playBunny: By agreeing one.

Putting Abigail's explanation of why a win and a loss is not equal a different way (for those who see 0 q, p r s and find their eyes glazing over and their mind going blank, lol): The points per game is based on the difference between the two players' ratings. After the first game that distance will have changed and thus the second game will be worth a different amount.

The backgammon formula gives a match a maximum value equal to the square root of the match length. Whether that's the "correct" function to use or not, it makes sense that longer matches earn more beans; more effort/risk, more reward/loss.

I've often been puzzled by this one. I've seen it in player's profiles at Vog but not been able to retrieve any match from the archive. How can you have a draw in backgammon?

AbigailII: Where's this bank that gives 10% interest? Please tell!

because it enables you to create staged handicap challenges
in those gametypes with one clearly advantaged colour ... ... ~*~

alanback: think I have noticed that a 3-wins match counts the same as a single game win -- is that correct? Seems like it should count for more.

Why should it count for more? Is a 2-1 win, with 15 draws a bigger win than a 1-0 win with no draws?

Hrqls: as those matches are calculated as a draw i would expect 2 games with the same player, directly after another, win and loss, have the same result as the 2 game match which was a draw

No, that's not what I expect. There is a difference between two one-game matches, and a single two game match, and that's the fact that in with the two matches, there's a rating adjustment after the first match, and unless there was no rating adjustment, the ratings of the opponents at the start of the second match differ from the ratings of the opponents at the start of the first.

Compare it to interest on a bank account. Say you have an account that gives 10% of interest a year, you have $1000 on that account - and you keep the money in the account for two years. How much interest have you made in those two years? $200? (10%/year of $1000 for 2 years) Or $210? (10% of $1000 for the first year, 10% of $1100 for the second year). Or even $215.50 (interest added every 6 months)?

alanback: you noticed right ... but why
change ? else a match would make no difference ?
appointing amount of points/games provides liberty ... . ~*~

Hrqls: I think I have noticed that a 3-wins match counts the same as a single game win -- is that correct? Seems like it should count for more.

AbigailII: *nod* thats how i expected it to work when i first paid attention to the ratings

but when you compare that to a 2 game match in which both players win 1 game .. its a (one) draw .. while in the rating system it should be actually be a slight loss of bkr for the player who won first, and a slight gain in bkr for the player who won the last game

as those matches are calculated as a draw i would expect 2 games with the same player, directly after another, win and loss, have the same result as the 2 game match which was a draw (although the change in bkr might be slightly less because the match is calculated as 1 event and the 2 games in the other case are calculated as 2 events

unlike the players who play on draw.
(lil poem) ~*~

grenv: Yes, it's a flaw. I was describing the situation how it should be.

AbigailII: Actually I have noticed that a win-loss against the same player is a net gain for both players in certain circumstances. This does seem like a flaw in the system.

Hrqls: shouldnt a win + a loss equal out to a draw

No. A win followed by a loss is slightly worse than two draws, while a loss followed by a win is slightly better. It's easiest to see when you have two players with equal rating, and an equal number of games played. Assume their current ratings to be R. Then a win will give an increase of r points, a loss will give a decrease of r points, will a draw doesn't change the ratings. So, after drawing the first game, it's still r points change for a win/loss, and no difference with a draw. With two draws, both players still have rating R. But what if player A wins the first game? Then her rating will be R + r, while player B's rating will be R - r. So, the expected change in rating for player A for the second game will be an increase of p for a win, a decrease of s for a loss, and a decrease of q for a draw, with 0 < q, p < r < s. So, if player A wins, then loses, his rating will be R + r - s < R. And player B, who first loses, then wins, will end up with a rating higher than R.

A win and a loss will be equivalent to two draws only if the rating is calculated after the entire match - but not if you calculate ratings after each result (which is what happens on Brainking).

pros indeed trim timing of resign according to the little difference ... ~*~

what i find funny about the formula used right now is that when you win and then lose to the smae player, both you as well as your opponent will have a net gain in BKR

(of course your opponent has to be within 400 points of your bkr, and sometimes it doesnt show as the net gain can be less than 1, but you will see if clearly when you arent established yet)

shouldnt a win + a loss equal out to a draw ?

WhiteTower: The DG formula seems to work more smoothly, if nothing else. It's supposed to be the same as FIBS.

Dailygammon Ratings

Is the formula there better or not?

