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Data regarding ABT open players' PR - Part 2

Posted By: David Presser
Date: Saturday, 29 November 2014, at 8:41 p.m.

In the beginning of the year I shared my data that I collected from my matches regarding the ABT open player's PR. As my 2014 backgammon year has ended I am posting my data for the year and accumulated data. To be clear, I excluded myself from the data, and it refers to my opponent's performance only. As you will see, I have added some information based on your recommendation and good logic:

2014: Matches 35; Average 6.57, SD 2.3; Median 6.59; Lower Quartile 4.83; Upper Quartile 7.77; Range 2.86 11.92.

Accumulated (from July 2013) Matches 76; Average 6.61; SD 3.0; Median 6.36; Lower Quartile 4.5; Upper Quartile 7.68; Range 1.36 18.41.

There is a lot that can be derived from the information. However, as I pointed in the past and many agreed, if you try to infer on the average PR of an open player, you get strongly biased results. I liked Matt's (MCG) approach of looking at the data more in terms of the average PR you are likely to face during an open tournament. This should incorporates many factors such as fatigue, the chance of facing a specific player more than another because of skill or frequent showing in ABT events. The data is still inconclusive in my view as it is a small sample, yet it suggests possible answers to questions that we all wondered about.

In my previous post Bob Koca proposed to segregate the data based on match length. This is an interesting and good idea which I followed. For my analysis I used three segments: Short length matches (basically 5 pointers); Medium length matches (7 or 9 points); Long length matches (11 or more points). The analysis is based on my accumulated data. Here are the results:

Long length matches (11 or more points) - Matches 28; Average 6.12, SD 1.7; Median 6.25; Lower Quartile 4.61; Upper Quartile 7.2; Range 3.19 10.86.

Medium length matches (7 or 9 points) - Matches 35; Average 7.05, SD 3.4; Median 6.68; Lower Quartile 4.78; Upper Quartile 8.64; Range 1.36 18.41.

Short length matches (5 points) - Matches 13; Average 6.48, SD 3.7; Median 5.82; Lower Quartile 4.48; Upper Quartile 7.49; Range 2.62 17.26.

I find the long length matches segment to be most surprising, especially with respect to the average, median and SD, which is half of the SD of medium length matches. I have run it twice on Excel and manually to make sure there is no mistake. My next step was to try and figure out what is the cause, and a few possible explanations came to mind (I am sure there are more which you are welcome to propose). The most likely explanation is that the sample is small and I expect the SD to increase in time. Two more possible explanations are that players put most of their effort in the main, and when they are dropped to the consolation or last chance they care less and allow themselves not to play their best or that there is a self selection bias, i.e. stronger players tend to go to high points tournament such as Novi, Las Vegas, NY where you either play more than 11 point matches, or get to play 11 point matches even if you lost one match. It should be pointed that the 5 point match segment includes only one match from 2014 since I developed less interest in recording those matches (mainly for overload of recorded matches at that point in the tournament). Therefore, the number of matches for this segment is small and its relevance is questionable.

In conclusion, I reach no conclusion :) Nonetheless, the data suggests that the average open player or, the average player that one is likely to face during an ABT open tournament may be underestimated by its fellow peers (this is a funny paradox). I encourage you to develop this discussion with further questions. I think we can extract a lot of added information with the right questions and analysis.

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