GRADING ANOMALIES

[Roger de Coverly]

the 40 point rule which "over rewards" the really top players if they play opposition well below their standard.

Just a follow up on this.

Player (a) 130 rated but a playing standard of 160
Player (b) 160 rated and a playing standard of 160
Player (c) 110 rated and a playing standard of 110

Grading points for (a) beating (c) is 160
Points for (b) beating (c) is 170 ( 40 point rule)
So the 40 point rule gives (b) compensation for the loss of points when (a) draws with him.

[Robert Jurjevic]

Roger, thanks for your reply and my apologise for a bit sharper tone in my previous post, it was me losing my temper.

As I said before, this is an effect which has been known about for around 40 years and in effect mechanisms exist which compensate for it.

With all due respect, may I ask if this effect which needs a mechanism to compensate for, "the lighthouse" effect, etc., might in fact be the clues that something is wrong in the current grading system?

I would also say that diluting the 160 pool to 159 is deflation not stretch because exactly the same effect will apply between the FMs at 200 and the GMs at 230. So the distance between GMs and "160s" remains unchanged but the whole distribution moves down a point.

It is in my opinion stretching in a sense that the grades between the 130 player and the pool have now drifted apart for 1 grading point when in fact they should have been the same. So it may seem that the gap between the pool and the GMs stretched for 1 point, and the gap between the pool and the weaker players shrank for 1 point, but as the stretching may occur in all grade classes, and need not to be the same, it is not easy to asses the overall effect on stretching using this particular example.

I used this example more for an attempt to find a sound logical explanation for abandoning the "equal grade for equal performance" rule in favour of a system which does not shrink nor stretch the grades, as it seems that the two are mutually exclusive (if you obey the rule you stretch the grades and if you do not stretch nor shrink the grades you do not obey the rule). One of the examples which shows how big the effect of stretching can be is given in Factors 'k' and grade stretching section at...

http://www.ecforum.org.uk/viewtopic.php ... 149#p10149

http://www.jurjevic.org.uk/chess/grade/ ... malies.htm

I would further say that there are other ways of getting from 130 to 160 than scoring 50% against the 160s. You could also score much better than 50% against the 130s thereby diluting them down to 129. You could do much better than 75% against 105s.

Yes, but in all these cases '(a2 - a) + (b - b2)' would be equal to '2*(q - p)' rather than to '(q - p)', i.e., the sum of the grade corrections would be twice the grade difference rather than the grade difference, i.e., new grades would drift apart.

We are talking about a model in which most players do not change standard much and trying to reduce rating lag for those that do.

Taking the issue in its simplest form, the difference between GS (current grading system) and AGS3 (the closest grading system to the current one which does not shrink nor stretches the grades) is in the rule:

GS:

Rule 1a: For a win you score your opponent's grade plus 50; for a draw, your opponent's grade; and for a loss, your opponent's grade minus 50. Note that, if your opponent's grade differs from yours by more than 40 points, it is taken to be exactly not 40 points above (or below) yours. At the end of the season an average of points-per-game is taken, and that is your new grade.

AGS3:

Rule 2b: For a win you score average grade plus 25; for a draw, average grade; and for a loss, average grade minus 25. Average grade is half of the sum of your and your opponent's grade. Note that, if your opponent's grade differs from yours by more than 40 points, it is taken to be exactly 40 points above (or below) yours. At the end of the season an average of points-per-game is taken, and that is your new grade.

[Roger de Coverly]

Rule 1a: For a win you score your opponent's grade plus 50; for a draw, your opponent's grade; and for a loss, your opponent's grade minus 50. Note that, if your opponent's grade differs from yours by more than 40 points, it is taken to be exactly not 40 points above (or below) yours. At the end of the season an average of points-per-game is taken, and that is your new grade.

AGS3:

Rule 2b: For a win you score average grade plus 25; for a draw, average grade; and for a loss, average grade minus 25. Average grade is half of the sum of your and your opponent's grade. Note that, if your opponent's grade differs from yours by more than 40 points, it is taken to be exactly 40 points above (or below) yours. At the end of the season an average of points-per-game is taken, and that is your new grade.

