The season is 186 days long.
This is how I did the math:
- NHL Salary = N
- AHL Salary = A
- Minimum Guaranteed Salary = M
- Percentage of the Season spent in the NHL = P
- Percentage of the Season spent in the AHL = 1-P
A player's total compensation is the amount earned in the NHL plus the amount earned in the AHL.
NP + A(1-P) = Total Compensation
To find the maximum percentage of the season that can be spent in the NHL for "free", we substitute in M for the Total Compensation. We can simplify the equation like so...
NP + A(1-P) = M
NP + A - AP = M
NP - AP = M - A
P(N - A) = M - A
P = (M - A) / (N - A)
Substitute in Rinaldo's actual numbers and solve for P: M=$225,000, N=$700,000, and A=$175,000 ...
P = (225-175)/(700-175) = 50/525 = 0.0952 = 9.52%
That means he can spend 9.52% of the season in the NHL (17.71 days) and make the same as his minimum guaranteed salary.
To check our work, plug the numbers back in to the equation and solve for M:
700,000(0.0952) + 175,000(1-0.0952) = 66,666.67 + 158,333.33 = $225,000.
EDIT: gvitaly, different method, same result.