#### The System used for Age of Wonders 3 is the Elo Pointsystem for ffa leagues (with start bonus)

About the pointsystem

A good ranking needs a good and fair Point System to rank and classify players. The ranking system on the Battlefield is based on the Elo system (see below). Players are sorted in descending Points order.

Which ranks can be achieved?

Beginner: 700-1000 points

Veteran: reached more than 1000 at least once (but may have gone back below 1000)

Elite: the top 30% of Veteran players

Master: the top 10% of Veteran players

Starting conditions

Players start with 700 points and are listed in the ranking.

Start Bonus

Beginners (under 1000 points) get a bonus: their point gains are doubled and they do not lose points. New players can thus climb the ranking faster.

The ranking points are based on the Elo system

Each player get a number of points based on the Elo system (see Wikipedia for more information on the Elo system). When players start, they get 700 points (see "Starting conditions" above).

The Elo system is based on the K-Number, the Difference number and the Result number, detailed below, for people wanting more details.After each match, the change in ranking for each player is calculated by a formula (see details below): Change = (Result - Difference) x K

K-Number

This number is the multiplier applied to the points gained or lost: a higher K-Number means more points won or lost. The K number varies according to the number of games played or current points. Its values are:

Less than 10 games played: 25

More than 10 games and less than 1400 points: 20

More than 10 games and more than 1400 points: 15

Difference number

A Difference number is calculated for each player involved in a match. For each player, its Difference is the subtraction of his ranking points with the ranking points of others.

Example:

If Player 1 has 1000 ranking points and Player 2 has 1600 ranking points.

The Difference number for Player 1 is 1000 - 1600 = -600

The Difference number for Player 2 is 1600 - 1000 = 600

##### Result number

This number represents the result of the player assessed against any of his opponent in the game assessed.

Its calculation depends on the relative position of player compared to its opponent:

- higher position (i.e. victory in a 1vs1): 1 * (total number of players in the game - position achieved by the player assessed) / (total number of players in the game - 1). The winner (1st position) will thus always have a Result number of 1.

- equal position (e.g. both players ranked 2nd in a game with more than 2 players): 0.5

- lower position: 0

Example:

Player 1 is #1, Player 2 is #2 and Player 3 is #3. Their respective Result numbers are:

Player 1 vs Player 2 = 1 (win); Player 1 vs Player 3: 1

Player 2 vs Player 1 = 0; Player 2 vs Player 3 = 1 * (3 - 2) / (3 - 1)= 0,5

Player 3 vs Player 1 = 0 (lost); Player 3 vs Player 2 = 0

Expectation number

The Expectation number represents the probability for a player to win the game: better players have a greater Expectation to win. The Expectation number is computed using the formula designed by Professor Arpard Elo (who gave his name to the Elo system).

Formula: Expectation number = 1 / (1 + 10^(- Difference number / 400))

Example:

If Player 1 has 1800 ranking points and Player 2 has 2400 ranking points.

Then the Expectation number for Player 1 is:

1 / (1 + 10^(- (-600) / 400))

That is to say, it is equal to 0,01958: Player 1 has a probability of winning of 1.958%.

Player 2 = 1 / (1 + 10^(- 600 / 400))

That is to say, it is equal to 0,98042: Player 2 has a probability of winning of 98.042%.

Change

The Change is the number of points the player will gain or lose. It depends on the Expectation number, the Result number and the K-Number, following this formula:

Change = (Result - Expectation) x K

Example

If we keep the same figures as in the example in the previous section:

Change for Player 1 = (1 - 0,01958) x 25 = 24.511

Change for Player 2 = (0 - 0,98042) x 15 = -14 ,706

##### Addition / subtraction

In games with more than 2 players, the higher the position of a player at the end of the game (being 1st is the highest position achievable obviously), the more points he will add to his ranking points.

Conversely, when a player finishes at the bottom of a game with many players, many points will be substracted from his ranking points.

Example:

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If we have the following positions at the end of a game: #1 - Player A; #2 - Player B; #3 - Player C and the change calculated between each players is as follow:

A vs B = 30 points

A vs C = 20 points

B vs C = 15 points

Then the changes will be:

Player A: 30 + 20 = 50

Player B: -30 + 15 = -15

Player C: -15 + -20 = -35

Team relationships:

When several players are in the same team, the points they gain will be reduced by applying the following formula:

Points * ((Total number of players – Number of team mates, excluding oneself) / Total number of players)

Example:

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Two teams of two with Player A & Player B (Team 1) vs Player C & Player D (Team 2)

Team 1 = 50 points for Player A ==> 50 * ((4-1)/4) ==> 50 * 3 / 4 = 37,5

Team 1 = 40 points for Player B ==> 40 * ((4-1)/4) ==> 40 * 3 /4 = 30

Team 2 = -50 points for Player C ==> -50 * ((4-1)/4) ==> -50 * 3 / 4 = -37,5

Team 2 = -40 points for Player D ==> -40 * ((4-1)/4) ==> -40 * 3 /4 = -30

##### What to do after the end of a game

The winner or one of the player in the game will report the game at the related Battlefield page!

All players (and the Admin) will then get an email Report about the game. Everyone can contest and delete the report if it is not correct or contact the Admin, who will then investigate it and maybe change the report and solve the issue. Players can also rate their opponents and the game from the report page.

##### Computing of Ranking Points

Every game reported in the FFA league will influence the ranking. All the players who played a game will get point changes!

If we go back to our example:

Player 1 won 25 points which means his updated ranking points will be 1000 (previous ranking points) + 25 (earned during the match) = 1025 points.

Player 2 lost 15 points, and his updated ranking points will be: 1600 (previous ranking points) - 15 (earned during the match) =1585 points.

##### In a report, the following values are displayed:

- Points: the points gained or lost

- Extra Points: the bonus points (generally due to the x2 bonus for Beginners)

- Missed Points: the difference between the points a player could have gained if he (or his team) had won the match and what he actually gained (or lost). The Missed Points can be significant if a player loses the match and loses points (e.g. if winning would have brought him 20 points and he lost and his points decreased by 15, his Missed Points value is 20 - ( -15) = 35

- Game Value: it indicates the value of the players involved, the interest of the game. It is calculated by taking the square root of the sum of the ranking points of all the players. Typically, a Game Value of 20 is relatively low and is generally a duel, whereas a Game Value of 90 or more indicates a very big game with 8 Veteran players.

##### Further Rules / Exceptions

Quitter Penaly -20 points

An activity status is displayed for each player based on how active they are in the ranking:

- Hot: three games or more reported in the last 90 days

- Regular: at least one game reported in the last 90 days or participating in at least one ongoing game where there has been a blog post in the last 90 days

- Cold: one game reported in the last 90 to 180 days or participating in at least one ongoing game where there has been a blog post in the last 90 to 180 days

- Freeze: inactive for at least 180 days