Two problems with AGS3

(1) why do want to increase grading lag? Simple example -- you only play players of your own grade, but you win nearly every game. On AGS3 you cannot go up by more than 25 points. On EGS you can go up by up to 50 points.
(2) how do you estimate new players? - you need to estimate their grade to work out their grading performance so you are looping on yourself.

[Robert Jurjevic]

(1) why do want to increase grading lag? Simple example -- you only play players of your own grade, but you win nearly every game. On AGS3 you cannot go up by more than 25 points. On GS you can go up by up to 50 points.

There are two extreme cases:

1) your grade goes up by 50 grading points and the grade of your opponents remains unchanged; you improved (say you've been coached by Kasparov during the summer break before the start of the season) and your opponents neither improved nor worsen,

2) your grade remains unchanged and the grade of your opponents goes down by 50 grading points on average; you neither improved nor worsen and all of your opponents worsen (say your opponents were all young men each of which has fallen in love on his summer break and they simply played poorly in all of their games as all they were thinking of were their girlfriends).

AGS3 will take a middle approach (between the to extreme cases above):

3) your grade goes up by 25 grading points and the grade of your opponents goes down by 25 grading points on average; you improved a bit (say you've been coached by an IM during the summer break before the start of the season) and your opponents worsen a bit (say your opponents were all young men each of which has fallen in love on his summer break and they played not so well in all of their games as they were thinking about their girlfriends).

Important thing is that the difference between your new grade and a new grade of the pool is exactly 50 grading points, as otherwise the system would stretch or shrink the grades.

AGS3 does this automatically, the grade difference will be exactly 50 grading points .

In case 1 above (your grade goes up by 50 grading points and the grade of your opponents remains unchanged) if using GS, in order to ensure the grade difference of 50 grading points, when calculating the grades of your opponents, you would have to omit from grading every single game the players played against you, as if you do not do that (assuming that the pool players played only against you and that each of them played 30 games) the pool grade would go down by 50 grading points on average, and you would stretch the grades (between you and the pool) for 50 grading points (which would be a huge grade stretch).

Note that GS (in the above example) gives the pool players some sort of special status (like saying they are the members of the pool). But there might exist another player, say me, who was playing another pool of players, one of which were you, and I might say, because you are in the pool, when I calculate the grades in our game I will assume that grade correction should be done on the basis that you neither improved nor worsen (as you are in the pool) and that I either improved or worsen (depending on the game results and our grades), which is in a sense wrong, as at the of the day this decision should depend on the facts such as have you or me recently got a girlfriend or have you or me recently being coached by a strong chess player, etc., and not if one of us has been (more or less arbitrarily) put in a pool of players.

AGS3 does not try to guess if you or me have got a girlfriend, if you or me have being coached, but rather assumes that we both equally contributed to the difference in expected and actual performance, i.e., either you improved a bit and I worsen a bit or either you worsen a bit and I improved a bit (depending on the game result and our grades).

(2) how do you estimate new players? - you need to estimate their grade to work out their grading performance so you are looping on yourself.

You estimate the grades of ungraded players as now, by assessing their grades based on the sample games they have played against graded chess club colleagues.

Please note that in ÉGS6 ungraded players automatically (implemented in formulae) do not affect the grades of graded players while the estimated grades of ungraded players change for the maximum possible amount. ÉGS6 also does this adjustments automatically if less active players (say players who played 2 games in the last season) play more active players (say players who played 60 games in the last season). ÉGS6 does not stretch the grades.

[Roger de Coverly]

your grade goes up by 50 grading points and the grade of your opponents remains unchanged; you improved (say you've been coached by Kasparov during the summer break before the start of the season) and your opponents neither improved nor worsen,

I've seen it happen. Future GM Matthew Sadler was 170ish one season and playing in the middle of the Kent team. The next season he was approaching 220 and playing board 1.

If he had been giving a grade of 195, this would have seriously lagged against his true strength. So players improving by 50 points in a year is not an extreme case. It's rare (and difficult) to get from 170 to 220 in a year. 70 to 120 ought not to be such a problem. Under rated players (particularly juniors) cause enough difficulties as it is without doubling the lag effect.

