I have been in the rental business 15 years and I can prove to you mathematically you will come out ahead just putting cash in reserves.

These might not be the Dave Ramsey recommended routes but mathematically it can be shown that historically the S&P route will provide significantly better ROI than paying down a conventional owner occupied home loan.  

"Regression to the mean" is the mathematical term.Fix and flipping, OTOH, is a job.

@Bill Bonds found a website that shows more of the mathematical way of answering your questions.

The result is a file that acts as a mathematical sand-table, where you can present data in any way you wish - any way folks should check it out - gotta go, takings the kids ice skating.

It was not a mathematical cost calculation like footings, framing, roofing, etc. 

Hey,a very interesting historical analysis and model of rents in San Francisco (with data source on GitHub).For numerical guys such as @Brian Burke, @J. Martin, @Minh Le etc etcSome excerpts:"Overall [rents], they wen...

Einstein also believed that the formula for compounding interest was the greatest mathematical discovery of all time. 

Let's try a mathematical simulation to see if @Scott Trench is wrong.Lets say you have $20,000 and buy a $100,000 rental property using banks money.

I'm an engineer not a mathematician so this may not be the most technical of descriptions, but should convey the general idea....in layman's term: the mortgage payment is mathematically determined based on your interest payment being logarithmic (i.e. it reduces each month) and your principal payment being exponential (it increases each month) such that the total payment stays the same.