[FTC]: Championship OPR?

[Ether]

Originally Posted by davidaustin

OK, thanks for helping me to understand this. I apologize for reporting those earlier results, which I have removed from this thread.

Here's what I am doing: N is the number of teams, and M is the number of matches.

--Form the 2MxN matrix A whose entries are zero except where A[2m+c][j] = 1 if team j played on the c (=0 for red and 1 for blue) alliance in match m.

--Form the 2M-dimensional vector S where S[2m+c] is the score of the c alliance in match m.

--We want to solve the overdetermined system Ax = S so we multiply by A^T to get

A^T A x = A^T S

--Write A^T A as L L^T using the Cholesky factorization so that we have

L L^T x = A^T S.

--We solve L y = A^T S and then L^T x = y to find x, which holds the OPRs.

Does this look correct? I'm not seeing the error in my code. Thanks again!

What you posted above looks correct, but the devil is in the details.

Post your A matrix and your S vector here and let me crunch the OPR. If I get the same result you did, then the problem lies in your processing of the raw data into A and S. If I get different result, the problem lies in your Cholesky processing.

By the way, if you are using Python, you can get the min L2 norm of residuals (least squares) solution directly from your A and S using np.linalg.lstsq(A,S), without forming and factoring the normal matrix A'A.

[davidaustin]

I found a mistake in my code and generated some new results. My average OPR is now the average alliance score. However, my results don't agree with those posted above.

I've attached my A and S matrices along with the ordered list of team numbers.

Thanks for your help with this. I'd really like to understand this better. I'll also look at numpy's least square result.

[Scott_4140]

The power scores I posted are not based on the same FRC style OPR calculation you're trying to implement. I would not expect them to be the same. I am curious to see how they compare.

[Scott_4140]

Based on the data you have in Matrix S, it appears you are using the scores that include penalties. If you want, I have a breakdown of the scores by Autonomous, TeleOp, End Game and Penalties. I can deduce a further refinement of End Game scores to identify which Alliances received credit for a Balanced Pendulum, Flag Raised to Low or High level, and Single vs. Double Hangs.

[davidaustin]

Originally Posted by Scott_4140

Based on the data you have in Matrix S, it appears you are using the scores that include penalties. If you want, I have a breakdown of the scores by Autonomous, TeleOp, End Game and Penalties. I can deduce a further refinement of End Game scores to identify which Alliances received credit for a Balanced Pendulum, Flag Raised to Low or High level, and Single vs. Double Hangs.

Can you send me the breakdown of the scores? That would give a better comparison of our results.

[Scott_4140]

They are from the Yellow Alliance Live. Not sure if they are still available.

Here's a .txt of the detailed match scores.

[Ether]

Originally Posted by davidaustin

I've attached my A and S matrices along with the ordered list of team numbers.

OK, I crunched those numbers with Octave.

Here's the Octave script I used:

format long
A = load('A.txt');
S = load('S.txt');
T = load('teams.txt');
x = A\S;
Tx = [T,x];
save Tx.txt Tx;

Attached is the output list of Team OPR's generated by the above script using your data.

Thanks for your help with this. I'd really like to understand this better. I'll also look at numpy's least square result.

Glad to help. From what I can see, I think you understand it pretty well so far.

When you have a set of overdetermined linear equations:

[A][x]≈[b] (notice the approx equal sign "≈" because there is no exact solution since the system is overdetermined)

...if you multiply both sides by [A]^T, you get:

[A]^T[A][x]=[A]^T[b] => [N][x]=[d]

...which is a set of n equations in n unknowns, where "n" in this case is the number of columns in [A] (the number of teams).

Notice the "≈" sign has changed to "=" since the system now has an exact solution. The above are called the normal equations (of the overdetermined linear system), and solving these normal equations for [x] gives the least-squares solution to the original [A][x]≈[b] problem.

But if you're using a language with a linear algebra library, you can solve the overdetermined [A][x]≈[b] for the least squares solution directly. In Octave the syntax is called "left division" (x = A\b). In Python you use np.linalg.lstsq(A,b).

Be aware that "least squares" (min L2 norm of residuals) is only one of many possible "best fit" solutions to the overdetermined system [A][x]≈[b].

For example, there's the "Least Absolute Deviations (LAD)" solution (min L1 norm of residuals). And there are other "robust regression" methods.

[davidaustin]

Thanks for sending that. It looks like we're in sync now. Yay!