In every one of my examples, I am assuming that perhaps 1 player in 20 shows a dramatic improvement, so 1 player's grade should change and the others stay virtually unaltered.

your grade goes up by 25 grading points and the grade of your opponents goes down by 25 grading points on average;

No - you play 30 people and take about a point off each of them. In fact as you are now nearly 50 points better than each of them (because you can score almost 100% against them), you are undergraded in your system by about 25 points. If you played the same person 30 times, then they would lose 25 and you gain 25. But that should not be the model. It's 30 different people.

You estimate the grades of ungraded players as now, by assessing their grade based on the sample games they have played against graded chess club colleagues.

So how exactly? Do you add up the grades of the opposition add 50 * the excess of wins over losses and divide by the number of games?

[Robert Jurjevic]

your grade goes up by 50 grading points and the grade of your opponents remains unchanged; you improved (say you've been coached by Kasparov during the summer break before the start of the season) and your opponents neither improved nor worsen,

In every one of my examples, I am assuming that perhaps 1 player in 20 shows a dramatic improvement, so 1 player's grade should change and the others stay virtually unaltered.

You have to make a decision on how much to change each player's grade for every individual game, of all games how do you identify the games with the players who made a dramatic improvement, in each game how do you make a decision who improved and who worsened, and for how much, do you take care that '(a2 - a) + (b - b2)' is equal to 'q - p' for every individual game, if yes how do you do that?

your grade goes up by 25 grading points and the grade of your opponents goes down by 25 grading points on average;

No - you play 30 people and take about a point off each of them. In fact as you are now nearly 50 points better than each of them (because you can score almost 100% against them), you are undergraded in your system by about 25 points. If you played the same person 30 times, then they would lose 25 and you gain 25. But that should not be the model. It's 30 different

If during a course of a season two 100 players play a match of 30 games and one of the players scores 100%, according to AGS3, new grades of the payees will be 125 and 75 respectively (note that GS would give here 150 and 50). The same would hold if the player played a pool of 100 players (grade of each player in the pool is 100) assuming he played 30 games against each payer in the pool. Consequently the player's grade rises for 25 points and the pool grade drops for 25 points.

You estimate the grades of ungraded players as now, by assessing their grade based on the sample games they have played against graded chess club colleagues.

So how exactly? Do you add up the grades of the opposition add 50 * the excess of wins over losses and divide by the number of games?

Right, I see your point. Well, then one could use GS for grading ungraded players in the games where they play graded players, omit grading of graded players in the games where they play ungraded players and grade players in all other games using AGS3 (or ÉGS5 or ÉGS6).

[Martyn Harris]

Brian Valentine quoted:
"Chess rating systems have many practical uses. For pairing purposes in tournaments, a tournament director should have some idea which players are considered the most likely candidates to win the tournament so the director can effectively avoid pairing them against each other during the earlier rounds of the tournament. Ratings are also used for tournament sectioning and prize eligibility; a section in a tournament may only allow players of a specified rating range to compete for section prizes. Ratings can also be used as a qualifying system for elite tournaments or events; invitation to compete in the US closed championships and to compete in the us Olympiad team are based in part on players' USCF ratings. The current title systems used by some chess federations base their title qualifications on the overall strength of tournament participants as measured by their ratings. But probably the most useful service of the rating system is that it allows competitors at all levels to monitor their progress as they become better chess players. (from: Rating the Chess Rating System by Glickman and Jones)"

In brief grades are used to resolve questions of eligibilty (entry, seeding, board order, selection), as a basis for calculating opponents grades, and for personal purposes such as tracking progress, target setting and putting individual results into perspective. They are widely regarded as a measure of strength arrived at by assessing performance.

When ECF grades are published each year they are often initially regarded as backward looking, giving official confirmation of players performance over the previous 12 months. Once play starts in the new season however grades are viewed in the present tense - eligibility ideally to be determined by current rather than past strength, grades calculated on the basis of the strength of opponents at the time they were played rather than on some past strength, players being regarded as over- or undergraded according to whether their grade matches their current strength rather than correctly describing their past performance.

