The Palmetto Region ranking system is based on ELO method. This system is used to generate chess rankings, by Jeff Sagarin as part of college football’s BCS, the World Football League (soccer), and the FIFA (soccer) Women’s rankings, among others.

Fundamentally, each team starts with a rating. The system then predicts a statistical likelihood of a team winning or losing a given match based on each team’s rating. For example:

- Team A has a rating of 2000
- Team B has a rating of 1900
- Team C has a rating of 1600
- Team D has a rating of 1000

Team A is expected to beat Team B, because it has a higher rating. However, the system understands that it won’t happen every time. The difference in the ratings represents how likely (the probability) that Team A is expected to beat Team B. In this example:

- Team A is expected to beat team B 64% of the time
- Team A is expected to beat team C 90% of the time
- Team A is expected to beat team D 99.7% of the time

How this system works is that each rating is then adjusted based on the previous results. So, if team A beats team B, A’s rating goes up a little (2012) and B ‘s goes down a little (1888). If B wins then the results are different, because B wasn’t expected to win, so A’s new rating is 1980, and B’s is 1920.

However, if team A plays team D and wins, then their ratings don’t change much at all because team A is statistically supposed to win almost every time they play. A’s rating moves to 2000.1 and D’s moves to 999.9. If D pulls out a victory the change is much more significant (A => 1968, D => 1031).

It’s also important to note that this system works on sets, not matches. So beating a team 2 out of 3 is not as strong a showing as sweeping a team in 2 sets.

Previously, a team was potentially rewarded (their rating improved) for “playing up,” either club to power or up in age, potentially even if they lose every match they play. In the new system, a team is only rewarded if they actually win sets. A team is also not punished for “taking a shot.” If you play against teams that you are expected to lose against, and you do, your rating does not change too much. If you win, you are rewarded.

Situation | Explanation |
---|---|

Teams playing up (e.g. 16 power playing 17 power) | Rating improves if they win more games than expected, decreases slightly if they lose more than expected. |

Teams playing down (e.g. a weak power team playing club) | Rating improves if they win more games than expected, decreases slightly if they lose more than expected. |

End of season effect | Matches at the end of the season can count more than those at the beginning, if performance differs from expectations. |

Out of region tournaments | Out of region tournament results are only counted for Palmetto Region teams playing head to head in out of region tournaments. Results must be submitted by club directors the Wednesday following the event. |

Tournament size | Tournament size is not relevant to the rankings |

Tiebreakers | Teams that win tiebreakers based on net points see no benefits to their rankings |

Strong or weak pools | No effect. Rankings are changed on performance vs. expectation, not order of finish. Note: Strong or weak pools can result from either poor seeding or general strength of teams at the tournament. |

Teams not playing enough region tournaments | Not playing in sufficient tournaments will cause you to be rated more towards the region average than an extreme. Every team’s ranking starts at the average. Continuing to perform better than expected is necessary to continue to increase you rankings. |

The mathematical explanation of the system follows.

Initial Ratings

Teams are assigned an initial rating based upon their division as follows.

- Probability_TeamA_wins_Set = [1/(1+(10^-((TeamA-TeamB)/400))) ]
- ExpectedTeamAWins = Probability_TeamA_wins_Set * NumberOfSets
**An example:**Suppose Team A has an initial rating of 1800 and Team B has an initial rating of 1750 and Team A beats Team B 2-1 (a 3 game match):- Probability_TeamA_wins_Set = [1/(1+(10^-((TeamA-TeamB)/400))) ] = 57.1%
- ExpectedTeamAWins = 57.1% * 3 = 1.71
- Team_A_NewRating = 1800 + (2 – 1.71) * 32 = 1804.6
- Team_B_NewRating = 1800 + (1 – 1.29) * 32 = 1745.4

- Note that the teams’ ratings always change by the same amount. The table below shows how ratings relate to probability of winning:

18Power | 3000 |

17Power | 2800 |

16Power | 2600 |

15Power | 2400 |

14Power | 2200 |

13Power | 2000 |

12Power | 1800 |

18Club | 2600 |

17Club | 2400 |

16Club | 2200 |

15Club | 2000 |

14Club | 1800 |

13Club | 1600 |

12Club | 1400 |

The team is assigned an initial rating based on how many tournaments in each division that they register.

For example, if a team registers for two 15 Power and two 15 Club tournament, their initial rating will be:

[(2 * 2400) + (2 * 2000) ] / 4 = 2200.

When two teams play, each match is treated separately. The number of wins each team is expected to achieve is calculated and each team’s rating is adjusted up or down, depending on whether they win more or less games in the match according to the following formulas.

- TeamA_New_Rating= TeamA_Old_Rating + (ActualWins – ExpectedWins) * 32 points
- TeamB_New_Rating= TeamB_Old_Rating + (ActualWins – ExpectedWins)* 32 points

For playoffs, multiply by 16 instead of 32 in each formula

The expected wins formula is calculated based upon the ratings:

18Power | 3000 |

17Power | 2800 |

16Power | 2600 |

15Power | 2400 |

14Power | 2200 |

13Power | 2000 |

12Power | 1800 |

18Club | 2600 |

17Club | 2400 |

16Club | 2200 |

15Club | 2000 |

14Club | 1800 |

13Club | 1600 |

12Club | 1400 |

The expected wins formula is calculated based upon the ratings:

- Probability_TeamA_wins_Set = [1/(1+(10^-((TeamA-TeamB)/400))) ]
- ExpectedTeamAWins = Probability_TeamA_wins_Set * NumberOfSets
**An example:**Suppose Team A has an initial rating of 1800 and Team B has an initial rating of 1750 and Team A beats Team B 2-1 (a 3 game match):- Probability_TeamA_wins_Set = [1/(1+(10^-((TeamA-TeamB)/400))) ] = 57.1%
- ExpectedTeamAWins = 57.1% * 3 = 1.71
- Team_A_NewRating = 1800 + (2 – 1.71) * 32 = 1804.6
- Team_B_NewRating = 1800 + (1 – 1.29) * 32 = 1745.4

- Note that the teams’ ratings always change by the same amount. The table below shows how ratings relate to probability of winning:

Your Rating – Opponent Rating | Probability that you should win |
---|---|

400 | 0.91 |

300 | 0.85 |

200 | 0.76 |

150 | 0.7 |

100 | 0.64 |

50 | 0.57 |

0 | 0.5 |