[davidaustin]

Here's what I have for the OPRs. After the team number follows the OPR, calculated without penalties, then autonomous, teleop, and end game.

Edison:
2753 217.8 63.0 71.9 83.0 Team Overdrive
4251 204.8 64.4 48.0 92.4 Cougar Robotics
4347 192.3 52.4 64.2 75.7 Nanogurus
5069 187.6 66.0 55.8 65.8 Robogamers
724 183.2 53.3 64.2 65.7 RedNeck Robotics Wun
7023 182.9 61.7 46.9 74.3 HexaSonics
5939 178.3 55.5 58.1 64.6 Team AFOOFA
6433 172.3 38.4 73.1 60.8 Neutrinos
8347 168.6 41.1 60.5 67.0 The BOLTS
6337 163.5 34.9 56.9 71.7 Metal Marauders
6424 161.6 45.3 69.4 46.8 Oly Cow
92 160.2 35.8 57.5 67.0 Junior Bomb Squad
5035 155.1 35.2 50.3 69.6 Wired
577 154.5 47.2 45.5 61.8 Wreckers Robotics
3486 154.3 44.0 48.3 61.9 Techno Warriors
3846 153.6 49.7 54.0 49.8 Maelstrom
4318 150.4 31.8 61.4 57.2 Green Machine
5414 149.7 53.8 45.6 50.3 Techie Tornados
3550 141.8 52.5 39.5 49.7 Beta
4029 141.1 34.0 46.4 60.6 2 Bits and a Byte
1369 134.5 37.6 46.2 50.7 Minotaur
4278 133.4 30.2 50.4 52.8 De.Evolution
3785 132.5 42.4 31.7 58.4 Beastie Bots
5501 132.3 49.9 36.9 45.6 USS Enterprise
4535 131.8 29.6 52.2 50.0 RedNek Robotics Too
5421 130.8 27.9 39.0 63.8 RM‐ed and Dangerous
5931 130.5 21.7 38.4 70.4 Cru‐Botics
6272 127.1 38.7 34.3 54.1 Iron Eagles Prime
4112 126.0 29.2 39.4 57.3 Warriors
3708 124.3 28.0 42.0 54.2 Iron Eagles Optimus
5140 123.9 26.9 44.2 52.8 WACO Aerobotics
4847 123.7 41.7 37.8 44.1 CHROME
5220 121.9 43.1 36.2 42.6 The RoboKnights
4220 121.3 23.0 48.4 49.9 Landroids
3162 118.5 46.6 27.4 44.5 HHS Gearheads
4140 117.9 51.7 33.4 32.9 Fish in the Boat
7440 114.1 42.3 27.1 44.8 Wingus and Dingus
5114 111.5 23.9 35.0 52.6 The Knights Who Say C
4982 111.2 22.1 34.3 54.7 Café Bot
4965 101.6 42.1 22.1 37.4 Animatores Romani
4150 97.7 31.1 34.9 31.7 Dark Matter
327 95.8 28.5 40.3 27.1 Gamma Factor
5977 95.3 40.5 31.7 23.1 Cyberswat
365 95.0 23.6 33.9 37.5 MOE FIRST
8360 91.8 22.5 26.9 42.3 Rawabi
7712 91.3 30.1 25.8 35.4 H& M Robotics Club
6109 91.3 17.6 40.4 33.3 Punabots
5609 89.4 20.7 21.8 47.0 Ciberbots
6100 89.1 41.6 20.8 26.7 Chariots of Fire ‐Black
7591 86.0 31.2 26.5 28.3 Voltage of Imagination
3595 85.6 35.8 19.3 30.5 Schrödinger's Hat
4625 83.9 28.3 24.6 31.1 Kings and Queens
6024 83.6 36.2 18.6 28.8 The Enterprisers
6002 78.0 54.8 5.6 17.5 Basilisks
4092 66.5 18.8 30.4 17.4 Nanites
8356 58.7 16.9 10.4 31.4 LET Lead out your Engineering Talent
8359 57.8 17.6 6.2 34.0 French Toast Mafia
8357 56.6 23.9 6.1 26.6 Desert Matrix
8336 54.1 11.8 13.5 28.8 Mars Gypth
8352 51.4 26.6 -0.5 25.3 Prime Numbers
4134 44.9 16.2 13.0 15.7 Wrench in the Works
8207 44.6 30.2 4.8 9.7 CanaBot
8349 25.5 15.9 -1.0 10.7 I love super big white cat
8337 24.4 -3.4 5.3 22.4 BaCoNeers

