# French Ladder

The French Ladder is maintained by the French Go Federation. The old system used to have the following characteristics

- Small board games can be taken into account
- Handicap games do not carry the same weighting as even games
- Inaccurate ranks/ratings are handled better through additional iterations of the algorithm. This is only handled by rank reset in GoR, but rank reset is forbidden by some countries.

This is no longer the case, and now there is instead used the GoR system with modifications of the internal parameters for ratings.

## Description of the Old System

NB = White's level in the ladder (100..199 = 2d, 0..99 = 1d, -100..-1 = 1k) NN = Black's level in the ladder H = Number of handicap stones (H = 1 for an 'even game' with komi of 0.5)

NFB = Effective level of White = NB White's level in the ladder NFN = Effective level of Black = NN Black's level in the ladder (if the game is even) = NN + 100*(H - 0.5) otherwise.

NFG = Effective level of the winner NFP = Effective level of the loser

## Stage 1 - basic change

The basic change in the level of the winner is 15 + (NFP-NFG)/15 limited to an interval of (1 .. 40). The basic change of the loser is opposite to that of the winner, but limited to the interval (-15 .. -1)

If the winner has a level above 400, the basic change in his level is limited to the interval (0 .. 40).

If the loser has a level below -2000, the basic change in their level is limited to the interval (-1 .. 0)

The basic change in the level of a player whose level is above or equal to -2000 against a player whose level is below -2000 is limited to the interval (-1 .. 1).

## Stage 2 - Handicap Games

The changes calculated from step 1 are multiplied by 1 - H/10 for the 2 players. Games with handicap above 9 stones do not count. For players whose level is less than -2000, conversion rate is 1 with no regard to the handicap

## Stage 3: 9x9 and 13x13 games

The changes calculated in stage 2 are multiplied by 0.2 for 13x13 or 0.1 for 9x9. Games other than 19x19, 13x13 or 9x9 do not count.(A table for conversion of handicaps on smallboards is on HandicapForSmallerBoardSizes)

For players whose level is below 2000, conversion rate is 1 with no regard to the Goban size.

## Stage 4: Rapid Games

Games with time of one hour per player and byo-yomi of 5 minutes for 15 stones count normally with a coefficient of 1. For games more rapid, but with a time minimum time of 30 minutes per player, the change as calculated in stage 3, is multiplied by 0.5 for the two players. Games faster than 30 minutes for each player do not count toward the ladder.

## Stage 5: weight as a function of level

The changes calculated in Stage 4 are multiplied by 1 - N/1000, limited to an interval (0,1 .. 2,5) for each of the two players, with N =NB for white and N = NN for black. Finally the new level NB and NR are calcualted as the sum of the old levels and the changes, and used for the next round of the tournament.

## Stage 6: Barrier

Where the level calculated at the end of stage descends beneath -2950 then it remains at -2950.

# Special Cases

Two cases deserve particular attention

- Players who are unknown to the ladder. Their initial level is their entry level in the tournament (1D = 50, 1k=-50). However, if after the calculations in 1 to 6 of all their games, the change in the player's level is above 50 points in absolute terms 1/2 a stone, the registration level is considered incorrect, we proceed to adjust it.
- Known players who have progressed (or regressed) a lot. It is a case typical with beginners, oh those who do not participate in tournaments for a long time. As with unknown players , if the calculations show significant change, we proceed to make an adjustment. For that the threshold is fixed at 100.

The adjustment algorithm: A complete calculation is made. Then, for all the players in the change who exceed the threshold (50 or 100), the level is corrected by delta-threshold. The algorithm is repeated until convergence where the change is less than 10. In both cases, the adjustments allow the opponents of the players not to penalised.