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#1




Help on OPR and DPR
Hi, I'm working on my teams scouting system right now and was wondering if anyone could explain how to calculate OPR and DPR. I realize these might not be the best methods for this years competition, but I want to make sure I have all the bases covered. Since this is our rookie year, no one really has any idea what we're doing here, which is why I'm asking.

#2




Re: Help on OPR and DPR

#3




Re: Help on OPR and DPR
BMartin, I read through that paper, and I got as far as 2i+j+k+l+m+n=p+q=B and putting that into a matrix with every team, and then was totally lost on Cholesky Decomposition. Is there anyone who can explain the decomposition algorithms to me? I've looked it up, and it's not really anything I've done before. Btw, if it helps, I'm currently in a precalc class, and I understand the material as far in as trig, which is what we've been doing the last month or so. Any kind of true calculus will probably be lost on me right now.

#4




Re: Help on OPR and DPR
Quote:
For each team TotalScore_{team} = sum over all teams( number of times played with team i * OPR of team i) So if you had team 1, who played 1 time each with teams 2, 3, 5, and 8 and had a sum of all their scores of 100, then you'd arrange it like: 100 = 4*OPR_{1} + 1*OPR_{2} + 1*OPR_{3} + 1*OPR_{5} + 1*OPR_{8} Let's say team 2 played twice with team 13 and once with team 21 in addition to their game with team 1. Their total score was 80. So your second equation is: 80 = 1*OPR_{1} + 4*OPR_{2} + 2*OPR_{13} + 1*OPR_{21} Notice that in both these equations, you have 4*OPR_{whateverTeam}. This is because a team plays with themselves once for each game they play. Once you've got equations worked out for every single team (if you were doing this by hand, anyway), you'd realize that you have n equations (one for each team) with n unknowns (one OPR_{i} for each team). This means that you can construct a matrix. With my examples above, the first 2 lines of the matrix would look like Code:
[100  4 1 1 1 0 0] [80  1 4 0 0 2 1] [ ... for team 3 ] [ ... for team 5 ] [ ... for team 8 ] [ ... for team 13] [ ... for team 21] If you get confused, think back to how you build that first equation, and then think of the meaning of that equation: "a team's total score for the whole regional is the sum of the OPRs of its partners, weighted by how many times they played together". For DPR, which I think might work well this year, it would be "The amount of points scored on a team is the sum of the DPRs of its partners, weighted by how many times they played together". Since a slow or poorlydriven robot will tend to get points scored on it, this should have some meaning this year. Most years DPR doesn't matter because what a robot does typically doesn't massively affect how many points its opponents score. Last edited by Bongle : 02102009 at 09:59 PM. 
#5




Re: Help on OPR and DPR
Thanks for the quick reply. I think I get it, but I'll have to play around with it a little bit. I'm actually hoping I can have a system by Saturday, since we've got a local scrimmage going on and I'd like to train scouts there. Also, I'll see if I can track down that code from last year. That might help even more. Thanks again.

#6




Re: Help on OPR and DPR
So will it work if, when I go to solve for [A]{x}={B} I change it to {x}={B}/[A]^1?

#7




Re: Help on OPR and DPR
Perhaps I should ask a different question...
Ok, so if I take, for example, the TBA data from 2008's Suffield Shakedown and create matrix A based on the number of matches each team played on an alliance with each other team and matrix B is the total combined score of each of the alliances team x played on. I then took the inverse of A and found BA^1. So would this, then, be correct? Code:
Team # OPR 40 5.335839956 88 10.9064837 125 1.874189107 126 20.9022442 173 16.1766485 175 23.76233256 176 13.22479694 177 28.94649135 178 33.50075682 181 5.801247409 195 7.939442306 228 5.275340498 230 30.37857031 236 24.79561887 348 8.741658516 500 1.772256265 571 5.296173934 716 4.886654548 839 19.84073344 999 2.339548465 1027 15.69966416 1071 6.45134427 1099 3.094166838 1124 14.84119862 1373 13.59377354 1784 17.20806737 1991 12.38365654 2064 0.156682971 2067 4.862487992 2170 19.44734797 
#8




