Mathematical fact.  

Now their numbers are incorrect.In either event, the value of your mathematical comparison is compromised.

He worked on sampling and mathematical modeling to decide which REOs would be put on the market.

You'll be doubling down.So, from a mathematical perspective, the correct answer is usually invest the difference.

At this point in time, I really don't know what my passion is - I just know that I don't want to deal with complex mathematics :-) a year from now, I may be majoring in Anthropology (I sure hope not, though).

Speaking only for myself, I "feel" better when I am making a mathematically correct decision regarding my finances rather than by making token payments on debts.

This is based on the indexing concept (see tomveatch.com/re/indexing.html) derived from three foundations, the mathematical theorem from information theory on horse race betting, the informational theory of pricing, and a 50-50 valuation ratio between all stocks and all real estate, which was approximately true last time I calculated it.  

Mathematically speaking, if Cap Rate = NOI/Purchase Price then by increasing the NOI, you are also increasing the Cap Rate.

I don’t know how many people use those but you’d have to be smart and good in mathematics and take the time to figure this out and I’d suspect many people don’t realize it.

(Disclaimer: This is an analytical interpretation based from what I see and had lumped those data into simple mathematical model in limits.