http://webdiplomacy.net/points.php

Sum-Of-Squares (SoS)
This is a centre-based scoring system. In a draw, each player gets a proportion of the pot scaled by their centre count:

(SC_count^2) / (sum of all players (SC_count^2))

So with a pot of 210 in SoS, then the points are divided up by the amount of centres you own. So if there are four people alive, with you having 12 SC's, and the others having 10, 8, and 4 SC's respectively, then you can work out how many points you will receive by following that formula, so 12^2 / (12^2 + 10^2 + 8^2 + 4^2) * 210 = 93 .

This kind of scoring is often used by face-to-face tournaments, because it allows for more distinction between players, encourages going for solos rather than cutting out surviving players, and doesn't drag games on just to get that last elimination.

In descriptive rather than mathematical terms, what this means is that the portion of the 100 you get increases non-linearly with SC you own, AND ALSO increases the more fragmented the other players’ SCs are spread out.

Let’s take an example [country: SC; points]:
England: 8; 27.83
Russia: 8; 27.83
France: 7; 21.3
Turkey: 6; 15.65
Italy: 4; 6.96
Austria: 1; 0.43
Germany: 0; 0

How did England get 27.83? Well, it’s 100 * (8^2 / (8^2+8^2+7^2+6^2+4^2+1^2+0^2)).

It should be immediately obvious how more SC means more points. While the numerator rises quadratic ally, the denominator does not rise as much (although it still does) due to being diluted out by the other scores.

The denominator is what’s really interesting here. To easily illustrate this, a score of 16 SC against a 9 SC and 9 SC power would give you 100 * (16^2 / (16^2 + 9^2 + 9^2)), or 61.24. A score of 16 SC against the other 6 powers each having 3 SC would give you 100 * (16^2 / (16^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2) = 82.58.

So this scoring system (A) has a WTA mechanic (B) non-linear scaling (C) promotes not eliminating other players unless you’re the one eliminating them. It actually hurts your score to allow weaker players to be taken over by others and (C.2) disregards amount of players in a draw, only their SC amounts