A ladder ranking system is designed to allow players to see how well they rate when compared against other players at the same game. This is acheived by giving each player a rating based on how well they've done against other players and their ratings at that time. Each player's rating fluctuates as they win or lose against other players with better or worse ratings than themselves. Here's how Sea3D's rating system works:

1. When Sea3D players finish a ladder game, Sea3D posts all of the game and player statistic information to the S3D Connector website (this site).

2. The site then sorts the players into winning order by the number of points they got in the game. The player who wins, even if they have the same amount of points as a second place player (i.e. the 2nd place player had victory point cards they didn't use to win) always gets full points against everyone else. In other words, the winning player never ties anyone else.

3. Once the players are sorted into the winning order, the winning player receives positive game rating points based on the relative difference between their rating and all of the players ratings who they beat. The losing players all receive negative game rating points against the one rating of the winner.

4. Each player's game rating is calculated using the ELO rating system, which is what the chess world uses. In this system, all new players come into the system with a standard rating of 1500, sort of a "lets see where you really belong" rating. Every time you play someone, the following formula is used to determine how many game rating points you scored against them:

P = K * (S - Se)

• P is the rating point total for the game
• K is a constant multiplier. In the S3D Connector rating scheme, K is always 20.
• S is the score for the game. For a win, it is 1, and for a loss, it is 0.
• Se is the expected score for the game. Se is calculated with the following formula:

  Se = (1 / (1 + (10 ^ (-dif in ratings / 400)))

  In English this says, "One divided by the total of one plus ten raised to the power of the difference in player ratings divided by 400." Four hundred is the "class" rater that says that players who are separated by more than 400 points in ratings really belong to separate classes of players (and probably shouldn't be playing each other!).

Let's look at an example. Let's say John plays Sarah (hypothetically in a 2 player game). John's rating going into the game is 1600 and Sarah's is 1500. Let's also say that Sarah pulls off the upset and beats John. The points she gets for beating John would be:

P = 20 * (1.0 - (1 / (1 + (10 ^ (100 / 400)))))
P = 20 * (1.0 - (1 / (1 + 1.7782)))
P = 20 * (1.0 - (1 / 2.7782))
P = 20 * (1.0 - (0.3599))
P = 20 * 0.6401
P = 12.802

So Sarah's rating would increase to 1513 for this upset. Meanwhile, John's rating would decrease by 13 points and he would fall back to 1587.

5. The the game rating points for each player in the game is then added to the players rating and that becomes their new rating.

6. That's how the ELO system works. If you want more information on it, check out this link for greater detail, including history. Interestingly, ELO is not an acronym for anything. It is actually the last name of the guy who invented it. That's pretty cool.