect. There is no way a formula could account for ganging, bad position, etc. With those imperfections in mind, the goal is to come up with a pretty good award (and subtraction) of points for a game that should count more than a 1 x 1 game but not so bad as to deter anyone from joining one.

I know it seems a bit complicated but comments are invited. The fault I see in this is that the winner and loser seem to get a bigger number than the others (of course, this could be changed some depending of Ratings of other than 1000). Or, revisit the thread below to look at other suggestions, too. But we need to arrive at some sort of rating agreement.

Note, this requires the computation to be done after the game has been totally completed (as it relates to rated players).