So that you can get an idea of how the calculations for the rankings lists are performed, we will first give you some background information. Afterwards we will present some detailed calculations in the form of examples. Calculating scores for the one-on-one rankings and the clan rankings follow the same rules.

The basis for calculating the points won or lost in a game depends first of all on the chances of each player to win. The higher a player's chances of winning are, the fewer the points that this player gets by winning.

A player's chances of winning are higher ...

...the more games he has played (Player experience)
...the more games he has won (Score)
...the more often he has played a race he has chosen (Specialization)
...the more often he has played a particular map (Map familiarity)

In general, if the favorite wins, fewer points are added to his score and fewer points are deducted from the loser's score. If, however, the underdog unexpectedly wins, considerably more points are added to his score and substantially more are deducted from the favored player's score.

This system is intended to keep the rankings lists more dynamic. Even for very good players and clans, it will be a challenge to remain at the top of the rankings because even a couple of defeats at the hands of a newcomer can mean taking a tumble in the rankings. This system also prevents a player from occupying a place at the top of the rankings by specializing in playing one race or even a particular map. More flexible players will soon overtake these "one map wonders" even if these specialists win all their games. Whoever really wants to be able to battle it out at the top, will have to play all the races and get to know all the maps!

So that newcomers aren't discouraged while gaining their first experience in ladder play, a kind of handicap system has been built in so that fewer points are deducted from a newcomer's score when he loses a game than from an experienced player's score. The result of this handicap will be that newcomers will be rewarded for hanging in there and gaining experience.

Before going into the detailed mechanics of the scoring system, a few general comments: Like all the other parts of THE SETTLERS III, the rankings lists system has been created to make game play as much fun as possible. When in spite of your ambitions, you experience a loss along the way, keep cool. You will have enough opportunities to come out on top.

The same thing applies to the rankings system itself. If there are hitches in the system, keep cool. We have already checked the system over and over again, but we are not immune to the surprises that sometimes occur. If a problem comes up, get in touch with us at Blue Byte, because we'll be continually working on improving the system!

Point Scoring
The following examples will show you how points are calculated and added or subtracted from the players' scores depending on the outcome of the game. These examples are naturally also valid for Clan games.

Starting Points for New Players
A new player begins with 8,000 ELO points and an experience factor of 50%. In the World Rankings Lists, however, Rankings Lists points, which consist of a combination of ELO points and the experience factor, are displayed:

Experience Factor
Each game played increases the experience factor of a player. As you can see in the following table, the experience factor first increases rather quickly but later, more and more slowly. After 25 games, a player is rated as experienced and the experience factor remains constant at 100%.

Table 1: Experience Factor

An Example:

Before a player's first game, he has 8,000 ELO points and an experience factor of 50%.

Number of Rankings Lists Points = 8,000 x 50% = 4,000.

The player goes into his first match with 4,000 RL points.

Assuming that the player loses his first game, the loss cost him, for example, 100 ELO points. After this match 100 points are subtracted from the player's 8,000 ELO points, leaving him a total of 7,900 ELO points. Having gained some experience, though, in his first match, the player's experience factor has increased. Now instead of 50%, 55% of the player's ELO points are displayed as Rankings Lists points. (see Table 1) The calculation for the new RL points is as follows:

Number of RL points = (8,000 - 100) x 50% = 4,345

As such, the player has won 345 RL points even though he has lost his first match. This system has been devised so that a good player will collect RL points faster than a poorer player but ensures that the point difference between them at the beginning does not get too big. The RL points gained in the player's first matches doesn't reflect so much his game performance but much more his constant increase in experience. A sucessful player will in any case rise in the rankings faster with a gain of 100 points as can be seen in the calculation below:

Number of RL points = (8000 + 100) x 50% = 4,455

Game Scoring System
The player wins or loses ELO points from a victory or loss in a game. A maximum of 100 points is given for a game. The number of points won or lost is based on the chances a player has to win. A player's chances of winning are estimated on the basis of 4 factors, which will be explained in detail later.

An Example for Winning or Losing Points
Player 1 has a 75% chance of winning, player 2 has a 25% chance.

Scenario 1, favorite wins
If player 1 wins, he is awarded 25 ELO points and player 2 loses 25 ELO points. In this case the favorite, player 1, has won and is awarded comparatively few points. The underdog, player 2, has lost as expected and loses comparatively few points.

Scenario 2, underdog wins
If player 1 loses, he loses 75 ELO points and player 2 wins 75 ELO points. In this case the favorite, player 1, has suffered an unexpected loss and loses considerably more points. The underdog, player 2, has pulled off an upset against a stronger opponent and is awarded considerably more points.

