Note: you can view your own position in the leaderboards via the Rankings tab in-game, where you can also find extra ranking information such as the number of games played.
Rankings - The Basics
Tropic Euro uses a system of ranking points (RP) for assessing each player's relative skill level:
- Your ranking starts at 1500 RP and is updated whenever you play a ranked game.
- A ranked game on the server is one where all islands are controlled by a unique human player (i.e. no computer players).
- Winning a ranked game will in general increase your RP, although coming in second place for a 4 or 5 player game will normally increase your ranking as well.
- If you do well in a game against players with higher RP scores then your ranking will go up more than if you outperform players with lower RP scores.
- The server maintains your RP scores separately for different types of game, including 3 to 5 player games (3-5P) and 2 player (1v1) games.
Gibbs Rankings Points System
For games developers and those of you curious about how the rankings are calculated exactly, Tropic Euro uses a special ranking algorithm called the "Gibbs Ranking Points System", developed by Chris Gibbs. The values start at 1500 and after each ranked game are recalculated as follows:
RP_{new} = RP_{old} + K_{ 1} . (RP_{game_weighted_average} - RP_{old} + S . (1 - G_{new_limited} / G_{new_limited_total} )^{K 2} )
Further clarification on what the parameters above mean and how they are computed:
- G_{new_limited}: the number of games the user/team has played, including the new one and limited to a maximum of G_{exp}.
(i.e. G_{new_limited} = MINIMUM(G_{exp}, G_{old} + 1)).
- G_{new_limited_total}: the total of G_{new_limited} across all players/teams involved in the game.
- RP_{game_weighted_average}: a weighted average of the RP values of all players/teams, using the G_{new_limited} values.
(i.e. RP_{game_weighted_average} = RP_{old} . G_{new_limited} summed over all players and then all divided by G_{new_limited_total} )
- S: indicates the level of success for the player/team in this particular game. It is set to a value between + K_{ 3} (first place) and - K_{ 3} (last place).
This ranking points system is broadly based on the Elo rating system, except with some improvements. The original Elo formula has fixed K values for different rating values and number of games played, whereas the Gibbs algorithm effectively has a K value that dynamically adjusts according to the relative number of games of each player - this allows new users to quickly gain RP against more experienced players, and decreases as the system gains more confidence about a player's level of ability.
The use of weighted averages also means that experienced players can play new players with only a small reduction in RP if they lose the game (and likewise only a small gain if they win), to reflect the fact that the system is yet to accurately determine the new player's skill level.
The algorithm has four parameters that can be used to adjust the RP calculations and distribution of values:
- K_{ 1}: Affects the maximum amount of RP that can be gained/lost in a single game. This is set on a per-game basis according to the number of players, to reflect that 5 player games take longer to complete than 3 player games.
(Current values: 3P = 0.07, 4P = 0.08, 5P = 0.09, 1v1 = 0.07, 2v2 = 0.12)
- K_{ 2}: An optional parameter that can be used to alter the way that the level of success (S) is affected by the user's games as a proportion of the total games across all players. A reduction in this value (the most likely use of this parameter) means that experienced players will gain/lose more RP against players with fewer than G_{exp} games. (Current value = 1.0)
- K_{ 3}: Primarily represents the maximum difference between a player's RP and the weighted average that could reasonably occur in a game, but also affects the max gain/loss in RP. This means that if a player has between 0.5 K_{ 3} and K_{ 3} RP more than the weighted game average (depending on the number of players/games) then they will not be able to gain RP, regardless of the game outcome. In future this will be solved in Tropic Euro by having separate game rooms for players of different RP / experience levels. (Current value = 503)
- G_{exp}: A number of games after which the system considers it has enough "experience" to accurately represent the player's skill level. It allows new users to gain/lose RP more quickly and results in the maximum base gain/loss decreasing to a stable value as the limit is reached. Note that the weighted game average still has a large impact on the calculations, both before and (especially) after the limit is reached. (Current value = 25)
Note to games developers: you are welcome to use this formula as a ranking system in your own games completely free of charge - a link back to this page would be appreciated in return.