Performance Rating

A performance rating is a number reflecting the approximate rating level at which a player performed in a particular tournament or match. It is often calculated by adding together the player's performances in each individual game, using the opponent's rating for a draw, adding 400 points to the opponent's rating for a win, and subtracting 400 points from the opponent's rating for a loss, then dividing by the total number of games. For example, a player who beat a 2400-rated player, lost to a 2600, drew a 2500, and beat a 2300, would have a performance rating of 2550 (2800 + 2200 + 2500 + 2700, divided by four).

The Elo System, used by the United States Chess Federation, FIDE, and many other online chess sites, is popular for two reason.  It has been around for a long time, and it is simple. The idea is that given two chess players of different strengths, we should be able to calculate the percentage chance that the better player will win the game. For example, Garry Kasparov has 100 percent chance of beating someone 4-year-old daughter. But he may only have a 60 percent chance of beating another grandmaster. So when playing that other grandmaster, if he wins 6 games out of 10, his rating would stay the same. If he won 7 or more, it would go up, and 5 of less, his rating would go down. Basically, the wider the spread of the ratings, the higher percentage of games the higher rated player is expected to win. So to calculate a person's rating after playing a few games you calculate the average ratings of his opponents, and then how many games he was expected to win, and then plug it into a formula that spits out the new rating. Simple enough. Well, it turns out, that is maybe too simple.

The Glicko System, used by Chess.com, the Australian Chess Federation, and some other online sites, is a more modern approach that builds on some of the concepts above, but uses a more complicated formula. This only makes sense now that we have computers that can calculate this stuff in the blink of an eye - when Elo created his system they were doing it on paper. It is a bit trickier than the Elo system, so pay attention. With the Elo system you have to assume that everyone's rating is just as sure as everyone else's rating. So my rating is as accurate as your rating. But that is just not true. For example, if this is your first game on Chess.com and you start at 1200, how do we really know what your rating is? We don't. But if I have played 1,000 games on this site, you would be much more sure that my current rating is accurate. So the Glicko system gives everyone not only a rating, but an RD, called a Rating Deviation. 

In each of the following worth-solving puzzles, Black is to play and enjoy.