Consequently there is a sense in which grades are a prediction of how well players will perform over the coming year. The task we set our graders is "Here are last season's results, how well do you think everyone will do next year?" For the large number of players whose standard has plateaued this is a relatively easy question to answer - the future will look like the past. However we also expect the graders to identify those who will play to a different standard, and by how much. This is pure crystal ball territory. The ECF uses a basic crystal ball which says that all juniors, and only juniors, will improve, and they will do so by an amount which is a function of their age. Inevitably this results in at least some players being ranked in the wrong order, and in time the grading methodology results in errors appearing in the ranking order of other players too. This misordering, which the grading team hopes to have temporarily corrected with their calculations for the new grades, is I suggest of rather more importance than overall deflation. Hence it would be encouraging if those with the skills to do so would direct their attention to improving the crystal ball technology.

Should they regard this as too nebulous a task to tackle, then the practice of using games from earlier seasons in grading calculations for less active players could usefully be examined. Clearly for those playing at a constant level examining more results allows one to home in on the exact level concerned. However it is not at all clear that a mechanism exists by which including results from a time at which a player was playing to a different standard improves our ability to identify the current standard of an improving or declining player. Perhaps the question that needs to be asked here is "What proportion of players need to be playing to a constant standard in order that the benefits to the system of including past games in the calculations of less active players outweighs the disadvantages?".

[Roger de Coverly]

You have to make a decision on how much to change each player's grade for every individual game,

No you don't. When you want to change a grade after every game, like for example in on-line servers, then you use an Elo type system. The ECF system is designed to measure performance over a series of games.

If during a course of a season two 100 players play a match of 30 games and one of the players scores 100%

Please do not use unreal examples. Matches of 30 games do not happen so it doesn't matter how well or badly the ECF system copes with them. My example is always of one 100 player who plays 30 games against other 100 players and scores some percentage or other. I'd prefer not to use the extremes of the system and just consider the 75% mark. So against 30 players all graded 100,

(a) an ungraded player scoring 75% would gain a grade of 125
(b) a graded player of 125 scoring 75% would retain a grade of 125
(c) a graded player of 100 scoring 75% would gain a grade of 125
and finally to balance it up
(d) a graded player of 125 scoring 50% would get a grade of 100

All the players of 100 would stay almost exactly put because they would be +50 against the 125 and -50 against the 100. (they would actually go up marginally because their average field is 29*100 + 1*125).

Given that grades are only accurate over 30 games (in the sense of telling you who is the better player) to about 8 points, I do not see any problems with this. If the English chess scene was full of players of equal grades playing long matches against one another and scoring results well away from 50% then you might wish to revisit the grading system. But it doesn't happen.

The same would hold if the player played a pool of 100 players (grade of each player in the pool is 100) assuming he played 30 games against each payer in the pool.

Again this doesn't happen. You play one or two games against distinct players.

omit grading of graded players in the games where they play ungraded players

It's one of the points of the ECF system, distinct from the pre July 2009 FIDE system , that it attempts (with varying degrees of success) to rate games between unrated players and rated players and unrated players against each other. The allocation of grades to new players is one of the factors behind inflation or deflation of a grading system

[Roger de Coverly]

However we also expect the graders to identify those who will play to a different standard, and by how much. This is pure crystal ball territory. The ECF uses a basic crystal ball which says that all juniors, and only juniors, will improve, and they will do so by an amount which is a function of their age.

Historically that's not quite correct. Many, many years ago there were no specific adjustments for juniors. It was however noted that if say a player improved from a 150 standard to a 175 standard, then this introduced a dilution (deflation) effect amongst the players that he or she was now on equal terms with. This was believed to cause an overall downwards drift of the whole system so you couldn't compare playing results over time. As an ad-hoc pre-computer measure they changed the rules so that when you played a junior, your score was (their last year performance) + (5 later 10) + 50 * (win=true) -50 *(loss=true). In the late eighties, investigations suggested this was leading to inflation (as measured by average grades) and the formula was refined to become age related. The published grade then became (last year performance) + (age related supplement). The latest investigations (Rough error permitting) suggest the total abolition of the supplement for 14+ but a higher increment for under 10s.

However it is not at all clear that a mechanism exists by which including results from a time at which a player was playing to a different standard improves our ability to identify the current standard of an improving or declining player.

