pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
 

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
 

It is possible, but I think the real driving force this year is the lack of defense. I think the top teams have always been this much better at scoring than everyone else, however facing regular defense from other teams dragged down their average scores significantly.

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
 

The 2015 distribution is flatter and more spread than I expected with extended tails at both ends. The number of teams beyond the top of 2014 is interesting as well.

Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
 

I would go further to say its in part a function of the lack of interdependency, both offense & defense. Our highest score came with only 2 robots on the field (although we would have gotten a higher score if our robot had grabbed a 2nd center can in one of the Sacramento finals with 3 bots on the field.)

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
 

Yup, we're back to a game where a single team can score a massive amount of points by itself, as opposed to something like 2014, where even without defense teams relied on each other to get those assists if they really wanted to score high, and it was sort of a limiting factor.

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

Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
 

What's absurd is that there are 60 teams BELOW the bottom of last year's distribution.

Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
 

Not really, it is easier to accidentally hurt your own alliance this year than it was last year.

Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
 

G40 would like a word with you.

Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
 

You're absolutely right, I had forgotten about penalties. I wonder how these graphs would compare if the OPRs from last year incorporated penalties.

Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
 

G40 didn't reduce your OPR though. It gave points to your opponents instead of taking away your own hard-earned points. You also were unable to de-score yourself by knocking over stacks, since it was pretty hard to get the ball to go backwards back through the goal after your scored.

Re: pic: Top 10% OPRs compared via standard deviation distribution - 2008-2015
 

Pretty sure last year's OPR included penalties, as with all previous years. The OPR calculation is simply a regression analysis on the total final score for each match with a dummy variable for each team.

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.