Adjusting teams ratings by opposition level

[stringerbell]

I'm trying to implement Ken Pomeroy's method and adjust offensive and defensive ratings based on opposition, but I'm stuck when trying to get the adjusted indices. To get an initial understanding, I thought about a 2 team-one-game league. So, I have tried to solve the following system:

AOE_i = OE_i * Avg(OE) / ADE_j

ADE_i = DE_i * Avg(DE) / AOE_j

for i, j = 1,2

But this is an undeterminated system: I can arbitrarily choose, say, AOE_1. ¿Am I missing some other conditions on what these parameters get pinned?

Thanks.

[sndesai1]

is that a circular calc? does kenpom use an iterative approach?

[stringerbell]

is that a circular calc? does kenpom use an iterative approach?

I don't know how he calculates it. I think he never explained his method.

[DSMok1]

I'm trying to implement Ken Pomeroy's method and adjust offensive and defensive ratings based on opposition, but I'm stuck when trying to get the adjusted indices. To get an initial understanding, I thought about a 2 team-one-game league. So, I have tried to solve the following system:

AOE_i = OE_i * Avg(OE) / ADE_j

ADE_i = DE_i * Avg(DE) / AOE_j

for i, j = 1,2

But this is an undeterminated system: I can arbitrarily choose, say, AOE_1. ¿Am I missing some other conditions on what these parameters get pinned?

Thanks.

If you have a single game, by definition there is now way to develop adjusted ratings. As you mentioned, it's indeterminate--all you know is how much one team did better than the other, and have no idea whether you've got GSW vs. SAS or Philly vs. the Lakers.

The determinacy comes from having way more games than variables, that, when solved together, will provide a determinate answer.

Does that make sense?