How ratings work

The short version

Everyone starts at 1500, give or take 350. The 1500 is the rating. The 350 is the deviation, which is the ladder saying it has no idea yet. Play, and the rating settles towards where your results say it belongs while the deviation closes in around it.

Two things decide how far a result moves you: how much was riding on it, and how well the two of you were already known. Beating somebody nobody has the measure of yet says almost nothing. Beating a well established player, especially a higher rated one, says a great deal.

The ladder is not a running total that gets nudged after each game. Every rating in the club is solved for at once, against every result at once. It is a Glicko-2 system, the same family of maths the chess and backgammon servers moved to, fitted rather than updated because a club this size can afford to do it properly.

Where the number starts

Every player is created at 1500 with a deviation of 350 the first time they appear in a recorded result. There is no seeding, no self-assessment, no starting bonus for anyone. A 1500 rating means "we have no idea yet", not "average club player", and the 350 next to it is the part that says so out loud.

Nothing is stored as a running total. The whole ladder is rebuilt from the complete list of results every time the Club page loads. That has a useful consequence: if a result was entered wrong and later corrected or deleted, the board that comes back is the board that would have existed if the mistake had never been made. There is no scar and no drift. History is never stuck.

How the ladder is worked out

The ladder asks one question of the whole club at once: what set of ratings would make the results we actually have the least surprising? It starts from the belief that everybody is 1500 give or take 350, adds every recorded result as evidence, and then moves everybody, over and over, until nobody wants to move any further. That settling point is the ladder.

Written out, on Glicko-2's internal scale:

Four things fall out of that, and they are the whole character of the system:

• The t term sits on the deviation and nowhere near the rating. Playing the same person over and over still moves your number by exactly what it always did. It just stops buying the certainty it used to buy, because the tenth game against one opponent is not a tenth reading of where you sit in the club.
• It is not zero sum, and it is not trying to be. The winner's gain and the loser's drop are worked out separately, from what each of them has done against everybody else, so they are rarely the same size. What the fit balances is not points, it is plausibility.
• A result against somebody the ladder has not pinned down yet is worth less, in both directions. That is the g term, and it is the difference between Glicko and plain Elo. Beating a stranger cannot make you, and losing to one cannot break you.
• Order does not matter to the ratings. The same set of results produces the same ladder whatever sequence they were played in, because nothing is applied in turn. The dates still matter for who is in the Club and who has been away, but not for the number itself.

The deviation, and why it moves

The deviation is how far out the ladder thinks the rating could be. It opens at 350, it never falls below 30, and it is printed next to the rating on every board because a rating without it is half a sentence.

Playing brings it down, and who you play decides how fast. Here is a player splitting their results evenly against well established opponents, so the rating stays put at 1500 and only the certainty changes. The same games, twice: once all against the same person, and once against somebody different each time.

Why the two columns differ

A first meeting tells the club where you stand in it. The twentieth against the same person tells it something much narrower: it firms up what you do against them, and it has already heard that. Counting all twenty as separate readings is how two people who only ever play each other end up with deviations claiming the club has their measure, when all it really knows is which way that one fixture goes.

So the nth meeting with the same person counts one over the square root of n towards certainty. The second is worth about seven tenths of the first, the fourth a half, the tenth under a third. Nothing ever counts for nothing, because a result is still a result, and every one of them still moves the rating by exactly what it moved before.

This is not a penalty for having a regular opponent. Play the same friend every week and your rating is whatever your results say it is, in full. What the club will not do is claim to be sure of a player it has only ever seen across one board. The way to close a deviation is to play a variety of people, which is the thing worth encouraging anyway.

It has one knock-on, and it is the intended one. A wider deviation makes you a softer reference for everybody who plays you, and it costs a place or two on a board sorted by rating minus a deviation. Nobody loses a single rating point by it.

Time away puts it back. A player who has not sat down since the spring is not as well known as they were in the spring, and this is where the ladder admits it. Starting from a settled deviation of 45:

Only the deviation moves while you are away. The rating itself is exactly where you left it. Nobody loses points for missing a month, they lose the club's confidence, and one night at the board buys most of it straight back.

One last use for it. The ladder is sorted on the rating minus one deviation, not on the rating. Sorting on the raw number lets somebody win three games and sit on top of the club with an estimate nobody believes, including them. Subtracting a deviation asks a fairer question: how good is this player at worst? A hot streak still climbs fast, because winning pulls the rating up and the deviation down at the same time. The number printed is always the rating itself; this only decides the running order. One thing is asked ahead of it, and it is covered under Below the line further down.

Stakes: what L actually is

L is how much the result was worth, and a result counts the square root of L times over in the fit. It is worked out differently for a single game and for a match.

Cube games

A cube game is one game with the doubling cube live. Either player can turn the cube when it is their turn to roll, offering to double what the game is worth; the other either takes it and plays on at the new number, or gives up the game there and then for what the cube already said. Whoever wins collects the cube value, doubled again if it was a gammon and tripled if it was a backgammon.

L is that number: the points that actually changed hands. It is capped at 8, so one wild cube war cannot rewrite the ladder. The result also counts towards gammons delivered and gammons taken on a player profile, as do gammons played inside a match.

Matches

L is simply the match length. A 5 point match is L = 5, a 7 point match is L = 7. There is no cap, because a longer match really is a better measurement: it takes more skill and less luck to win a race to 7 than a race to 1.

The score line inside the match does not matter. A 7-3 win and a 7-6 win are worth the same, exactly as they are on the online servers. Winning the match is the result.

