While your stated goal of promoting equity and fairness in the officials assigning process is a good one, it will take a whole lot more than just getting a look at the master schedule.
Speaking as a person that was an assignor for several years, I will freely admit that my master schedules would show some officials with many more assignments than others. I will also tell you that the master schedule at the beginning of the season looked a whole lot different than the one at the end of the season.
A big reason for that is availability. If I had an official that was retired, worked from home, or had an otherwise flexible work situation and had shown me in the past that he would work games on short notice, that was most likely my first telephone call when a new game came on the schedule or a game was rescheduled, etc.... I'm not going to spend an hour on the phone when I can get the game covered in five minutes.
I'm also going to consider the contest itself. Do I want a new official on a potential high tension rivalry game? Of course not. I made the effort to watch and work with as many of the officials in my association as possible so I would know who the stronger as well as weaker officials were. This doesn't mean that the weaker officials intentionally received fewer assignments, but I am going to put the best officials available on the contests when necessary.
One of my goals as an assignor was to be fair and equitable and try to evenly spread out the assignments amongst the association membership. However, if you were to judge soley based on the master schedule, you would not think that goal had been met.
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It's what you learn after you think you know it all that's important!
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