An improved Stellar Crisis ranking system

The original version of this very good ranking system has been used to rate french PBM chess players for years. So why reinvent the wheel ? Here I have adapted it a little.

Presentation

New players

Every new player gets a Rank of 500 and an Index of 500.

Ceilings

• The Rank can't be smaller than 100
• The Index can't be smaller than 100 or higher than 500.

Index

• For each match, the Index of the players involved is decreased by the (adjusted) stake won or lost, up to 100. A player with an Index of 100 is established.
• If you haven't got results (nukes or nuked, draws don't count) in the last 3 months, your Index becomes max(200,Index). If it's 4 months, it becomes max(300,Index). 5 months: max(400,Index). 6 months: max(500,Index).

Stakes

Stakes are points added to the winner's Rank and subtracted to the loser's Rank. Unless the following article apply, the stake is the same for both players.

If the weaker player wins, the stake is 10. If the stronger player wins, the stake depends of the gap between their respective Ranks :

Ajusted stakes

Stakes don't need to be adjusted in the following cases :

• Index is 100 for both (they are established).
• Index is 500 for both.

Otherwise the stake is multiplied by a different factor for each player. Let's call A the hundredth part of his Index and B the hundredth part of his opponent's. Then the factor is (1 + 19A - B - 3AB) / 16. So, to get the adjusted stake won or lost by a player, you multiply the unadjusted stake by the factor and you round down.

Example

If P1 whose Rank is 520 and Index is 453 wins against P2 whose Rank is 648 and Index is 131, the (unadjusted) stake is 10 so :

• J1's Rank gets 10.(1 + 19x4.53 - 1.31 - 3x4.53x1.31) / 16 = 42 points
• J2's Rank loses 10.(1 + 19x1.31 - 4.53 - 3x1.31x4.53) / 16 = 2 points

Current implementation

Stellar Crisis 3.2+

To quote Andy Graves in Stellar Crisis v3.2 - Motivation, Among the most significant new features is the introduction of the Bridier Ranking System for 2-player (Grudge) games, enablement of which is a server-level option, and if it is enabled, it becomes a series configuration option.

Winning without getting points ?

With these systems, it can happen that you don't get any points even if you win, providing your opponent's Rank is much lower than yours. This can be depressing. It has been suggested in the Yahoo! SC Club to restrict game access in a way that your rank would at least increase by one no matter who you nuke, and I think it's a good idea. The best way IMHO to avoid great differences in rank in a given game is to restrict entry to players within a given Rank interval and/or Index interval (both more meaningful than wins). These parameters would be series configurable.

Nuke order

It should not be possible to get more points by first getting a nuke in game A, then in game B, instead of doing it in reverse. You avoid this problem entirely if the scores used for the calculation are taken from the beginning of the game (i.e. it doesn't matter whether you have nuked people elsewhere meanwhile). But what if you nuke several people in the same game ? This is something that can't happen in chess, for which the Bridier system was initially designed. I would suggest you use the initial scores anyway, so that nuking X then Y is not any different from nuking Y then X. Otherwise you might soon find games lasting longer than necessary...

This said, goth raised a valid concern on SC Yahoo! lately (2000-10-07): what if someone started 20 games with his initial Rank of 500 and won most of them ? That's why he proposes that my Bridier change is based on my rating at the end of the game, but on my opponent's rating at the start of the game. I don't think this is much of a problem though, because I've experienced that if you try playing too many games at once, your playing level decreases...

Other suggested improvements

Nuking while allied

If you nuke (or are nuked by) someone while allied, the Rank used to compute the stakes is the average of people in your alliance. So that if you were allied with an SC God you'll get less points [or lose more] than if you were allied with Mr. Stupid. This said, it only makes sense when alliances are fair, at least at the beginning (not 3 on 2 in a 5 player games for instance).

Ruins

In my SC proposal, someone falling into ruins is also considered as nuked. So, to score the ruin itself, I suggest the ruiner's Rank loses X (5 for instance) times (the number of previous ruins + 1). So, if it's your first ruin, you don't lose too much (only what you lost for being nuked plus X), but if it's your 7^th, your Rank won't like it ! It works a bit like cumulative upkeep in Magic The Gathering: at the beginning, it's ok, but after a while, it becomes prohibitively expensive.

Tell me (replace localhost by agt-the-walker.net) if you have comments / suggestions / etc. about this page, since feedback is always appreciated !
Last Update: 2006/01/18 23:31:29