There's a rather difficult tradeoff between rating lag and volatility with frequency of reporting also complicating the issue.
It's more obvious in the Elo systems that over a period you might score + 1 against your expectation in one tournament and -1 in the next. If there is no reporting between tournaments, then your rating is unchanged. If you insert a rating list between tournaments , then you appear to gain points in one event and lose them in the next. This would be magnified by increasing the k factor. Those of us that normally play more than 30 games in a season forget that the ECF system has its own k factor equivalent in the 30 game rule. If you reduced the 30 game rule to 20 (increasing the k), then you would increase the volatility of players in the 20 to 30 game zone whilst possibly reducing the effects of rating lag.

[Robert Jurjevic]

Roger de Coverly, let me try to clarify my point using the two rules:

GS:

Rule 1a: For a win you score your opponent's grade plus 50; for a draw, your opponent's grade; and for a loss, your opponent's grade minus 50. Note that, if your opponent's grade differs from yours by more than 40 points, it is taken to be exactly not 40 points above (or below) yours. At the end of the season an average of points-per-game is taken, and that is your new grade.

AGS3:

Rule 2b: For a win you score average grade plus 25; for a draw, average grade; and for a loss, average grade minus 25. Average grade is half of the sum of your and your opponent's grade. Note that, if your opponent's grade differs from yours by more than 40 points, it is taken to be exactly 40 points above (or below) yours. At the end of the season an average of points-per-game is taken, and that is your new grade.

Rule 1a...

In order not to stretch nor shrink (drift) the grades you should apply rule 1a only for one of the players in the game. Say, if payers A and B have played a game, when grading it, if you apply rule 1a for correcting the grade of player A you should not apply it for correcting the grade of player B (you should omit grading of player B in that game) and vice versa. The reason for that is that rule 1a sets a maximum possible correction for a player's grade and if you would apply it for correcting the grades of both players the grades would drift apart (as you would apply too much correction).

There is nothing intrinsically wrong in grading a game in a way to change one player's grade for a maximum amount and leave other player's grade unchanged. The problem is though that the number of games in which such a grade correction distribution applies is rather small, in most games either it does not apply or you do not know if it is applies.

Let me give you an example. Let us assume that there are two player pools, pool 1 with average grade of 130 and pool 2 with average grade of 160. Let us assume that player A graded 130 is a member of pool 1 and that player B graded 160 is a member of player pool 2. Let us assume that player A played all players in pool 2 and that player B played all players in pool 1 and let us assume that the game between player A and B ended in a draw. You are facing a problem of correcting the grades of players A and B for the game they drawn.

You can argue, as player A played a pool of players with average grade of 160 I will increase grade of player A for a maximum possible amount and leave the grade of player B unchanged, this is equivalent to saying that the players drew because player A improved and player B neither improved nor worsened. Fine, you apply rule 1a for the game grading only player A.

But you can also argue, as player B played a pool of players with average grade of 130 I will decrease grade of player B for a maximum possible amount and leave the grade of player A unchanged, this is equivalent to saying that the players drew because player B worsened and player A neither improved nor worsened. You apply rule 1a for the game grading only player B.

Which argument is correct? Could be one or the other, could be neither, there are infinite possibilities, you could try to estimate if one of the players improved or the other worsened and for how much, but basically in order to make such an assessment you would need a thorough analysis of players' lives, maybe the game itself, etc., so the best guess would be to change both player's grades for half of the maximum amount, you increase the grade of player A and decrease the grade of player B for half of the maximum amount.

Every player eventually plays a pool of prayers with some average grade, this pool should have no bearing on a decision how to distribute grade corrections when grading individual games.

The main flaw in GS is that it applies rule 1a for correcting the grades of both players in the game (should apply it only for one player). This causes grade stretching (or grade drifting).

Rule 2b...

In order not to stretch nor shrink (drift) the grades you should apply rule 2a for both players in the game. The reason for that is that rule 2b sets half of the maximum possible correction for a player's grade and if you would apply it for correcting a grade of one of the players only the grades would drift towards each other (as you would apply too little correction).