Re: Help on OPR and DPR
Quote:
Matrix A: you've got this: the (i,j)th element is how many times team i played with team j Vector S: This is a vector where the jth element is a sum all of team j's scores. Vector OPR: This, once solved for, is the OPR for each team. The i'th element is the OPR of team i. So you've just got to solve: A*OPR = S Which would result in: OPR = A^{1}S So yeah, I think your math is correct so long as by "matrix B" you meant "vector B". Last edited by Bongle : 02152009 at 09:31 PM. 
#9




Re: Help on OPR and DPR
If what you're calling a vector is what I'm considering to be just an nx1 column matrix where each line in this case is just a total score, then yes, I think "Matrix B" is "Vector B," though a confirmation would be appreciated. If that is the case, then I'd just like to say, WHOO!!! Because if I'm understanding you, then the worst part of setting this up should be over!
EDIT: I just looked up vectors, in which case, I've got it figured out. Thanks for checking my work over Bongle, as well as helping me get my terms straight. Now all I have to do is implement a system for it, which aught to be cake after all of this. Thanks again Bongle for helping me get things straight, and Martin for getting me going in the first place. I'll see you guys in Atlanta Last edited by Zholl : 02152009 at 10:46 PM. 
#10




Re: Help on OPR and DPR
Quote:

#11




Re: Help on OPR and DPR
Quote:
Anyway, I'll try and have a beta version of my system up by the end of the week for people to look at. That way I can maybe get some advice on how to tweak it. 
#12




Re: Help on OPR and DPR
Somewhat resurrecting a dead thread but.... Does the matrix on that sheet even work with Cholesky Decomposition? I entered it into Mathematica and an online calculator and both returned errors (possibly because of those zeroes in there...). If the reason is because of the zeroes, won't that not work because you're not going to be playing with every team and there will be some zeroes in the chart (then again, since I don't exactly understand how the decomposition works, I could easily be very wrong).
Also, for those using inverse matrices, what happens when the matrix does not have an inverse ? Don't think it'll happen, but, it's a possibility (btw the example on the posted sheet also does not have an inverse). Even better... If we're keeping track of relatively detailed robot performance anyways, does it even matter? Last edited by kirtar : 03082009 at 08:37 PM. 
#13




Re: Help on OPR and DPR
Quote:
I have been posting 2009 FRC results with OPR and CCWM at the link below. http://www.chiefdelphi.com/media/papers/2174 Starting from week 3, you can use it during each regional and just press one button to get updated OPR and CCWM information for that regional provided you have internet access. The source code to calculate OPR and CCWM is in there also. I don't invert matrix since it is not necessary. I use Cholesky Decomposition which is included with the source code. If you have any questions, please let me know. Ed 
#14




Re: Help on OPR and DPR
Quote:
Because of the way our matrices are assembled, as long as every team has played at least one match, the matrix is invertable. That is because the diagonal terms are the number of matches that team played, which is why OPR can not be calculated until you have some matches done. Otherwise you will have some zeroes at the diagonal terms and it will make your matrix become singular and can not be inverted. Ed 
#15




Re: Help on OPR and DPR
Ed, I don't have access to a computer with Excel at the moment, so I figure I might ask if you're referring to the 2009 or the 2008 Suffield Shakedown. I ran those numbers with the data on TBA for the 2008 Shakedown.
Oh, also, a note on how I'm running my calculations. In Excel, I created the matrix of the matches played with each team, took the inverse of it, and multiplied it by the total score vector as was my understanding and as Excel allowed. I have the file here on my thumb drive, so I've uploaded the spreadsheet here.It should be on a sheet named Match Matrix, I believe, though I don't know if the test matrix is in there. There should be vectors in there as well to enter the scores for OPR, the margins, and it should spit out WM and OPR next to them. I think I just used letters to label them, and can't remember using anything really obscure, so they should be easy to identify. If my test matrix isn't there, there will be an empty matrix for match data, and then it'll spit out its inverse next to it or below it. I've done both, and can't be sure which... If I've done something wrong, it'd most likely be in the math there, I'd think. 
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