PBW League Idea...

[LazarusLong42]

OK, because no one asked about it... my suggestion for a ranking/ladder system, in full fledged mathematical glory. Math-impaired people may wish to stop here.

OK. For any given game, assume you have N players, each of whom has a rating, R1, R2,... RN. These players will "donate"--virtually--a portion of their Ratings to a pool which will go to the winner of the game. The total pool of points would be equal to 50*N.

The "donation" for player i will be equal to Di = (50 * N * (Ri^2))/(R1^2 + R2^2 + ... + RN^2). This donation is equal to the total amount the player will *lose* if they fail to win the game. If the player wins, however, they gain (50 * N) - Di points -- or the total of the donations of the other players.

Let's take two examples. A two-player game is simple. The total point pool is 100 points. Now, let's take two players with rating 1000 and 1200 respectively.

Player 1 donates 50 * 2 * 1000000 / (1000000 + 1440000) = 41 points.
Player 2 donates 59 points via the same math.

So, if player 1 wins, he gains 59 points and player 2 loses 59 pts.
Conversely, if player 2 wins, she gains 41 points and player 1 loses 41 pts.

In other words, if the stronger player wins, he gains fewer points than the weaker player does if he wins. In a two-player game that ends in an agreed draw, each player loses their inital donation, then takes back 50 points. So, player 2 would lose 9 points to player 1 if this game had ended in a draw.

Now... because I'm a masochist, let's take the case of a *5* player game. Total pool is 250 pts. I'm not going to show the calculations, but I'm going to give you a quick table:

code:

---

Player  Rating  Donation

1       1300    80

2       1200    68

3       1000    48

4       800     30

5       700     23

---

Which ever player wins gains the sum of the other players' donations; each player who lost loses his donation. Of course... that's assuming a Last-man-standing game.

In some games, team games for instance, players will know going in that they plan to cooperate. In some games, mainly large games, players will agree to a cooperative win rather than fighting a final battle. Both of these are parts of the SE experience. However, they muddle a Ratings system of this sort. I'm not going to write out the math here because without being able to show real equations they'd become hopelessly illegible.

Suffice to say: if two people win, take the other three players and add their donations together. The two players each take a share of those points proportional to both their initial donation, and to the total number of points they would have earned had they won. So if, for instance, players 1 and 3 in the above example share the win, player 1 earns 71 points and player 2 earns 51 points.

I'll leave the math on that as an exercise for the reader <EG>

Comments? Flames?

Eric