[Ether]

Originally Posted by sirwin

I'm intrigued. I'm relatively new to FIRST...

Welcome!

so bear with me.

Not to worry.

OPR refers to offensive power rating, correct?

yes

You're referring to using the Choleski decomposition

I did not explicitly mention Cholesky, but yes that factorization can be used to factor the Normal Equations matrix

to produce an estimate of how many points any single team should be expected to contribute to an alliance score, based on past performance?

Yes. A very rough estimate, since the model assumptions are not very realistic.

There's an R package that supposedly does this -- it's called optR and it's available on the CRAN repository. It has a function called choleskilm that should do the trick.

For small matrix associated with a single event

Of course the raw data has to be shaped into a positive definite matrix first.

... AND the Aij design matrix (attached to post9 in this thread) must be read by R before it can be used to compute the normal equations matrix N.

The size of the matrix could be a problem.

A big problem

The description that I found on this method for calculating OPR focused on using this method for data from a single competition -- generally no more than a 100 x 100 matrix.

Yes.

But 2700 x 2700?

Full-matrix Cholesky is roughly proportional to O(n^3).

(2696/40)^3 = 306182

Big problem. Unless you use sparse matrix algorithms.

I'll experiment with smaller data sets over the weekend and see if I can figure out what the computation time will be.

Please let us know what you find out