RyuAqua wrote:Dwight: with people such as Coach C and myself looking back to they days of an objective (if flawed, as Byko's was) ranking model for teams, is there any way one could engineer (and run) a new nationwide set of team rankings from the statistical stuff you've been working on? Or would that require a completely different approach, since this model only works for an individual question set?
So as I understand it, Byko's model (and the KRACH model it derives from) and NAQT's model (and the ELO model it derives from) both use only
W-L record and compute rankings recursively that way. What this model does is use actual question-conversion statistics to generate a theoretically-more-real model of how teams that don't play each other might fare in a real game.
We can use a modified KRACH rating. Let's start with every team having a value of 1000, because that's a nice number. If we input the "expected long run" W-L matrix into the KRACH ratings, we should get new ratings. (If we want, we can then run the KRACH ratings for each individual tournament on that packet set, using actual W-L data.) Use these ratings as the initial conditions to the KRACH rating of the next packet set, with "expected long run" W-L matrix on a new set (let any teams with no data have a value of 1000).
We can do the exact same thing for the ELO ratings - start every team with a value of 1000 (or 1200 as in NAQT's model), input the "expected long run" W-L matrix into the ELO ratings, compute new ELO ratings (and then modify with actual tournament W-L data, if preferred), input another tournament's "expected long run" W-L matrix (and actual W-L data, if preferred) into the ELO ratings. Actually, with ELO, we can also use the "Monte Carlo simulation" win percentages as well, which is likely going to give more accurate results at the cost of much more computation. The other thing that the ELO ratings allow us to do is assign different K-values (a modifier that says how much a team's ranking increases/decreases) to different tournaments - for instance, "regular" sets could have K-values of 32, while "novice" sets could have K-values of 16.
While I'm at it, one thing I'd love to see is NAQT using the "expected long run" model (or some variant of the "Monte Carlo" model) on the HSNCT prelim statistics to seed teams for the HSNCT playoffs, rather than their current use of PP20H that does not take schedule strength into account. I don't know exactly how feasible this is, though.