AbigailII: That's filled a gap. I'm not a chess player and only read as much of that Chess Rating link's info as needed to work out how my provisional ratings were being generated, and to note how much more complicated their scheme is than that in backgammon! Now that you mention matches I've reread that page and seen where match length comes into it. Thanks Abigail :-)

whoo hoo. 30 - 40 would have made it worth an objection
still the same dimension thus and not at all touching
the core of the sense. checked a year ago last time btw ... ~*~

danoschek: 21 players are within 400 points of you in small pente

which has no impact in backgammon - some game types aren't that crowded ...
in small pente I am so far ahead, there are only 3-4 players within 400 points
- still I bother to play for a team to be available sometimes after all ... ~*~

playBunny: In chess I believe you play only single games and each game is worth 1 or 1/2 a point whereas in backgammon there are matches worth multiple points.

It's not as simple as that. The chess rating system works just fine over longer matches - in fact, it works even better. If the real rating of two players would be known, one could calculate by which margin a player would win (or lose). For instance, a rating may predict that one player would win 65% of the games. Obviously, this would never be possible in a single game (the score being one of 0%, 50% or 100%), but in a 10 game match, it certainly is possible to get 65%, or at least get closer to it than 50%. In chess, if players play a match of more than one game, or even a complete tournament, ratings aren't adjusted game-by-game, but the result of the entire match or tournament is used. So, if you play a match or tournament, and according to your rating, you should score 58%, but you only scored 45%, your rating will drop.

alanback: absolutely correct. a diligent player (stable rating)
won't lose more than 8 points to an opponent withing the 400 points range ... ~*~

The chess formula is based on single games where skill is the only factor. A player deemed better than another is expected to win by skill alone and the gains from winning are meagre and the losses from losing are punitive for the better player when the difference between them are large.

In the chess formula, a rating difference of 400 points favours the expert who is expected to win 9/10ths of their games against the average player. In the backgammon formula, the effect of luck is such that experts (500 higher than average) are expected to lose in the region of a third(!) of games against an average player. The losses and gains are much less per match to account for this luck effect.

In chess I believe you play only single games and each game is worth 1 or 1/2 a point whereas in backgammon there are matches worth multiple points. Though the expert backgammon player is expected to win only 2/3s of their single games against an expert, in an 7-point match that goes up to around 80%. So an expert is expected to win a decent length match but the chances of the beginner's lucky win are by no means negligible.

Chess maxes out at 2700 or something, with backgammon 2200 is unusual.

More info:
The US chess formula

Rating calculator for backgammon
Complicated looking but also informative.

Press the [Newbie] button (it uses 1600, not 1500) and the [500] button and look at the percentages in the first table to see that the expert, P2, should only win 64% of single games but 82.1% of 7-point matches and 90.3% of the 25-pointers.

grenv: Your observation seems to be correct as long as the opponent is within 400 points of your rating. If the difference is greater than 400 points, then you will be penalized heavily for losing while gaining very little if you win. This is why I try to limit my opponents to those within 400 points of my rating.

Mike UK: I've always been concerned by the fact that after a while I tend to just go up or down 8 when I win or lose.

The problem here is that if I am even a little above average and win, say, 55% of my games, I will eventually move my rating up as I play a lot of games.

What is wrong with my reasoning here?

alanback: I think the underlying theory is similar in both systems, but in practice they behave very differently. First of all the parameters in the USCF formulae are set up for chess and are not suitable for games like gammon where luck plays such an important role. Secondly the provisional formulae are designed to allow a relatively small number of new entrants to quickly reach their correct rating in a large established pool of players. When applied to a startup situation they just introduce a random element. Similarly the formulae for established players only work in a mature rating system. So even for chess, the rating distribtions here are nothing like those of the USCF itself. You only have to look at the number of players here who achieve the rating ceiling of 2700 to see this. At times it seems that ratings are just proportional to number of games played.

As you know in FIBS everyone starts at 1500 and have to work their way up (or down) the ratings over the course of at least 400 games. Because of this, nobody gets a high rating by luck. By the very nature of gammon, it is impossible to try and get to a realistic rating playing less games than this.

The USCF itself uses a different rating system for correspondence chess which I believe is a lot like the FIBS system. I think this would be the obvious one to use at a site like this for chess and the other games. Again probably without the provisional formulae.

Mike UK: Do you understand the two rating systems well enough to explain the differences? I thought they were basically the same, but clearly they are not.