So you have no problem in deciding how to distribute the grade correction in each individual game, by applying rule 2b, you increase the grade of one player and decrease the grade of other player for half of the maximum amount.

[Roger de Coverly]

Let us assume that player A played all players in pool 2 and that player B played all players in pool 1 and let us assume that the game between player A and B ended in a draw. You are facing a problem of correcting the grades of players A and B for the game they drawn.

The ECF grading system doesn't work on the basis of individual games

you calculate the new grade for player A based on all his games and for player b on all his games.

If arguably A(130) plays a field of 30 *130 and 1*160 then his new grade is 131(rounded) if he scores 50%. If B (160) plays a field of 30*160 and 1*130 and scores 50% his new grade is 159 (rounded). I have had no need to express any opinion about the result of individual game between A and B. If they didn't play or we left the game out of the calculations, then their respective grades remain at 130 and 160. So you could assert that the effect of them playing and drawing is that 1 point is added to A and 1 point subtracted from B.That's an equivalent sort of result to what you would get in an Elo system. Each individual game contributes 1/n to the final tally.

I think your system would score it as 30.5 * 130 + 0.5 * 160 = 130.5 and 159.5 which increases either stability or lag.

The point of the ECF method is that an ungraded new player with the same results would get 30 * 130 +160 = 131. My defence of the ECF method is that it's perfectly fair and reasonable to treat new and existing players in the same way

when grading individual games.

The ECF system does not grade individual games other than as their contribution to an aggregate result.

The main flaw in GS is that it applies rule 1a for correcting the grades of both players in the game. This causes grade stretching (or grade drifting).

this is equivalent to saying that the players drew because player B worsened and player A neither improved not worsened

Somewhere you have to bring in the issue that playing strength is a random variable and that all 3 results are possible in any game regardless of whether the grades of the players are correct and that you should make only limited inferences about relative strength from one result. Brian Valentine's example was that in an all play all tournament of players with equal grades and equal strength, one of the least likely results is that they all score 50%.

If you are worried about grading drift it would be better to consider the issue that an individual game for a player playing 60 games has half the effect of one playing 30. So the player playing more games gains or loses fewer points than their less active counterpart.


I'm probably not going to write any more on this - the only chance of adopting a system which treats players differently for the same opposition would be if the ECF adopted some form of Elo based approach. In this approach you draw inferences from the result of an individual game as to whether the players prior game rating needs to be adjusted. The amount of adjustment depending on the amount of "trust" you have in the prior game rating. You bring in new players by working out their ratings against existing rated players using the ECF approach of adding up the opposition ratings and adding a factor based on the (win -loss) total.

If you actually try looking at the published grades over consecutive seasons, you see very little change in either the mean or the standard deviation so theories of drift or spread are not confirmed by practical observation of the outcomes.

[Robert Jurjevic]

Rules...

GS:

Rule 1a: For a win you score your opponent's grade plus 50; for a draw, your opponent's grade; and for a loss, your opponent's grade minus 50. Note that, if your opponent's grade differs from yours by more than 40 points, it is taken to be exactly not 40 points above (or below) yours. At the end of the season an average of points-per-game is taken, and that is your new grade.

AGS3:

Rule 2b: For a win you score average grade plus 25; for a draw, average grade; and for a loss, average grade minus 25. Average grade is half of the sum of your and your opponent's grade. Note that, if your opponent's grade differs from yours by more than 40 points, it is taken to be exactly 40 points above (or below) yours. At the end of the season an average of points-per-game is taken, and that is your new grade.

Formulae...

Let 'a' and 'b' are the grades of players 'A' and 'B', 'p' expected performance of player 'A' (expected performance of player 'B' is then '100 - p'), 'q' actual performance of player 'A' (actual performance of player 'B' is then '100 - q') and 'a2' and 'b2' new grades of players 'A' and 'B'.

'a2' and 'b2' are calculated using the following formulae (holds for any grading system mentioned here, including the current one):

Code: Select all

a2 = a + ka*(q - p);
b2 = b + kb*((100 - q) - (100 - p));

(if players 'A' and 'B' had played only one game in the season 'q' is either 100, 0 or 50, if they played more than one game it can be a number between 0 and 100 inclusively)

Note: The formulae are used to calculate a new grade of player 'A' for every opponent 'B' he or she played in the season. At the end of the season an average of the calculated grades (for every opponent 'B') is taken, and this average is a new player's 'A' grade for the season (if a player has not played enough games in the season, some games from previous season or seasons need to be taken into account).