Chances of Winning
The chances of winning are calculated based on a comparison of the strengths of the two players. For this comparison, 4 factors are taken into consideration. Each of these factors will be described in detail later.

Strength of a player = ELO factor x Experience factor x Race factor x Map factor

The chance of winning for a player is:

Chance of winning, Player 1 = 8,000 ÷ (8,000 + 2,000) = 0.8 = 80%
Chance of winning, Player 2 = 2,000 ÷ (8,000 + 2,000) = 0.2 = 20%

Here it can be clearly seen that the higher the a player's strength is the larger his chances of winning are. The larger chances of winning, however, mean fewer points in case of a victory. In view of the factors, it is worthwhile for a player to have the smallest possible chances of winning and nevertheless to win. This brings the player the most points.

Factors

1. ELO factor
The ELO factor reflects the general strength of a player and can be calculated as follows:

Power = 10^(8,000 ÷ 2000) = 10,000

2. Experience factor
The experience factor acts primarily as a buffer for new players, a kind of handicap as in golf, so that losses during the first games do not lead to a dramatic fall in the rankings. This factor is calculated using values from Table 1 which is displayed above.

Example: Player 1 has played a total of 10 games so far. His experience factor is 86.5%. Player 2 has already played a total of 40 games and has an experience factor of 100%.

3. Race factor
This factor reflects the frequency with which a player chooses to play a specific race. If a player prefers playing a particular race, his chances of winning increase when playing against another player who has not specialized in playing one race. The race factor is included to reduce this advantage of specializing in one race. A value of over 100% reflects a greater chance of winning; a value of under 100% reflects a smaller chance of winning. Keep in mind that the smaller chances of winning yields more ELO points in the event the game is won.

In calculating the race factor, the last 25 games played are taken into consideration. The important considerations are how often a player has played a particular race and whether he has played this race very recently or not.

Table 2

An Example:
Player 1 has only played a total of 7 games, every time with the Romans. This automatically means that he has played his last 7 games with the Romans. From table 2, the first 7 percentages are added together:

Subtotal 1 = 12 + 10 + 8 + 7 + 6 + 5 + 5 = 53%

Since Player 1 has only played a total of 7 games so far, the "missing" 18 games are given an averaged value. This averaged value is the sum of the last 18 percentages from table 2 divided by 4.

Subtotal 2 = (4+4+4+3+3+3+3+3+2+2+2+2+2+2+2+2+2+2)÷4=11.75%

Total (Subtotal 1 + Subtotal 2) = 53% + 11.75% = 64.75%

Finally, using Table 3, the Race % corresponding to the race specialization percentage can be determined. In this case, 64.75% corresponds to a race % of 150% (64.75% is closer to 65% than 60%).

Table 3

If a player doesn't choose a particular race, but uses a "random" race, he will be rewarded for his willingness to take a risk. In this case, his race % will be multiplied with the factor .8, thus reducing it.

In clan games the race % for each player in the clan will be determined, only on the basis of previous clan games, of course. An average will then be calculated for the clan's race %.

4. Map factor
The map factor is built in to compensate for the fact that many players specialize in playing a particular map and as such can have considerable advantages over other players. A value exceeding 100% reflects a greater chance of winning while a value below 100% indicates a smaller chance. Again, keep in mind that the smaller chances of winning yields more ELO points in the event the game is won.

For the map factor, there are two different cases, one for player-chosen maps and one for randomly chosen maps. Self-made maps can't be played in world rankings games.

1. Player-chosen maps
Let us assume that player 1 has always played the same map in the last five games and is now entering a new game with the same map. In order to determine the map factor for the current game, it is again necessary to use Table 2. Since player 1 has always used the same map for the last 5 games, the calculation is as follows:

Total = 12 + 10 + 8 + 7 + 6 = 43%

The remaining values are not taken into consideration here because there are so many player-chosen maps available.

Looking into table 4, we can see that the value corresponding to 43% for map usage % shows a map % factor of 240%.

Table 4

2. Random Maps
Let us assume that player 1 has played 5 games so far. In his third and fifth game, he played random maps. In order to determine the Map % factor for the current game, it is again necessary to consult Table 2. The calculation is as follows:

Subtotal 1 = 8 + 6 = 14%

The percent values of the 20 games not yet played are added together and divided by 2.

