I work for HR department of a company.
Every year, different managers evaluate different employees.
We are trying to upgrade our evaluation system to make it fair for all.

Here is our current system:
- Our company has many branches.
- For every branch, 3 different managers in that specific branch would evaluate employees in that branch. Therefore, an employee is only evaluated by the managers in that specific branch. Also, managers in that branch only evaluate employees in that specific branch. So there is no overlap among the branches.
- For every branch, 3 different managers evaluate employees within that branch. Perfect score is 100.

The problem we encountered is this.
- Every manager has different scoring tendencies.
Manager A in branch A would just give out relatively high scores to everyone. For Manager A in branch A, 100 would be good, 90 would be average, and 80 would be poor.
However, for Manager B in branch B, 80 would be good, 70 would be average, 60 would be poor.
Therefore, employee A in branch A with a "poor" score of 80, gets better evaluation than employee B in branch B with an "average" score of 70.

It would be better if we just allowed managers to evaluate the employees with categories "good, average, poor". However, we must keep the "scoring scheme" because we need to rank the employees every year.
So, employee A, who gets lucky, ends up getting a better score than employee B, although employee B is a better employee.

In order to avoid this bias, one of us came up with this equation.

Adjusted score = original score given out by a specific manager + (average of all employees in the company - average of scores given out by that specific manager).

Let's say there is an employee C and D in different branches.
Manager A gave C 70. Average of all employees is 70. Average of scores given out by Manager A is 60. Then, adjusted score of employee C is 80.
Manager B gave D 70. Average of all employees is 70. Average of scores given out by Manager A is 80. Then, adjusted score of employee D is 60.
Even though original scores of employee C and D are equal, adjustment gives C 80, and D 70, which means employee C is a better employee than D.

Would this method be an improvement? and if you could statistically say WHY.. that would be very much appreciated.. thanks for reading this long post.