This book is great in teaching you how to create a P&L's and how to model a property mathematically.

If not, the leveraged option, (putting 20-25% down and financing the rest) is the mathematical answer to the question of which is better.

For a guy with an analytics education you seem to lack basic ability to crunch IRR, ROI, NPV, PB, and other financial concepts that help make decisions based on mathematics.

Everything else is just basic mathematical equations.So to get a good underwriting of a deal, you need to have true insights into the market conditions and factors that will impact the financial assumptions you input and ultimately the net underwriter result.

The difference between the average daily balance of the HELOC by depositing ALL your income into it - and using it as a checking account is what does the trick.The fundamental mathematical principle is not "paying extra on principal" it is REDUCING ACCRUED INTEREST - which results in more money going toward principal. 

Mathematically it would be better to ditch the lease and buy a good used car.Assuming you are keeping the car, then I see nothing wrong with converting the lease to purchase.

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.