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Use mean and not median !!!

Posted By: Bob Koca
Date: Monday, 25 March 2013, at 1:59 p.m.

In Response To: PR question for the mathematically inclined (Phil Simborg)

"Obviously, I am against averages since one or two unusually good or unusually poor matches can affect the numbers far more than I believe they should. What we really want to know is where you are likely to play on any given day, and I believe the median is far more reflective of that than an average."

Let's say you are a decent player in the top half of open division with PR = 5 on average for 7 point matches. Your worst matches will hurt you more than your best matches will help you. The best matches could only be 5 better than your average but the worst are potentially much worse than 5 worse than your average.

Suppose you play a match and have one of your terrible matches. Maybe part of the problem was that you just didn't see a winning hit from an acepoint game or blanked out on not auto recubing several moves in a row. You might think of it as a fluke and not representative of your real skill.

But ignoring such matches is just fooling yourself for at least two reasons. The first is that the better a player is those terrible matches should occur with far less frequency and severity. The fluke may not really be so much a fluke in other words. Secondly when you do get one of them it really does influence your chances of winning the match by a tremendous amount. They thus should indeed have a heavy influence on your PR.

Here is one more way of looking at it. Suppose two players Steady Eddie and Wild Willy play two sets of DMP matches against a perfect player. Eddie plays each game with a total of .05 given up from errors. Note that is a very strong performance giving him 47.5% win chance in a DMP against a perfect opponent. Wild Willy plays 9 games perfectly and in one game gives up .50 equity from errors. Those numbers are typical for what happens to each of them in a ten game session. They each have the same expected win total of 4.75 wins in the ten matches.

You essentially want to say how great Willy is because of how often he plays great but you just ignore almost entirely that when he plays bad he plays really bad.

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