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

[Citrus Dad]

[cdm-description=photo]41818[/cdm-description]

[nuclearnerd]

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.

[IKE]

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.

[JamesBrown]

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.

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.

[nuclearnerd]

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/0B16qRDFhn0uuMTZRenZQOUU4dUE/view?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!

[Citrus Dad]

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/0B16qRDFhn0uuMTZRenZQOUU4dUE/view?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!

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.

[Citrus Dad]

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.

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.

[Abhishek R]

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.

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.

[nuclearnerd]

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/0B16qRDFhn0uuTkNSaDRmTnNMbTg/view?usp=sharing

[Citrus Dad]

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/0B16qRDFhn0uuTkNSaDRmTnNMbTg/view?usp=sharing

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

[Caleb Sykes]

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

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

[Woolly]

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

G40 would like a word with you.

[Caleb Sykes]

G40 would like a word with you.

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

[Pretzel]

G40 would like a word with you.
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.

[Citrus Dad]

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

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.

[Caleb Sykes]

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.

I should have been more clear. What I meant to convey was that penalties last year had no direct impact on the offending team's score. Thus, OPR would have no way to tell that a team was hurting their alliance because of penalties. Since penalties this year are subtractive, they are reflected in the OPR calculations.

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?

[Ether]

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?

Is this at all helpful?
http://www.chiefdelphi.com/media/papers/download/4037

Column headings are as follows:


L2s Final Score OPR
L2f Foul OPR
L2h Hybrid OPR
L2t TeleOp OPR
L2os Opponent's Final Score OPR
L2of Opponent's Foul OPR
L2oh Opponent's Hybrid OPR
L2ot Opponent's TeleOp OPR
As Average Final Score
Af Average Foul
Ah Average Hybrid
At Average TeleOp
Aos Opponents Average Final Score
Aof Opponents Average Foul
Aoh Opponents Average Hybrid
Aot Opponents Average TeleOp
uOPR unpenalized OPR = L2s - L2f
uDPR unpenalized DPR = L2os - L2of
uCCWM unpenalized CCWM = uOPR - uDPR
EPA uOPR - (As - Af)
M Matches Played

N.B. : The usual Twitter data caveats apply

[Conor Ryan]

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.

[smurfgirl]

Thanks for sharing this - it's really interesting!

[Caleb Sykes]

Is this at all helpful?

Thank you, that is indeed very helpful. I will play around more with this after my team competes this weekend.

[Citrus Dad]

There are more teams this year than ever before. The 1% is getting bigger and more elite ever year.

Actually 2014 was one of the most flat years in distribution so there's not an obvious trend. The SD calculation normalizes for the size of the pool of teams--it should be the same regardless of whether there are 100 or 10,000 teams. The difference in the distribution is really driven by the nature of the game.

More than anything I think this statistic is showing the complete absence of defense from this years game.

See my points above: It's not only lack of defense but the particular difficulty of gaining the highest point activities. There's been posts on that issue in other threads.