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pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
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Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
Thanks for this. The chart really shows how the top 2-3% (maybe 50 teams) earn a much larger share of the points than the average team, more so than any other year (and a huge jump from 2014).
It's good to see that there doesn't appear to be a broader trend towards less equal OPR distributions over time. RR seems to be an outlier. |
Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
Thanks for posting. I have made of looked at this sort of trend for a handful of years, but use a different normalizing function.
To a certain degree, I expect that the 2015 data might decrease a bit thanks to weeks 5&6. There will be more teams playing their 2nd event during those weeks which will raise the median pervormance quite a bit. |
Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
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Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
Here's another way of looking at some of the same data. I'm just showing histograms of OPRs between 2015 (the most skewed game) and 2014 (one of the least skewed games), normalized by standard deviation as Richard has done:
https://drive.google.com/file/d/0B16...ew?usp=sharing The difference between the games isn't as stark as I thought. Certainly there were more people with OPRs in the 0.5 to 1.5 SD range in 2014 than there are this year, but the curves are otherwise remarkably similar. That said, 1114's placement way out at 6.25 SD looks all the more impressive on this chart! |
Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
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But that's further enhanced by the technical challenge of capping stacks which is akin to climbing beyond the first level of the pyramid in 2013. Not many teams could do that back then either. |
Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
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Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
Here are the two histograms again, but this time I've clipped the top of the scale so we can focus on the "tails" (the 50 or so teams at the top and bottom of the distribution). I also screwed up the last plot and didn't show 2056 with an OPR at ~6 SD above the mean. 2056 and 1114 look lonely out there :)
https://drive.google.com/file/d/0B16...ew?usp=sharing |
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So I go back to my original comment that the low end spread is quite interesting. I think it might be reflective of how difficult it is for a newer or less experienced team to contribute to the game, but I didn't think they could detract so much. BTW, there are special statistical properties to include when running regressions with a continuous dependent variable (score) and 0-1 dummy variables (i.e., whether a team is present on the alliance). I haven't looked at that issue for quite a while so I don't remember much beyond that but it is a consideration in the OPR estimation. |
Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
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What I am curious about is an alternate OPR calculation for last year which would use the following formula in the match score matrix instead of the nominal score: adjusted score = (nominal score) - (penalty points incurred by opposing alliance) + (penalty points incurred by this alliance) Actually, I do remember uOPR (unpenalized OPR) being calculated last year. Was this the method of obtaining that? Or did it just subtract out all penalty points incurred without adding any back in? |
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http://www.chiefdelphi.com/media/papers/download/4037 Column headings are as follows: Code:
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Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
There are more teams this year than ever before. The 1% is getting bigger and more elite ever year.
More than anything I think this statistic is showing the complete absence of defense from this years game. |
Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
Thanks for sharing this - it's really interesting!
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Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
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