Help on OPR and DPR

[Ed Law]

Originally Posted by Zholl

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.

Hi,

The data I used was from whatever link to TBA you had in your post so I think it is 2008. I would be glad to take a look at your spreadsheet and see what possibly could be wrong. I can output the matrix and vector from my program and compare to yours. It is getting very late here in Michigan and I need to get up in about 5 hours. I will look at it tomorrow. By the way, I saw that you downloaded my spreadsheet. The program is fixed now so the corrected week two data is available for you to download. Sorry for the inconvenience.

Ed Law

[kirtar]

Originally Posted by Ed Law

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

Ah that would be it. The matrix in the pdf has a team which has played no matches.

[Zholl]

Lol, yeah, I had that same problem. That's why I had to create a matrix from TBA data. Didn't stop me from running his example 8 different ways though.

Also, tracked down my test matrix for the Shakedown. I've attached it below if you'd like to take a look at what actually generated that data.

Suffield Shakedown Test.xls

[Ed Law]

Originally Posted by Zholl

Lol, yeah, I had that same problem. That's why I had to create a matrix from TBA data. Didn't stop me from running his example 8 different ways though.

Also, tracked down my test matrix for the Shakedown. I've attached it below if you'd like to take a look at what actually generated that data.

Attachment 7645

Hi,

I looked at your spreadsheet Suffield Shakedown Test.xls. I think you assembled your matrix A incorrectly. For example, the diagonal terms represents the number of matches each team played. They should all be 4. Team 126 and Team 181 did not play 9 matches. Also Team 40 never played with Team 173 so that term should be 0 but you have a 2 there. You must have entered the numbers wrong by hand.

I am attaching the matrix A and vector B. You can try it out and see if you get the same OPR number.

I also looked at your spreadsheet Scout_System_beta_v.5.xls. Even though I am already posting a similar one for everyone to us, I would strongly encourage you to continue to develop yours and customize it for your team. You will learn a lot from doing it. If you need any help or have any questions, just let me know and I will do my best to help.

Regards,

Ed Law

[Zholl]

Thanks Ed. So my question now is, should I have only based this matrix on the qualifying rounds? If so, I think that may have been my mistake....

[Ed Law]

Originally Posted by Zholl

Thanks Ed. So my question now is, should I have only based this matrix on the qualifying rounds? If so, I think that may have been my mistake....

Sorry, I didn't realize you were adding the elimination matches also. That explains why some teams had more than 4 matches. Can you try doing it with qualifying matches only and see if you get the same results as mine? You probably would. I think there were quite a bit of discussions a year ago about whether to include elimination matches into calculating OPR and the consensus on CD is not to include them. The reason is it will bias the results because some teams will have a lot more matches than others. I need to come up with a better explanation when I have time.

Ed

[Zholl]

Yeah, that's what I was starting to think. Well, this at least explains why my numbers weren't right. Thanks Ed. I'll run it again tomorrow and compare what I get with your data. Right now, though, I should probably go to sleep. Thanks again for your help

[Zholl]

Well, I just tested the numbers again, and they seem to match up with what you have Ed. There is only a very, very slight difference in a number of them, but it is incredibly minuscule (in the ballpark of 10^-14), so it shouldn't affect the numbers in any significant way. I've also figured out how to have excel rank everything, so I'll update the search on my system to include ranks as well as stats, and I'll make a few minor tweaks as well and should have it up here by Sunday.

Did I mention I have nothing better to do right now than to calculate these minuscule differences and make tweaks to the system while I watch recorded tv in the middle of the night?

[Zholl]

Ok, so to clarify one thing before I actually finalize this, low DPR is good, right? Since it's how many points a robot can be expected to contribute to the other team, I'm pretty sure that a low positive is good, a negative better, right? This should be the last question I have, since going through it the only other things I'm not entirely sure how to do I can look up on excel tutorials.

[Q. Sheets]

Originally Posted by Ed Law

Sorry, I didn't realize you were adding the elimination matches also. That explains why some teams had more than 4 matches. Can you try doing it with qualifying matches only and see if you get the same results as mine? You probably would. I think there were quite a bit of discussions a year ago about whether to include elimination matches into calculating OPR and the consensus on CD is not to include them. The reason is it will bias the results because some teams will have a lot more matches than others. I need to come up with a better explanation when I have time.

Ed

The better reason is that alliances can be "stacked" in eliminations... i.e. seed 1 picks seed 2, whereas in qualifying it's all random; one pairing could really help a team and the next could hurt them.


And for my question: What is the mathematical formula for CCWM?

[Zholl]

The way I've been doing it, which seems to work, isn't incredibly complicated. It's based off the equation [A]^-1[b]=[C]
[A] is the number of matches each team played with each other team. So make each column and row each team number in numerical order. At all of the intersections put the number of matches played by team x with team y. Any spot x,x will be their total number of matches.

[b] is the winning margin margin for each team in a collumn. I believe, and someone correct me if I'm wrong, that you take the average winning margin for this. I'm not sure on that off the top of my head though.

Take the inverse of matrix [A], multiply it by [b], and you should get a collumn with the CCWM of each team.