Relevant 'p = f(d)'s are:

Code: Select all

g = 50; s = 40;
If[d >= 0, If[d > s, p = 90, p = g*(1 + d/g)], 
    If[d < -s, p = 10, p = g*(1 + d/g)]];
p = 100/(1 + 10^(-d/g));    

My finding is that 'ka + kb' should be equal to 1 in order not to stretch nor shrinking the grades, for GS it holds that 'ka + kb = 2' so it stretches the grades.

Our debate...

Let us assume that player A played all players in pool 2 and that player B played all players in pool 1 and let us assume that the game between player A and B ended in a draw. You are facing a problem of correcting the grades of players A and B for the game they drawn.

The ECF grading system doesn't work on the basis of individual games, you calculate the new grade for player A based on all his games and for player b on all his games.

As far as I can see both rules 1a and 2b talk about scoring based on every individual game, pool of players are comprised of individual players (actually the whole ECF player pool is comprised of individual players), and finally the player actual performances comprise of sets of results of individual games. I cannot see how can you find a correction for one's grade based on his or her individual game results if you would not have a rule for grading every individual game.

The point of the ECF method is that an ungraded new player with the same results would get 30 * 130 +160 = 131. My defence of the ECF method is that it's perfectly fair and reasonable to treat new and existing players in the same way.

It think not, you actually do not know grades of ungraded players, and you would wish to grade the games between graded and ungraded players so that the grade of graded player remains unchanged (that basically means apply rule 1a for the ungraded player but omit grading of the game for the graded player).

Rule 1a is equivalent to:

Code: Select all

g = 50; s = 40;
ka = 1; kb = 1;
d = a - b;
If[d >= 0, If[d > s, p = 90, p = g*(1 + d/g)], 
    If[d < -s, p = 10, p = g*(1 + d/g)]];
a2 = a + ka*(q - p);
b2 = b + kb*((100 - q) - (100 - p));

where 'a' is your grade (meaning of symbols is the same as in "Formulae" section above).

So though rule 1a does not require to know your grade in order to score your games it does correct your grade which (if you have it) is equal to 'a = b + d', where 'd = a - b' is the grade difference (can be negative).

'a2' can be expressed in terms of 'b' if you substitute 'a = b + d'

Code: Select all

g = 50; s = 40;
ka = 1; kb = 1;
d = a - b;
If[d >= 0, If[d > s, p = 90, p = g*(1 + d/g)], 
    If[d < -s, p = 10, p = g*(1 + d/g)]];
a2 = a + ka*(q - p) = b + d + ka*(-50 - d + q) = -50 + b + q;

so in order to calculate 'a2' (your new grade) you do not have to know your grade 'a' nor the grade difference 'd' (which is a convenience if you are an ungraded player).

Consequently if you have the grade 'a' then it should be equal to 'a = b + d', where 'b' is your's opponent's grade, but if you are ungraded you do not know grade difference 'd', though, as 'a2 = -50 + b + q', you can calculate your new grade 'a2' (for each game you played) only knowing your opponent's grade 'b' and your performance (in the game) 'q'.

Though in this system 'a2 = -50 + b + q', 'a2' is still calculated using the general formula 'a2 = a + ka*(q - p)', where 'a' is your grade and 'ka*(q - p)' the correction you apply to it.

Note that in other systems 'a2' may be a function of 'd', as you well observed for AGS3, where 'a2 = (-50 + 2*b + d + q)/2'.

The point of this mathematical "torture" was to emphasize that in all systems you are actually correcting grades, though I admit that applying rule 1a for the ungraded player but omit grading of the game for the graded player is probably the best one can possibly do (this is one of the rare cases where you know that you want to credit or penalize only one player in the game for a full allowed amount).

