Profit Sharing without a Cap

I am not sure what you mean by "a cap"
It seem to me that the amount to be distributed must not total more than the 15%, thus a "cap" seems to be inevitable

There is a cap to the pool of money, but not to the individual. Usuall ypu wpuld have a target incentive per person - say 20%. So the most a person making 100 grand could get is around 20 grand. Often in plans it would look like this:

(100,000 × 20% cap) x 0 - 120% for group performance x 0 - 120% for individual performance.

If I don't have that 20% target incentive, is there a mathematical way to do the above calculation?

"There is a cap to the pool of money, but not to the individual"
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If there is a cap to the pool there MUST be a cap to the individual. Furthermore if, for example, there are 30 people and
and 4 of them earn 25% of the pool, there is nothing left for the other 26 no matter how deserving they are.

You probably have some heuristics and concrete use case scenarios that you would like to model. If you could post a few examples of how you would distribute the pool , then we could try to help you come up with a model that formulates your ideas .

Each employee's share should be established by taking into account their job level (the more they earn the more they are entitled to), the performance of their area (the better their area does the more they are entitled to) and their individual performance (the better they do the more they are entitled to).

Employee 1:
Makes 75,000
Her area achieved 100 of target so is entitled to full area portion profit sharing
Her individual performance was a 2 out of 5, so she is entitled to less profit sharing

Employee 2:
Makes 40, 000 so is entitled to less profit sharing than Employee 1
His area exceeded projections so is entitled to more profit sharing for area portion.
His individual performance is a 4 put of 5 so is entitled to more of the individual portion of profit sharing

Employee 3:
Makes 100,000 so is entitled to more profit sharing than 1 or 2
His area missed it's target so he receives a lower share of the area portion
His individual performance is 3 out of 5 which is average so he receives an average portion of the individual profit sharing share

This all needs to fit into the enveloped of 15% of profits before tax on all profit after the first 0.5% profit.

Thank you!

If initial entitlement is based on salary as the indication of higher job level, then you could do what we did.  You start with a max percentage say 15%.  If these person is upper management, it could be 30%.  In other words, you can use a flat percentage that automatically increases those with a higher base but then make higher targets for executives, et cetera to further segment high performers.

We then took each of the buckets and assigned their max.  Taking 15%, it would be 5% per bucket.
You then align each number of their target with a percent payout (e.g., 1 - 7, must hit a 3 before you get 1% and increase by 1% as you go up)
If employee hits 7, they get 5%.
If company profits exceeds target levels, employee gets appropriate percentage of that 5%.
If employee performs high, they get 5%.

You can make all three contingent on a base profit of the company to make sure you are not paying out at the detriment of staying in business (they would rather have a job than a bonus if they are honest with themselves) but as you can see it creates a natural spread of benefits based on performance.

Now same results for a manager whose maxes are 7.5% or 10% can earn up to 30% bonus versus another employee who earns 15% total.

I hope that makes sense.

Based on the way you laid it out above, you could just do your number system but just have a multiplier for employees that should get more like my solution above where you increased percent for some individuals, so you could have number go 1 to 7 but then 4 to 10 for others.  At the end you will have the total number earned by all employees.  Take this sum and divide $10M to get award per point, then multiply that number times each individual's points to get their portion of the $10M.

This is a crude spreadsheet but hopefully it helps clarify the solution suggestion with the point system you have (at least as I understood it).  I used 1-7 in first bucket to represent you first measure, 4's in second bucket to represent company performance but could be different if you assign different value by region, third bucket is the individual performance review then I added fourth bucket to break tie between two employees who both do well but one is paid more per your examples.  Kept this fourth bucket a simple divide salary by $10K to get an integer.  Taking the sum of all the results, I find a dollar amount something like $17K that I then multiply for each employee.  As you see there is no cap on an employee based on percentage of their salary but ensures it is within your $10M available.
EE-Profit-Share.xlsx

I would say that the real problem is solved and that any modifications are due to differing objectives / definitions.

Agree.  Love your quote by the way.  Hope my post came across that way.  I misinterpret perfectly requirements all the time, coming up with really cool solutions and proud of myself only to be told no we want X even though we said Y.  The claim is IT people speak a different language, so it always is good start out with a good working definition.

Take care, Fred, Laura, et al!

I can't tell you how helpful the two of you have been. Thank you so much!!

You are very welcome!  We get very excited about getting bonuses. *laughing*

Thank you!  Now and then even a typo becomes a quoted phrase.  So I get no credit, just my "all thumbs" fingers!!

Ha! Yes! Of course. And I will obviously put you in at the top level for individual performance!