Incorporating Opposing Alliance Information in CCWM Calculations

[Ether]

Originally Posted by wgardner

I'm hoping to get the match results (b with red and blue scores separately) for other 2014 tournaments to see if this is a general result.

I wrote a script last night to download all the 2014 match results from TBA and generate Aopr, Awmpr, bopr, bccwm, and bwmpr for all the 2014 qual events. I'll post them here later this morning.

[Ether]

Originally Posted by Ether

I wrote a script last night to download all the 2014 match results from TBA and generate Aopr, Awmpr, bopr, bccwm, and bwmpr for all the 2014 qual events. I'll post them here later this morning.

Make sure to read the README file.

[wgardner]

Iterative Interpretations of OPR and WMPR

(I found this interesting: some other folks might or some other folks might not. )

Say you want to estimate a team's offensive contribution to their alliance scores.

A simple approach is just compute the team's average match score/3. Let's call this estimate O(0), a vector of the average match score/3 for all teams at step 0. (/3 because there are 3 teams per alliance. This would be /2 for FTC).

But then you want to take into account the fact that a team's alliance partners may be better or worse than average. The best estimate you have of the contribution of a team's partners at this point is the average of their O(0) estimates.

So let the improved estimate be
O(1) = team's average match score - 2*average ( O(0) for a team's alliance partners).

(2*average because there are 2 partners contributing per match. This would be 1*average for FTC.)

This is better, but now we have an improved estimate for all teams, so we can just iterate this:

O(2) = team's average match score - 2*average ( O(1) for a team's alliance partners).

O(3) = team's average match score - 2*average ( O(2) for a team's alliance partners).
etc. etc.

This sequence of O(i) converges to the OPR values, so this is just another way of explaining what OPRs are.


WMPR can be iteratively computed in a similar way.

W(0) = team's average match winning margin

W(1) = team's average match winning margin - 2*average ( W(0) for a team's alliance partners) + 3*average ( W(0) for a team's opponents ).

W(2) = team's average match winning margin - 2*average ( W(1) for a team's alliance partners) + 3*average ( W(1) for a team's opponents ).
etc. etc.

This sequence of W(i) converges to the WMPR values, so this is just another way of explaining what WMPRs are.