Slappy Ranking
Slappy currently supports 3 ranking systems. Ladder administrators can select one of the following ranking systems for the ladder:
- ELO ranking - recommended
- Leapfrog ranking
- Swiss Table Tennis ELO ranking
ELO Ranking
The ELO ranking system used by Slappy is based on the ELO ranking system used in chess. Each competitor is allocated points based on their performance. Competitors with more points are ranked higher than competitors with less points, provided their ranking confidence is the same.
When a new competitor joins a ladder, they will be assigned 1500 points and based on the fact that they have not recorded any games, they will have a ranking confidence of 10%. After each recorded match, the competitor's points and ranking confidence will be adjusted, taking into consideration the following factors:
- The competitor's points at the time of the match
- The opponent's points at the time of the match
- The number of games, points or sets the competitor won in the match
- The number of games, points or sets the opponent won in the match
- The opponent's ranking confidence at the time of the match
Ranking Confidence
A competitor's ranking confidence is calculated based on the number of games, points or sets they have recorded, and the number of different opponents they have played against, in the last 90 days.
"Recorded games" are individual games in a match. For example, if a competitor wins a match 3 - 2, this will count as 5 recorded games (or sets) for each competitor.
Ranking Confidence (%) = minimum(nGames/60, nOpponents/10) x 100, where:
- nGames = the number of games recorded in the last 90 days (up to a maximum of 60)
- nOpponents = the number of opponents played against in the last 90 days (up to a maximum of 10)
Expected Result
Given the difference in points between 2 competitors, an expected result can be determined for a match between those 2 competitors. The expected result can be calculated as follows:
Higher Ranked Competitor's Expected Games = Winner Games
Lower Ranked Competitor's Expected Games = (100 - Points Difference) / 100 x Winner Games
So, for example, if 2 competitors play a best of 5 games squash match (i.e., a competitor needs 3 games to win), and the difference between those competitors' points is 32:
Higher Ranked Competitor's Expected Games = 3
Lower Ranked Competitor's Expected Games = (100 - 32) / 100 x 3 = 2.04
Hence, the expected result is that the higher ranked competitor wins 3 games to 2.04 games. If this was the final score (which is obviously not possible since you can't have fractional games), then there would be no change in either competitor's points. If the higher ranked competitor performs better than this (e.g., 3-0, 3-1 or 3-2), then that competitor's points will increase and the opponent's points will decrease. If the higher ranked competitor performs worse than expected (e.g. 3-3, 2-3, 1-3 or 0-3), then that competitor's points will decrease and the opponent's points will increase.
The amount of change in points will grow proportionally, the further the actual result is away from the expected result. A competitor's points will also change more if the opponent's ranking confidence is higher.
Points Change Calculation
Without going into too much detail, the basic idea of the points change calculation is that, based on the competitors' current points relative to each other, there is an expected outcome for the match. The competitor who performs better than expected will gain points, while the other competitor will lose points. Therefore, if a competitor wins a match by a smaller margin than expected, that competitor's points will decrease. Winning a match doesn't guarantee an increase in points.
When comparing competitors, it is possible to view the points changes for each possible result (premium version only).
Ladder ranking
If a competitors has not recorded enough recent results, it is difficult to determine their true ranking. For this reason, their ranking confidence is used to adjust their points on the ladder. These weighted (ladder) points are used to rank competitors on the ladder, instead of their unweighted points, which are used to calculate rating changes. Competitors are ranked in order of their ladder points, from highest to lowest.
Ladder points = Unweighted Points - (100 - Ranking Confidence)
For example, if a competitor has 1560 points, with a ranking confidence of 40%,
Ladder points = 1560 - (100 - 40) = 1500
If a competitor's ranking confidence is below 10% (i.e., they have not recorded any games in the last 90 days), their displayed points are further decreased by 2 points each day that they remain inactive.
Ladder points = Unweighted Points - 90 - (Days Since Last Result - 90) x 2
For example, if a competitor has 1560 points, but hasn't played in 120 days,
Ladder points = 1560 - 90 - (120 - 90) x 2 = 1410
Competitors who are not recording games will gradually move down on the ladder until they reach 0 points.
