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#1




[TBA Blog] The Math Behind OPR  An Introduction
The Math Behind OPR  An Introduction
OPR, or Offensive Power Rating, is a stat that's often used in the FIRST community to compare the performance of teams on the field. It's also common to hear things like "this game is a bad game for OPR" or "OPR is a pretty accurate indicator of performance this year." In order to understand OPR's strengths and limitations, learning the math behind it is key. This blog post will provide an introduction to the math behind OPR, and a future post will delve into how game design affects OPR's usefulness as a statistic. Check out the rest of the article here: https://blog.thebluealliance.com/201...introduction/ 
#2




Re: [TBA Blog] The Math Behind OPR  An Introduction
Great post. I'm always interested in seeing applications of math in FRC. Looking forward to the next one!

#3




Re: [TBA Blog] The Math Behind OPR  An Introduction
Having taken a decent few math classes in college, I think this write up does a great job of explaining the math at a high school level without sacrificing on accuracy or rigor. This will definitely be recommended reading for the Shaker Robotics scouting team.

#4




Re: [TBA Blog] The Math Behind OPR  An Introduction
Another great post by the folks at The Blue Alliance. Next time someone asks for an overview of OPR, send them to this page.

#5




Re: [TBA Blog] The Math Behind OPR  An Introduction
This is a great post!
I find myself very jealous of all these FRC kids who are heading into college with a super concrete application of Linear Algebra in their heads. I struggled mightily with LA because I didn't really perceive the value in it and didn't put in the necessary work to come to a complete understanding. I might even find a MOOC course and take another stab at learning it...if I can find some free time. #TBAIMFD 
#6




Re: [TBA Blog] The Math Behind OPR  An Introduction
+1

#7




Re: [TBA Blog] The Math Behind OPR  An Introduction
After scouring through tactics resources over the years, I think this is probably the best explanation of OPR I have seen. +1

#8




Re: [TBA Blog] The Math Behind OPR  An Introduction
I never thought about self multiplying the robot match matrix by its on transpose to get the A matrix. I had always just kept a running sum of match occurrences of an N x N matrix (where N is the number of robots). I like the transpose method better.

#9




Re: [TBA Blog] The Math Behind OPR  An Introduction
Quote:
When I was first taught linear algebra, I had no idea how ubiquitous it would be in realworld engineering applications. As a result, I had to reteach it to myself years later once I fully understood its value. 
#10




Re: [TBA Blog] The Math Behind OPR  An Introduction
I remember when I found out that that after Calculus you took Linear Algebra. I thought, "I already took Linear Algebra in 9th grade, how hard could it be?!"

#11




Re: [TBA Blog] The Math Behind OPR  An Introduction
Quote:
For M matches involving T teams, the overdetermined system in matrix form is [A][x] ~ [b] Where [A] is the 2MbyT design matrix, [x] is the Tby1 column vector of team OPRs, and [b] is the 2Mby1 column vector of alliance scores. When you multiply the above by the transpose of [A], the result is known as the Normal Equation: [A]'[A] = [A]'[b] I personally use [N] to represent [A]'[A], since it is the matrix of the Normal Equation: [N][x] = [d], where [d] = [A]'[b] Notice that the system [N][x]=[d] is not overdetermined; it is a system of T equations in T variables (where T is the number of teams in the dataset). The solution of the Normal Equation is the leastsquares approximate solution to the original overdetermined system. Quote:
Also, you will need the design matrix if you want to explore options other than OPR, as discussed in this thread and this paper. 
#12




Re: [TBA Blog] The Math Behind OPR  An Introduction
I've posted a quick followup on more of the Linear Algebra that makes this tick. http://imjac.in/ta/post/2017/10/08/o...ralgebra.html
Thanks to Ether for the help, and thanks to Eugene for another great TBA Blog post 
#13




Re: [TBA Blog] The Math Behind OPR  An Introduction
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