I don't really have a problem with players deciding to rest on their laurels. The problem is that their ratings are unrealistic to begin with. As has been said many times before, the rating system here is not suitable to the gammons. FIBS works well at dailygammon and GT. It is a simple formula so why can't we implement it here. If someone leaves with a high FIBS rating at least you know they earned it.

aware of all those normal and self-declaredly reasonable default characters ... ~*~

danoschek: Thanks for pointing that out, I can hide that crazy German character now ;-)

for the hide function protecting me from the sillliest ideas after all ... ... ~*~

Luke Skywalker: ah yes :) i forgot .. thanks :)

Hrqls: half-life (german: Halbwertszeit)

grenv: hmm .. nice idea! .. a half-time (dont know the english term, in dutch its 'halfwaarde') like in radioactivity :)

alanback: The problem is that building this into the formula doesn't have any effect on those that choose not to play at all.

If there was some way to penalize not playing, perhaps some sort of natural decay could be built in to the rating.

Alternatively just remove players who don't either start or finish a game in a set period (I suggest 3 months). If they play again after that they get a provisional rating again.

playBunny: The observation I referred to was statistical -- I can't prove it, but the point was that any history more than 400 experience points old had little effect on your rating -- I think we have all experienced how ratings can swing. If you've been winning recently, your rating is relatively high; if you've been losing, relatively low; it doesn't matter much what it was this time last year. This is different from the 400 points needed to get past the "newbie" factor, of which I am also aware.

should be only an additional value - why punish serious players who play continuously ?
irrigardlessly a penalty rating for inactive players seems reasonable after a while,
let's say 100 down after 3 months not giving a flying stuff at challenges ... ~*~

alanback: FIBS uses a backgammon formula which is used on many sites. Like the chess formula that is used here, it encapsulates the entire playing history. The 400 figure that you're remembering is used when a new player is establishing their rating. For the first 400 experience points the amount gained or lost by a match is multiplied by a number proportional to how many of the 400 points are left. The multiple is 5 at the start and 1 by the time the player has reached 400.

I also don't care to see the same 6/0/0 at the top of the rankings table. Perhaps the cocktail has lost his bottle? I like pgt's suggestion of using a limited history but it might be expensive to administer. A reasonably easy to write method would be that the ratings are recalculated every day for every player (and presumably for every game type). I don't know how much server time that would take but it would certainly be a growing amount as the site gains in popularity. Doing it monthly would be a reasonable compromise; a different set of players could be done on each day of the month.

bumble: ah nice! it will be fun i guess :)

Hrqls: There have been long conversations about ladders on Features and other boards.

Ladders will be implemented at a later date.

what about ladders ?

each player holds a position on a ladder, lower players can challenge higher players, they have to accept (or drop a bit on the ladder) ... the outcome of the game (if accepted) calculates the new ladder position for both players

it would introduce a new system next to the bkr .. and i am not sure if fencer likes this ... but it sounds interesting

in active players would drop because they dont accept the challenges

of course this will be tough for the top player because he will receive a lot of challenges which he might not be able to accept (because a person can only play a limited amount of games during a certain time)

pgt: Certainly worth considering. For those of us with paid subscriptions, it would not be a hardship; but Pawns who play a lot of different game types might find it hard to keep up.

alanback: You need to read to the original post on the subject - the peeve concerned players achieving a high rating and then refusing invitations to continue playing. Hence the "elapsed time" suggestion.

pgt: I've heard it said that on FIBS, your rating is pretty much determined by your most recent 400 experience points anyway. So, why not base ratings on that?

pgt: That is an interesting idea I have not heard before, and it seems like it could be an good idea. Will have to think about that some more.

BIG BAD WOLF: Why not change the ranking so that only games completed in the last 6 (or maybe 12) months are included in the rankings - then we would get a better idea of current form, scores gained "learning" games would eventually be eliminated, and the peeve would eventually disappear. (anybody without sufficient completed games in the chosen period could revert to a provisional rsnking)

bumble: Yea, Fencer talked about it - not sure how high it is on his list. Something like removed from the ranking list after 2 months (Pawn) or 3-4 months (Knight & above) - or something like. Of course play one game, and back on there - but at least keeps the player active a little bit.

alanback: I'm sure I read on another board that Fencer is addressing that problem and that something along the lines of what you suggest is to be implemented.

My pet peeve on this site is players who achieve a ridiculously high rating in just a few games (I still don't understand how the rating system allows that to happen) and then just sit there refusing to play more games. I have had a challenge outstanding with the #1 ranked nackgammon player for months with no response. He is not obligated to play me, but I think he should be obligated to play someone and defend his position. A very high rating based on a limited number of games is not an accurate indicator of ability in any case. Some system should be devised to prevent players from sitting forever at the top of the ratings without playing. Perhaps they could be moved back into provisional status if they don't finish a game in a given timespan (such as two months).