Grades Grades are used within chess to help determine fair and predictable pairings in competitions, to measure progress, and as one indicator to team managers that a player might be asked to play for a county team.

Berkshire Junior Chess have been running our own grading system for several seasons. Player rankings, based on these Berkshire Junior grades are also published in the Year Book.

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Grading systems This website displays 3 different grades for players, and for event results. The three grade types are: Berkshire Junior, ECF Standard Play, and ECF Rapidplay (ECF = English Chess Federation). On a player detail page, all three grades may be displayed if the player has gained a grade of each type. A results page will only display grades of one type.

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ECF Grades ECF Standard Play grades are assigned to players if they have played matches where the time limit is not less than one hour for the initial 30 moves (and, of course, where the match result has been submitted to the ECF for grading purposes). A Standard Play grade can be gained by playing in certain county matches (e.g. under 18 matches), in the adult Berkshire League, or in some tournaments such as the Berks and Bucks Congress. At the start of the 2006-07 season, 22 Berkshire Juniors had a standard play grade, although many are based on little more than the minimum number of games required.

ECF Rapidplay grades are calculated from the results of games of less than one hour for the initial time period, but no faster than 15 minutes sudden death. There are currently 22 Berkshire Juniors with a rapidplay grade.

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Berkshire Junior Grades As of September, 2004, the ECF (BCF as was at the time) no longer grade junior events for free. It has been estimated that to carry on submitting results at the same rate as the 2003-04 season would cost us £800! Instead of increasing tournament entry fees to cover ECF grading charges, we have decided to calculate our own grades, and call them "Berkshire Junior Grades". Further, we have decided to adopt a modified version the FIDE grade calcuation methods, which are different from the method used for ECF grades.

At the end of the 2006-07 season, there were 735 players with a Berkshire Junior Grade, and it has become the standard measure used to pair players at the popular Saturday afternoon events. We publish end-of-season ranking lists based on these grades, but only team managers can access the current point-in-time rankings.

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Grade Calculation The nitty-gritty part. How are tournament results turned in to Berkshire Junior grades? First, all match results for a tournament are entered into the website database (this level of detail also allows the website to display a "crosstab" section on a results page). The method for calculating grades is different for players who start with an existing grade, and those without a grade. In outline, the following method is used for players with an existing grade:

• The player's grade, and the average of their opponents' grades are used to calculate an expected score. Note that results against ungraded players are not included. If the opponent's grade is more than 350 points higher or lower than the player's grade (at the start of the event), then it is adjusted such that the difference is exactly 350, before the averaging calculation is done. This prevents players from making large grade gains by losing to a very highly graded opponent within a set of otherwise roughly "expected" results.
• To get the whole system going, if a player does not have a Berkshire Junior grade, but does have a ECF Rapidplay grade, then an initial Berkshire Junior grade is estimated from the ECF grade.
• The difference between a player's expected score, and the actual score obtained against graded opponents is then used to calculate an increase or decrease in the player's grade.
• The player's grade is adjusted in proportion to the difference between their expected and actual scores, and their new grade is used in later events.

For ungraded players, a different computation is performed:

• There must be at least 5 graded players in a tournament in order to estimate initial grades for ungraded players. If this minimum condition is met, a straight line best fit between grade and points scored is calculated using graded player results. A simple least squares linear regression is used initially, but if the highest or lowest grades are far from this line, they are removed from the value set, and the regression is re-calculated. The minimum requirement for 5 graded players does not include anyone removed from the value set as described.
• The straight line is then used to estimate initial grades for all ungraded players. No grade is calculated is the player scores 0 points (byes do not count toward the score for grading purposes).
• The calculation as described above for graded players is now performed for ungraded players (who now have an estimated initial grade) to give a published initial grade. Note that the original batch of graded players do not have their grades re-calculated.

The following conditions apply to both calculations:

• The minimum grade for any player is 300. If the calculation for an ungraded player yields a value below 300, no grade is published - if the player enters another tournament, it will be as an ungraded player. If a newly calculated grade for an existing graded player drop below 300, it is set to 300.
• A tournament bonus is added to all entrants' grades. This is intended to reflect an expected improvement in playing standard simply through the practice gained by competitive play. The bonus is currently set at 5 for all events, but it is possible that the bonus may be increased for the more challenging events such as the Berkshire Junior Congress.

This approach means that:

• Ungraded players have no impact on the grade of graded players (even if the ungraded player wins).
• Grades change continuously throughout the year, after each event for which the above calcuations are performed. Since young players often improve rapidly, this system gives them some immediate feedback on how well they are doing.

The actual formulae used to perform the "calculations" mentioned above are given below. (note: * is used for multiplication, and ** is the exponent (to the power of) symbol):

• For a player with no Berkshire Junior grade, but with a ECF rapidplay grade:
  BG = (RPG * 8) + 600
  where BG = Berkshire Junior grade, and RPG = Rapidplay grade.
• Estimated Score:
  ES = GM / (1 + 10**( (AOG - BJG) / 400 ) )
  where GM=graded matches; ES = expected score; BJG = Berkshire Junior grade; AOG = average opponent grade;
• Change of grade:
  GC = K * (AS - ES)
  where GC = grade change; K = 40 (the progression coefficient); AS = actual score (against graded opponents); ES = expected score.
  For players who are ungraded at the start of an event, a value of 50 is used for K.

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Example Calculations Suppose player A, who has a current Berkshire Junior grade of 1000 competes in a tournament and plays 6 matches against opponents with the following grades: 800, 1150, no-grade, 1280, 1190, and 1310. Further suppose that the player scored a total of 3.5 points against the graded opponents. The result against the ungraded player is irrelevant for the purposes of grading calculations.

First calculate AOG (average opponent grade), which gives 1146. Use the ES formula above to calculate expected score, which comes to 1.51 (to 2 decimal places). Next use GC formula to determine the grade change: GC = +79.6. Finally apply the grade change and tournament bonus (5) to the current grade to give 1085 (rounded). This is the player's new Berkshire Junior grade, and will be used as the initial value for BJG in any future tournament.

The following is a brief table of grade changes for a number of grade differences for a single game (player grade - opponent grade). The first entry shows that if you out-grade your opponent by 400 points, then if you win you gain only 4 points, if you draw then you lose 16 grading points, and a loss results in a grade reduction of 36. (In reality, a grade difference of 400 would be treated as 350, with resultant amendment to the grade changes mentioned).

Grade diff	Win	Draw	Lose
+400	+4	-16	-36
+200	+10	-10	-30
+100	+14	-6	-26
0	+20	0	-20
-100	+26	+6	-14
-200	+30	+10	-10
-400	+36	+16	-4

As you can see, the grade gains and losses are symmetrical, and indeed the whole system is a "zero-sum game". For any tournament, or single game, the aggregate grade change is close to zero. However, our implementation also includes a 5 point bonus per tournament entrant. The aggregate sum may also vary from zero due to rounding.

It is too early to tell if the competing effects of how the system operates will lead to grade inflation or deflation over time:

• including new players into the system (mostly with lower than average grades) brings the average grade down. However, many of these players may only ever enter one or two events.
• throwing extra grading points into the pot with the tournament bonus has an obvious inflationary effect.
• the tendency for higher graded players to enter fewer events (effectively taking their high grades out of the system and reducing the average)

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