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Data regarding ABT open players' PR

Posted By: David Presser
Date: Sunday, 9 March 2014, at 9:28 p.m.

As some of you may know, I record and transcribe most of my matches in the ABT Open events and some Jackpots. I have started from the last Michigan Open (2013) and did so in six different tournaments in 2013. I am doing it mainly for learning purposes and am always happy to share the file with my opponents. This post is not about me, but about interesting data that many, including myself, have shown interest in. It is for sharing my data on open players. My 2013 data includes 41 open matches from the main, consolation, and last chance. It is strongly biased for reasons that I`ll partly elaborate, but first I want to share the data:

Average – 6.64; Standard Deviation – 3.45; Median – 6.2; Range – 1.36 – 18.41

I believe this is indicative, although far from significant, and I believe the average PR is strongly biased downward. The bias is for many reasons and I will name a few that come to mind:

• The sample includes matches from many rounds. The more advanced the round is the more likely it is an opponent with a "better than average" PR which strongly affects the results.

• The tournaments I chose to go to have affected the data. I enjoy the challenge and prefer strong tournaments with high level of competition. On that note, it is worth mentioning that the best average for my opponents was at the Florida tournament in October 2013. The average PR for my opponents was 4.98 (8 matches). That was a small tournament with many strong players who probably fought for the final ABT standings.

• I played some opponents more than once and their PRs have more weight on the sample which leads to a bias toward their true PR.

A datum that I believe should attract just as much interest as average PR does is the SD (Standard Deviation). This is important and a lot can be inferred based on that. For example, if we make the ridiculous yet simplifying assumption of normal distribution, we can infer that two thirds of the PRs generated by an open player ranges from 3.2 to 10.1 (6.65-3.45, 6.65+3.45), and that 95% of the PRs generated by an open player ranges from 0 to 13.55 (6.65-3.45*2, 6.65+3.45*2). Clearly, the distribution of an open player PR isn't normal. Intuitively, it belongs to the chi square family (or more accurately chi family), but I see no reason to go further with this discussion (unless there is interest). My point is that when discussing a player's PR, his SD should be part of the talk and the better the player, the lower his PR, and the lower his SD.

In summary, I reach no conclusion, but the data is interesting and therefore, I am sharing with you. Because of my believe that the data is strongly biased downward, my guess for an average players PR would be somewhere around 7.5, but I won't be surprised by any deviation.

David

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