Okay, so I'm no mathematics genius as you'll soon see, so don't know what to google for here, so thought I'd give you nice folks a try.
Imagine my Salesperson X has a 33% closure rate; i.e. from every 3 prospects they have, they turn one of them into a sale.
If I need Salesperson X to make 100 sales, I'd need them to have 300 prospects.
What I want to figure out is the formula I need to create to reach that conclusion from the (variable) closure rate.
Any guidance appreciated.
Cheers, D.
I assume here by "variable closure rate" you mean one where it could be different for each person.
For a closure rate $R_c$ and a required number of sales $S$, the required number of prospects is $$ P = \frac{S}{R_c}. $$ If Salesperson Y has a closure rate of $0.5$, or $50\%$, (so they close on half of all sales they attempt) and you want them to successfully close on 31 sales, they will need to attempt $$ \frac{31}{0.5} = 62 $$ prospects.
These numbers are true on average. If you want someone to close on $1$ sale and they have a success rate of $0.25$, then on average it will take $4$ attempts, but may take $1$ if they get lucky or an infinite number if they get very unlucky. Think of flipping a coin until you get a heads; sometimes you'll get it first time, sometimes it will take more attempts, but for a fair coin over enough trials it will take two attempts on average.
If you want to read up on the mathematics behind this then I suggest finding an introductory resource on the Binomial distribution. If you are happy doing some basic algebra or have studied a bit of statistics in the past (so are familiar with mean averages and standard deviations) it could be useful if you want to generalise these results.