Subtotal 2 = (5+5+4+4+4+3+3+3+3+3+2+2+2+2+2+2+2+2+2)÷2=28.5%

Total = 14% + 28.5% = 42.5%

Looking into table 5 we can see that the value corresponding to 42.5% is

Table 5

The Recording of Scores
Before any scoring of the game can take place, the game results of all the players has to be received. The various possibilities are:

If the results are clear, that is, all players report the same results to the Lobby, for example, "Team 1 has won", then the game is scored.
If the results are clear (all results are the same) but incomplete, for example, because a player shuts his computer down, then the game is scored.
If the results of a game with more than 2 players are not clear, but a clear majority, for example, 3 of the results indicate a victory for team 2, then the game is scored. This applies as long as only one result is contradictory.
If the results are not clear, for example, in a one-on-one game when 2 different winners are reported, then the game is not scored.
If the results are not reported to the lobby because, for example, all the players are disconnected from the lobby, then the game is not scored.

A Detailed Example
Player 1 and player 2 enter into a game. The chances of winning for both players must be calculated.

Step 1: The ELO factor

Player 1 has 8,000 ELO points
ELO factor = 10^(ELO points ÷ 2,000) = 10,000

Player 2 has 10,000 ELO points
ELO factor = 10^(ELO points ÷ 2,000) = 100,000

Step 2: The Experience factor

Player 1 has played 7 games so far. From table 1, an experience factor is determined.
Experience factor = 78.7%

Player 2 has played 25 games already. From table 1, an experience factor is determined.
Experience factor = 100%

Step 3: The Race factor

Player 1 has played the Romans in all 7 of the games he has played and chooses the Romans for the coming game too. Following the example described above in the section on the Race Factor, a race factor is calculated.
Race Factor = 150%

Player 2 has played the Asians twice before, in his third-last and fifth-last games and chooses the Asians for the game coming up. In all of the other 23 games he has played, he has chosen another race. From table 2, a raw percentage for the third-last and fifth-last game of 14% can be calculated. From table 3, the corresponding race factor can be determined.
Race Factor = 90%

Step 4: The Map factor

Player 1 has played the same player-chosen map in his last 5 games. A map factor can be determined.
Map factor = 240%

Player 2 has never played the map for the forthcoming game. A map factor is then determined from table 4.
Map factor = 0%

The Final Calculation

Now all the different factors can be applied to determine the chances of winning for both players on this particular map with the races they have chosen.

Player strength = ELO factor x Experience factor x Race factor x Map factor

For player 1:
Strength player 1 = 10,000 x 78.7% x 150% x 240% = 28,332

For player 2:
Strength player 2 = 100,000 x 100% x 90% x 50% = 45,000

The chances of winning for both players are then as follows:

Chances of winning for player 1 = 28,332 ÷ (28,332 + 45,000) = 38.64%
Chances of winning for player 2 = 45,000 ÷ (28,332 + 45,000) = 61.36%

Point Scoring

In this example, player 1 is the underdog and player 2 is the favorite. By choosing a familiar race and map, player 1 increases his chances of winning but remains the underdog. Fewer points are awarded for the victory of the favorite and more points are awarded if the underdog is able to upset the favorite.

If player 1 does pull off an upset, then he is awarded 61 ELO points and player 2 loses the same number of points. Player 1 would then would then increase his ranking list points from a total 6,296 (8,000 x 78.7%) to 6,578 (8,061 x 81.6%). See Experience factors in table 1.

If player 2 wins as the favorite, then he is awarded 39 ELO points and his opponent loses the same number of points. Player 1, however, loses no ranking list points as a result of this loss but, to the contrary, gains ranking list points because of his gain in experience. Player 1 increases his ranking list points from 6,296 (8,000 x 78.7%) to 6,496 (7,961 x 81.6%)! This does not mean that both players have won. Player 1 has simply become a better player because of this new game experience. His ELO points are now lower and gradually this loss in ELO points will show more impact on his ranking list points as he approaches his twenty-fifth game where his experience will have risen to 100%.

Two Final Remarks

A maximum of 100 ELO points can be won or lost in one game.

The purpose of using these factors is to encourage players to regularly use a variety of maps and races. Whoever employs the strategy of specializing in playing a particular race on a particular map will have as a result much higher chances of winning a game, but will be awarded far fewer ELO points and ranking list points, and will ultimately rise in the world ranking lists more slowly than a "non-specialist" player.

Changes - Nov 3, 1999
Players that are resting on their laurels and inactive in defending their positions will now gradually lose points. After a week of inactivity, every further day without play will mean a loss of 15 points for single players. For clans the loss will start after two weeks of inactivity.

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