Incorporating "gamestate" into APM/RAPM, design matrix ?s

[A Gravity Well]

Performed a "test" running two ridge regressions of the season to date

Regression one:
Each row is one game
Y = (home margin - away margin)
X are the whole teams rather than their offensive and defensive halves. 1 for home, -1 away, and HCA always set to 1.

Regression two:
Each row is one team's possessions in one game
Y = offensive rating of the team on offense
X are teams split into offensive and defensive halves and are assigned 1 for their offensive unit if on offense and -1 for their defensive unit if on defense. There are offense home court advantage and defense home court advantage columns: if the home team is on offense, HCAo is assigned a dummy of 1 and HCAd is assigned a dummy of 0. If the home team is on defense, HCAo is assigned a dummy of 0 and HCAd is assigned a dummy of -1. The sign of the present HCA column will always match the sign of the home team's present unit and will always be signed opposite of the away team's present unit.

Results:
The sum of the results for each team's offensive and defensive half from regression two were almost identical to each team's whole return from regression one.
Regression one gave zero point repeating zeroes for the value of HCA, but its intercept was 1.36, and the total of each half of HCA from regression two was 1.35.

Is it wrong to conclude that regression one and regression two are functionally equivalent? Regression one would use rest/gamestate columns as wholes, no halving, with 1/-1 for home team/away team "parameters", and a (home team - away team) result vector. Regression two would split rest/gamestate columns into two halves, with 1/-1 for offense/defense parameters. The sign of the present HCA column will always match the sign of the home team's present unit and the home team's present rest/gamestate parameters and will always be signed the opposite of the away team's present unit and conditions.