I'm probably not going to write any more on this - the only chance of adopting a system which treats players differently for the same opposition would be if the ECF adopted some form of Elo based approach. In this approach you draw inferences from the result of an individual game as to whether the players prior game rating needs to be adjusted. The amount of adjustment depending on the amount of "trust" you have in the prior game rating. You bring in new players by working out their ratings against existing rated players using the ECF approach of adding up the opposition ratings and adding a factor based on the (win -loss) total.

Right, I am sorry for writing so much on the subject, if you wish me I can stop. I am doing this only with the best intention in order to try help to improve the system. Of course, I may be wrong though I think that I pretty clearly laid out my argument using both mathematics and logic.

Just one last point, you cannot apply FIDE Élo approach for a league competition directly, as FIDE 'k' factors would not apply, and you would have to correct them (I am a bit surprised as you are so vigorously opposing me in my attempt to change the ECF 'k' factors from '1' to '1/2'). Besides, ÉGS5 is equivalent to FIDE Élo with scaled grades to ECF standard and 'k' factors adjusted for grading once a year, and ÉGS6 is even improving on current FIDE Élo (has Glickman 1 improvement over FIDE Élo).

Thanks a lot.

[Robert Jurjevic]

I do apologize for bringing this subject up again.

Code: Select all

--------------------------------------------------------------
grading   stretches  uses FIDE   changes less     preserves      
system    grades     'p = f(d)'  trusted grades   total system    
          ('k')      (yellow)    more rapidly     grade         
--------------------------------------------------------------
GS        yes        no          no               yes                 
AGS3      no         no          no               yes                 
ÉGS5      no         yes         no               yes
ÉGS6      no         yes         yes              no
--------------------------------------------------------------

Table 1: Main differences between GS (current Grading System), AGS3 (Amended Grading System three), ÉGS5 (Élo Grading System five) and ÉGS6 (Élo Grading System six).

Please be reminded that a detailed discussion on the mentioned grading systems can be found in "Grading anomalies" document at... http://www.jurjevic.org.uk/chess/grade/ ... malies.htm

(I would like to thank you all who helped the idea to be developed and contributed to a number of document revisions, now the document should be fairly accurate and cover the matter from various angles and points of views, the latest version is 2.1 released on 12/06/2009.)

My current grade (performance) for 2009/10 season is as follows (my grade 121, games played 5, score 2-2-1 50.0%, average opponent's grade 102)...

Code: Select all

---------------------
GS   AGS3  ÉGS5  ÉGS6
---------------------
105   113   113   116
---------------------

[The extension zip has been deactivated and can no longer be displayed.]

Calculated with ECF_grades computer program (version 3.0 which includes GS, AGS3, ÉGS5 and ÉGS6 calculation) which (command line executable for Windows including C source code and a sample input file) can be found at... http://www.jurjevic.org.uk/chess/grade/

[Roger de Coverly]

My current grade (performance) for 2009/10 season is as follows (my grade 121, games played 5, score 2-2-1 50.0%, average opponent's grade 102)...

If you didn't play any more games this season, your next season grade would be ( 2* (av result for 2007) + 23 * 121 + 5 *102) /30 = 118

I've assumed (av result for 2007) was also 121 and that you scored 50% this season against the 102 field.

This also assumes you aren't a junior as the grading system is now broken for less active juniors.

[Robert Jurjevic]

If you didn't play any more games this season, your next season grade would be ( 2* (av result for 2007) + 23 * 121 + 5 *102) /30 = 118

Roger, thanks a lot for the formula, so I should stop playing in this season then, just joking, I will try to perform better.

I've assumed (av result for 2007) was also 121 and that you scored 50% this season against the 102 field.

This is a fairly good assumption, I think, as I was 90 (old) in 2007/08 which should be about 120 (new), and yes I did score this season exactly 50% (2 wins, 2 loses and 1 draw) against 102 field.

If we assume that I am 120 and that I will score 50% against a pool of 100 players in 30 (or more) games in 2009/10 season, according to GS (current Grading System), my new grade would be 100, while in fact IMHO it should be 110 (AGS3, ÉGS5 and ÉGS6 would roughly give 110).
My I suggest not to enter into a discussion (in this thread) why I think it should be 110 rather than 100 (the mentioned document discusses a similar example in detail in "Equal grade for equal performance" section).

Have a nice day!