Nor does anything else that happened inside it, as far as the rating is concerned. The cube was turned, somebody was gammoned, and the length already allows for all of it. There is also no such thing here as a match to 1. The only 1 point match in backgammon is the Crawford game at the end of a longer one, and a single game played on its own is a cube game, which is what the Score Card offers and what it files.

Gammons inside a match are still counted, though. They do not touch the rating and they never will, but a gammon is a real thing that happened at the table and it belongs on a player's record. The Score Card keeps a running count for each side as the match goes and files it at the end, the report form asks for it, and the Director can set it by hand on any game. Both players can score them: losing a match 5-3 having gammoned somebody along the way still puts a gammon delivered on your profile.

What a result is worth

Every number below came out of the engine that draws the ladder. This first table is one result on its own, taken from a standing start: what the classical Glicko step does to the winner. The deviation column is the mover's own, before and after.

Look at the last two rows. The same two players, the same match, and the underdog winning is worth five and a half times what the favourite winning is worth. Then look at rows three and four: a regular beating a newcomer gains two thirds of what beating a fellow regular gains, off an identical 50-50 board. Nobody knows what beating the newcomer proves yet.

The second table is the fit doing its actual job. Two players, nothing else in the world, and a run of single games between them. This is not a sum of steps; it is the answer to "what ratings make this record least surprising", worked out in one go.

The last row is the point of the whole thing. Seventy wins in ninety is the same rate as seven in nine, and the fit puts the gap in the same place: about 218 points. What changed is the deviation, 136 against 44. The fit did not become more sure that one player is better. It became more sure of how much better.

And this is why the ladder is fitted rather than updated. Take those same nine games and apply them one at a time, the way a classical rating system would, and you finish 259 points apart. Fit them all at once and you finish 217 apart. Applying results in turn double counts the early ones, because each of them moved a rating that later results are then measured against. The fit measures everything against the answer instead.

Run your own numbers

Set two ratings, two deviations and a stake, and this works out the classical Glicko-2 step for a single result. It is the textbook one-result formula, and it is worth being clear that it is an approximation of what the ladder does rather than the ladder itself: the ladder has no single result to update, it has the whole match list and it solves for everybody at once.

The direction and the rough size are right, which is usually what the question is asking. If you want the exact number for a game between two real club players, the Score Card carries the real engine and works out both outcomes before you start.

Getting into the Club

A rating built on three games is a rumour, not a measurement, and a place in the Club is a thing to be earned rather than collected on the way past. There are two bars, and both have to be cleared:

• Ten recorded results. Games and matches both count.
• Half the Club, rounded up, faced as distinct opponents. Playing the same friendly opponent ten times gets you a record, not a place.

The second one is a goalpost that moves. It is measured against the Club as it stands on the night, so joining gets harder as the club gets bigger, and the standard nobody had to meet on opening night is not the standard forever:

Until both bars are cleared a player sits on the Provisional board, which is sorted by how close they are rather than by rating, because how many more nights it will take is the thing a newcomer actually wants to know.

The rating is completely real the whole time. It is worked out by the same fit from the first game onward and it counts in full for the opponent. Joining changes nobody's number, including yours: the whole ladder is refitted from every result on every load, so your rating was never waiting on your membership. What changes on the night you join is which board you appear on, and that the bar quietly rises for everybody still climbing.

Below the line

Not everybody on the Club board arrived by climbing. The founding members were members before a die was thrown, which is right, because somebody had to be the club, and the Director can name a member outright. That is a fine way to become a member and a poor way to earn a rating. Ten games and a spread of opponents is the bar everyone else clears, and it is the bar that makes a number worth reading.

So the Club board asks it of everybody. A member who has not yet played ten games, or has not yet faced their share of the Club, is drawn below a line, under the members who have. Above the line and below it the order is the same as it always was, rating minus one deviation. The line only says which of the two groups you are sorted within.

Nobody loses anything by it. It is a running order and not a demotion: membership is untouched, the rating is untouched, the count of members that sets the bar for everybody climbing is untouched, and the way out is the thing the club wanted anyway. Play, and play a variety of people. Because both halves of the bar are cleared at once, the game that clears it is usually the largest single move anybody makes on this board, which is deliberate.

Time away

Forty five days without a result and a player is set aside on the Inactive board. Nothing is lost. Every game, every rating and every step of progress is exactly where it was, and one result puts them straight back where they left off.

A hundred and eighty days and a Club member lets their place go. This is not a punishment and it is not meant to read like one. It is what keeps the rest of the ladder honest: a member who has not played since last spring still counts towards the club size, and therefore still raises the bar every newcomer has to clear, which would have the club getting harder to join in exact proportion to how many people had stopped turning up.

Coming back is not starting again. Three results back at the board and the place is theirs, so somebody returning after a year is a member again inside a fortnight rather than back at the bottom of the climb. The rating they come back to is the rating they left with.

What the rating is not

• It is not a count of wins. Ten wins against the same beatable opponent is worth less than two against the top of the ladder. The Record column is there if you want the raw tally.
• It is not comparable to an online server rating. Same shape of maths, completely different pool of players. A 1600 here means 1600 among this group and nothing more.
• It is not a judgement of how well you played. Backgammon has dice in it. Over a handful of games the rating is mostly noise, and over a hundred it is a decent read. That is why we keep recording them.
• It is not a settled fact, and the deviation printed beside it is the ladder saying so. A 1650 give or take 40 and a 1650 give or take 200 are two very different claims.
• It does not decay. Take three months off and the number is the number you left with. What fades is the club's confidence in it, not the value.