"Joe's future is giving handjobs behind dumpsters to pay the mortgage." 😂

I agree with the basis of your post, but it's not QUITE as simple as that. There is also the question of how MUCH you put into in each investment. The maths is no longer so simple when you start to invest vastly different amounts based on the risks of what you are investing in.

Let's say you have $300 to invest. You put it all into three low risk. low return investments. They each have a projected ROI of 20% and a success probability of 90%. The maths for that is easy.

Now you have the same $300, but you decide to put $30 apiece into 10 different investments. Medium risk, medium returns. Projected ROI is 100% for all of them and success probability is 65%. Again, easy calculation.

Now you take the $300 and put it into 30 different high risk/high return investments. Projected possible ROI is 1000% and chances of success are all 10% each. Easy to calculate.

But what if you put $100 into one low risk, low return investment, $30 apiece into three medium risk, medium return investments and $10 into eleven high risk, high return investments? Well you can STILL calculate it as an overall system, get a figure, and compare to your other potential investment strategies.

BUT that's not the whole story. Because now you have cast a nice wide net and diversified your portfolio. You have now vastly increased your chances of picking up erratic market behaviour in at least one investment, you've moved away from the bell curve.

Up until now you've assumed a normal distribution of probability in your calculations, it's what you've actually based your very risk and reward figures on! But now you have over populated this bell curve to the point where you must have a few outliers, those in the area beyond two standard deviations or so. If you're luck they fall on the right side of the curve and you make a lot of money. If you aren't so lucky then they fall on the other side and you lose a lot.

The same could actually be said for many small high risk investments, but in practice that is a very difficult and possibly costly portfolio to manage, and quite frankly, you must be crazy to invest like that. But investing just a third that way can be done.

But what's my point? Well the point is that probability breaks down once you start investing in enough different things. This makes it impossible to calculate the chances of success and to evaluate a portfolio on numbers alone. Note: it does not make the portfolio BETTER (though I personally prefer to spread risk and have a very diverse portfolio), it just makes it much harder to predict future performance.