An improvement to OPR

[RyanCahoon]

Originally Posted by Frenchie461

This should yield an OPR matrix containing complex entries, which theoretically should have a least squares average for both teleop and auton.

Originally Posted by SoftwareBug2.0

What advantage does this have over simply calculating independently with just auto scores, and then just teleop scores, and then just climb scores?

Since the OPR calculation boils to down to

P = (A^-1) * S

where P is the OPR, A is the binary matrix denoting teams in each alliance and S is the alliance scores, then Frenchie461 is essentially advocating

Pt + Pa*i = (A^-1) * (St + Sa*i)

and since matrix multiplication is distributive

Pt + Pa*i = (A^-1) * St + ((A^-1) * Sa)*i

So you'll end up with the same result as calculating each OPR component independently. You'll get least-squares best fit for each component (as you would otherwise), but there won't be any additional interaction gained between them. This makes sense, because the least-squares fitting part of the operation happens when taking the inverse of A, and isn't affected by the value of S (whether real or complex) that it is post-multiplied by. Performance-wise, I would guess they would take about the same amount of time, assuming you're not re-calculating the value of A^-1 when doing the calculations independently.



note: the inverse operation written ^-1 above becomes the generalized inverse for non-square cases of A

[efoote868]

I'm not sure how this is an improvement; your code might be more concise but only if you're working with a computational package like MATLAB.

[Frenchie461]

Originally Posted by efoote868

I'm not sure how this is an improvement; your code might be more concise but only if you're working with a computational package like MATLAB.

It's only an improvement so far as it's more data than most teams usually compute, and it should be computationally faster than a pair of OPR calculations. Hypothetically, let's say that OPR is a O(N^3) operation, with this method it's N^3 to find auton and teleop rather than 2(N^3).

[Ether]

Originally Posted by Frenchie461

it should be computationally faster than a pair of OPR calculations.

In the formula for OPR, namely [A][OPR]~[SCORE], [OPR] and [SCORE] need not be vectors - they can be matrices.

So instead of [OPR] being a Nx1 column vector, it can be an Nx2 matrix... and [SCORE] can be a (2M)x2 matrix.

The first column of [OPR] and [SCORE] can then be for TeleOp, and the second column for Autonomous.

This can be extended to any desired number of columns. For example use 4 columns for TeleOp, Autonomous, Climb, and Foul points.

Adding extra columns to [OPR] and [SCORE] increases the computation time only minimally, since the lion's share of the computation is spent factoring [A]^T[A].

[Siri]

Originally Posted by Ether

This can be extended to any desired number of columns. For example use 4 columns for TeleOp, Autonomous, Climb, and Foul points.

Minor detour: does someone have comprehensive foul point data broken out from teleop scores? (because I would love them forever )

Other than that, it's a cool idea and would be a fun way to team the concept to new students around that level. In terms of data though, I don't know that it brings something new. It'd actually complicate my work to do it that way, because the matrix case Ether describes allows the simultaneous calculation of endgame OPR by the same method (i.e. it's not limited to 2, and we're looking for at least 3 basically ever year).

[AGPapa]

Originally Posted by Siri

Minor detour: does someone have comprehensive foul point data broken out from teleop scores? (because I would love them forever )

Other than that, it's a cool idea and would be a fun way to team the concept to new students around that level. In terms of data though, I don't know that it brings something new. It'd actually complicate my work to do it that way, because the matrix case Ether describes allows the simultaneous calculation of endgame OPR by the same method (i.e. it's not limited to 2, and we're looking for at least 3 basically ever year).

Ether has created a spreadsheet with all of the twitter data from every match.
http://www.chiefdelphi.com/forums/sh...t=twitter+data

It has everything you need.

[Ether]

Originally Posted by Siri

Minor detour: does someone have comprehensive foul point data broken out from teleop scores? (because I would love them forever ).

A few weeks ago I posted a least-squares analysis of foul points using Twitter data:

http://www.chiefdelphi.com/forums/sh...53&postcount=1

As with any analysis using Twitter data, caveat utilitor.

[Siri]

Originally Posted by AGPapa

Ether has created a spreadsheet will all of the twitter data from every match.
http://www.chiefdelphi.com/forums/sh...t=twitter+data

It has everything you need.

Originally Posted by Ether

A few weeks ago I posted a least-squares analysis of foul points using Twitter data:

http://www.chiefdelphi.com/forums/sh...53&postcount=1

As with any analysis using Twitter data, caveat utilitor.

Sorry, I should have been more specific about comprehensive (Twitter this year is missing a good chunk of MAR data). Thank you though, you're correct, I'll use this. Awesome analysis as always, Ether. Thanks!

[/and now back to your regularly scheduled thread]