### Port Macquarie Club Rankings

Club Ratings/Rankings

Port Macquarie Table Tennis Club has started using the Ratings system developed by David Marcus at Ratings Central.

Our Ratings are based on results from our Tuesday Night competition.

There are other views that may interest you.
For example:
Point Change,
Rating History Graph,
Final Rating,
Player's results,
All members of Club

Message from Phil Gammon, your Ratings Central Director

Quite a few people have been asking me questions about the number of points gained and lost in the Ratings Central system. If you have read the scientific article in the Journal of the Royal Statistical Society you’ll appreciate that it’s not an easy question to answer. In the email below I was able to give Richard a partial solution by producing a table that shows the probability of a player winning based on the difference in rating points between the two players. By way of example, if you are rated 100 points higher than your opponent you will need to win 82% of your matches against them to maintain that average difference of 100 points.

Breaking news: I have managed to replicate the Ratings Central algorithm in a spreadsheet and can now calculate the actual number of rating points that will be gained or lost when you win or lose a match.

Note that at this stage it has been written to only calculate point changes for one match between two players. A tournament is more complicated because the initial ratings of all your opponent’s are first adjusted for the results of all of the other matches that they played in the tournament i.e. the results of all matches need to be processed simultaneously. I’ll try to implement this in the future but in the meantime the calculator in this attachment should closely replicate the Ratings Central algorithm for point changes in a single match.

To use the spreadsheet you just need to enter values for both players into the yellow cells on the “Calculator” tab. The resulting change in rating points are shown in the blue cells in row 28.

I’ve used the calculator to generate a few tables that demonstrate some of the main features of the system. In this first table Player A defeats player B and gains more rating points as the strength of his opponent increases. It also shows that if your opponent is rated a long way below you there will be very little gain. Observe too that when both players have exactly the same standard deviation that the points gained by the winner are the same as the points lost by the loser.

 Player A Player B A's B's Rating SD Rating SD change change 1000 ± 50 def 600 ± 50 0 -0 1000 ± 50 def 700 ± 50 1 -1 1000 ± 50 def 800 ± 50 3 -3 1000 ± 50 def 900 ± 50 7 -7 1000 ± 50 def 1000 ± 50 15 -15 1000 ± 50 def 1100 ± 50 24 -24 1000 ± 50 def 1200 ± 50 32 -32 1000 ± 50 def 1300 ± 50 35 -35 1000 ± 50 def 1400 ± 50 37 -37 1000 ± 50 def 1500 ± 50 37 -37

The standard deviation (SD) is a measure of the level of confidence in the rating that has been assigned to a player by the algorithm. A high standard deviation means that there is a greater possibility that your rating is not at the right place. Generally, the more matches you play the more information the algorithm has to determine your true playing strength with respect to other players and your standard deviation will be low.

The next table shows the importance of the standard deviation when calculating point changes. In each match Player A defeats an opponent who has exactly the same rating but I have used a variety of standard deviation values for Player B. The table shows two things. Firstly, that you will gain more points for defeating a player with a low standard deviation. This is because the algorithm assigns more weighting to the result because it is more confident that your opponent really is at the level indicated by their rating. Secondly, it shows the imbalance in the points gained and lost by players with different standard deviations. The player with the lowest standard deviation will always move a lot less than the player with the higher standard deviation.

 Player A Player B A's B's Rating SD Rating SD change change 1000 ± 50 def 1000 ± 30 16 -6 1000 ± 50 def 1000 ± 40 16 -10 1000 ± 50 def 1000 ± 50 15 -15 1000 ± 50 def 1000 ± 60 15 -21 1000 ± 50 def 1000 ± 80 14 -35 1000 ± 50 def 1000 ± 100 13 -50 1000 ± 50 def 1000 ± 150 10 -91 1000 ± 50 def 1000 ± 200 8 -134 1000 ± 50 def 1000 ± 250 7 -177

The above table also works in reverse. The player with the 250 standard deviation would gain 177 points for defeating the player with the standard deviation of 50 but their opponent would only lose 7 points.

Take a copy of the spreadsheet (see attachment below and have a play if you’re interested.

Phil G

22/7/15

Ĉ
Neil Cossey,
20 Jul 2015, 03:32