Franklin:
7013 206.8 51.3 67.2 88.3 Hot Wired
6253 191.1 71.5 53.8 65.8 Avalanche
5257 188.7 48.6 58.4 81.7 Eagles Robotics XPerience
8221 185.8 47.7 57.3 80.8 Cubix
3409 176.1 45.9 51.2 79.1 Astromechs
4250 172.3 47.9 60.9 63.5 LIGHTSABERS
5026 170.2 55.7 52.2 62.3 Tesla Coils
4507 167.9 57.2 34.5 76.2 Robo Chargers
7907 167.2 56.9 42.9 67.4 Stark Industries
5309 164.5 56.5 49.2 58.7 Plan B
4997 164.3 54.3 46.6 63.4 Masquerade
4240 164.0 48.9 37.8 77.3 4‐H Techno Clovers
7398 162.2 38.3 45.6 78.2 BLUE CREW
7149 151.3 60.6 39.2 51.5 Enforcers
6299 148.2 31.6 58.3 58.3 ViperBots QuadX
4106 148.1 34.2 54.2 59.7 Supposable Thumbs
5096 147.9 51.3 46.7 50.0 Monkey Madness
6081 147.7 48.4 43.6 55.7 I2R Robotics
6508 147.2 47.8 46.1 53.4 Radioactive Raiders
4530 142.8 62.3 51.1 29.4 Infinite Resistance
4855 141.6 45.8 40.7 55.1 Batteries In Black
5661 138.7 38.4 46.8 53.5 SHPE Wolves
5555 136.8 58.2 53.0 25.7 Option 16
5279 134.9 35.5 37.1 62.2 Positrons
4211 133.5 40.5 42.4 50.6 The Bombers
5452 129.8 52.8 38.0 39.1 Robots to the Knee
2888 129.4 43.3 43.5 42.7 Oddly Charged Particles
7129 127.6 38.7 39.2 49.8 Robo Raiders
5815 126.0 28.0 43.4 54.6 Disgruntled Robots
4443 125.6 38.3 47.5 39.8 Sock Monkeys
6451 123.1 28.7 28.0 66.4 Tarpon Robotics
5169 123.0 34.6 44.2 44.2 Watts Up?
8338 122.7 19.3 45.5 57.9 Shatterdom
4999 122.0 38.0 43.9 40.1 Imagine It
6051 122.0 51.6 29.6 40.8 Quantum Mechanics
2844 121.3 27.3 34.1 59.9 Valley X
248 120.8 23.8 28.1 68.9 Fatal Error
8231 113.4 24.1 39.7 49.6 Skyhawks
5972 107.3 47.5 21.8 38.0 Patronum Bots
8348 107.2 30.9 36.3 40.0 Crazy Shooter
7817 106.9 51.6 36.2 19.1 TaterBotz
8361 106.5 28.2 49.6 28.7 Garrins Metal‐lics
6055 101.1 33.6 26.2 41.3 Gearticks
4961 100.9 30.5 38.8 31.6 Robo Raptors
38 100.9 36.3 28.6 36.0 Pakbots
8350 99.3 39.3 19.8 40.1 Don't Throw Block
4745 92.6 26.2 30.7 35.7 Orozco's Army
5009 92.0 16.0 22.6 53.5 NET ZERO
3141 92.0 11.6 46.3 34.1 Bears
5843 91.9 33.9 34.0 24.0 AutoVortex
5604 90.9 23.4 32.8 34.7 Thunderbots
4924 90.5 24.1 17.3 49.1 Tuxedo Pandas
4475 89.7 8.2 44.6 36.8 Purple Reign
3781 85.3 10.7 22.7 51.9 Westlake Pi‐Rho Maniacs
8339 78.8 17.0 37.5 24.3 Galaxy Robo Techs
6935 78.6 31.5 25.1 22.0 Paradox
6221 78.0 23.8 14.4 39.8 Panther Bots
5875 77.6 29.2 9.7 38.7 GENIUS
101 74.1 20.1 12.2 41.9 The Indivisibles
8351 69.1 3.8 34.2 31.2 Siberian Beast
3954 62.6 10.7 22.2 29.7 Watt's Up
4287 50.1 24.1 10.7 15.3 Red Meteors
4107 37.4 24.8 7.7 4.9 Mohon Bots
4183 33.7 19.6 2.7 11.4 ICEBREAKERS