We operate a small call center with multiple "levels" of call
distribution (queue). We are assessing the performance of each
salesperson in the queue in an effort to determine gross sales dollars
per hour of "pre-sale opportunity call". This will result in a ratio
describing "opportunity utilization" - how well the person takes
advantage of opportunities presented. This ratio will then determine
the percentage of a sales pot the user receives when a sale is made.
The problem as I see it is that we receive multiple types of calls and
calls are not distributed evenly among users - they are distributed in
a tiered fashion. Complicating this, the length of the call is
different based on the type of call (explained below), causing an
unfair disparity between users.

First, let me describe the components and then you'll more fully
understand my question.

The Call Queue
David, the first person in the queue will get every call when he is
available (not currently on a call). Andrew, the second person, is on
the "second level" in the queue and will receive an inbound call when
David is on a call already. Jason, the third person in the queue will
receive a call when both David and Andrew are on calls AND when the
caller has been holding more than five minutes.

Call Types
Calls are "typed" based on the end result and what we know about the call.
(1) Pre-Sale: A call is considered a "pre-sale" call if the caller ID
for the call is the same as the caller ID for a sale made in the
future. The average time spent on a "pre-sale" call is 7.5 minutes.

(2) Unknown: A call is considered "unknown" if the caller ID does not
have a future reference to a sale or quote and is not a "known
call".The average time spent on a "pre-sale" call is 4.5 minutes.
These calls include wrong numbers, hang ups, telemarketers, customers
looking for products we don't sell and opportunities that we didn't
close well. While the conversion to a "pre-sale" call is highly
dependent on the skill of the salesperson, at this time we receive
approximately 3 unknown calls for every "pre-sale" call.

There are two more classifications of calls that are not relevant to this question:
(3) Post-Sale: A call is considered "post-sale" if the caller ID is
linked to a sale and the call occurred after the sale.

(4) Known: A call is considered "known" if the caller ID is linked to
an existing order or quote.


The question is: Is the distribution of "unknown calls" and "pre-sale
calls" statistically even between David, Andrew and Jason (1st, 2nd
and 3rd tier queue users)? In other words, will the percentage
distribution between David, Andrew and Jason of unknown vs. pre-sale
calls be even?

Pay all your staff well and stop looking to use maths to give the
excuse for pay differentials.  Train your staff well, treat them with
respect and provide services that are invaluable to your customers. 
That will improve the sales ratios of your employees.  Not the type of
discrete random variable that models telephone queues.

I agree with the above comment.  
If you used a system to distribute the "pot", it must be varifiable
and justifiable to those involved.  Basing it on the time for
different types of calls could lead to hurried responses to non-sale
calls, which would not be good for customer relations.  This would
still be the case if you had a telephone system with "press one for
sales", "press two to trace shipments" etc. that just let the caller
define what he wanted, but still routed the calls in the way you
describe.
Your staff should treat each call as a potential "pre-sale" call.