Leapfrog Ranking
With the leapfrog ranking system, when a competitor joins a ladder, they are initially ranked at the bottom of the ladder. They can then challenge higher ranked competitors and, if they win, they will move above their opponent on the ladder, shifting the opponent, and all competitors ranked between the 2 competitors, down 1 position on the ladder.
Leapfrog Options
Leapfrog challenge limit: If enabled, this option limits the players that a competitor can challenge to the configured number of positions on the ladder above them. Competitors can still arrange matches and record results with anyone on the ladder, but only results against opponents who are less than, or equal to, the configured number of positions above them will affect their ranking on the ladder.
Swiss Table Tennis ELO Ranking
The Swiss Table Tennis ELO ranking system is used by the Swiss Table Tennis Association to rank players. The calculation for this ELO ranking system is simpler than that used by the Slappy ELO ranking system. Although the ranking system was developed for table tennis, it can be used with any sport in Slappy if you would prefer an easier to understand ELO ranking system. It does however have the following drawbacks, when compared to the Slappy ELO system:
- There is no concept of ranking confidence. New ladder competitors' results will therefore have an exaggerated effect on other competitors' ranking points.
- The system only takes into account who won/lost a match, and does not consider the margin of a victory.
- There is no way to account for inactive players. Unlike the Slappy ELO ranking system, where inactive players' ranking points will gradually decrease over time, players using this system will remain at the same ranking points until they play again.
Each competitor is allocated points based on their performance. Competitors with more points are ranked higher than competitors with less points.
When a new competitor joins a ladder, they will be assigned 1500 points. After each recorded match, the competitor's points will be adjusted, taking into consideration the following factors:
- The competitor's points at the time of the match
- The opponent's points at the time of the match
- The number of games played
- Who won the match
Expected Result
This system doesn't have a concept of an expected result, but there is a probability of who will win a match. Given the difference in points between 2 competitors, the probability of each player winning a match can be calculated as follows:
Points Difference = Higher Ranked Competitor's Points - Lower Ranked Competitor's Points
Lower Ranked Competitor's Probability of Winning = 1 / (1 + 10 ^ (Points Difference/200))
Higher Ranked Competitor's Probability of Winning = 1 / (1 + 10 ^ (-Points Difference/200))
The sum of these 2 probabilities will always add up to 1.
So, for example, if 2 competitors, with a points difference of 100 points, play a match, the probabilities of each of them winning are as follows:
Lower Ranked Competitor's Probability of Winning = 1 / (1 + 10 ^ (100/200)) = 1 / (1 + 10 ^ 0.5) = 0.24
Higher Ranked Competitor's Probability of Winning = 1 / (1 + 10 ^ (-100/200)) = 1 / (1 + 10 ^ -0.5) = 0.76
As expected, the higher ranked player has a higher probability of winning the match.
Points Change Calculation
After each match, each competitor's points can change by up to 25 points, depending on the number of games or sets played during the match:
Number of games or sets | Maximum points change |
---|---|
Best of 1 | 5 |
Best of 3 | 10 |
Best of 5 | 15 |
Best of 7 | 20 |
Best of 9 (or more) | 25 |
The winner's points will increase, and the loser's points will decrease by the same amount. The points change is calculated as follows:
Winner's Points Change = Maximum Points Change * (1 - Winner's Probability of Winning (before the match))
Loser's Points Change = - Maximum Points Change * Loser's Probability of Winning (before the match)
Continuing with the above example, if the higher ranked player wins a best of 5 match, the points change will be calculated as follows:
Winner's Points Change = 15 - 15 * 0.76 = 3.60
Loser's Points Change = -15 * 0.24 = -3.60
If the lower ranked player wins the match, the points change will be as follows:
Winner's Points Change = 15 - 15 * 0.24 = 11.40
Loser's Points Change = -15 * 0.24 = -11.40
When comparing competitors, it is possible to view the points changes for each possible result (premium version only).