Moreover, if there were 63 games rather than 7, the problem could actually be worse.  This is because the BKR system as it presently is implemented will predictably drive my rating downward if I play a large number of games against lower rated players.

For example, suppose that on average, I should win 65% of my games and receive +4 points for a win, -12 points for a loss as described below (the actual win/loss disparity is probably greater).  If I play 100 games and win 65 of them, I will receive 65 x +4 points = +260.  However, I will lose 35 x -12 points or -420.  Therefore, simply by winning the predicted number of games I lose 160 points!

In actuality, I would lose fewer points, because as time went on my rating would be lower and the adjustments would moderate.  However, the principle is still the same, which is that as long as I and my opponents play at our respective skill levels, my rating will fall simply because I play lower rated players.  This should not happen.  If my average winning chances are 65%, then wins and losses should produce point adjustments in a ratio of approximately 1:2 (e.g. +4, -8).

The objection may be raised that, under my standard for a fair system, players would not be able to rise and fall significantly in the rankings.  The answer to that is that players should not rise and fall unless their skill level changes.  Everyone starts at the same level, and moves to a certain rating according to his or her skill level.  After that, changes in ranking should occur only if players get better or worse at the game.

It seems that, under the BKR system in place today, if everyone were constantly playing everyone else, all players should tend toward some average BKR.  I guess the only reasons this does not occur are that (i) new players are constantly being introduced to the system, (ii) old players leave, and (iii) players tend to select opponents closer to their own level.