See below. What am I missing?

Your math is correct. The Roth IRA and Traditional IRA are mathematically identical in many cases. If your tax bracket is the same when you retire as when you were working (which is true for many people until congress changes the tax brackets), then there isn't as much of a difference between the two as people think.

I didn't read the article, so I am not sure what part it focusses on. But, there are two key things that your math is missing.

1) Your math put $5000 into both the Roth and the traditional IRA. If you not are wealthy, then that isn't an issue. But imagine the person can afford to invest more than the maximum. Suppose you could afford to invest $6470.59 a year instead of $5000. In the Traditional IRA, you are capped at $5500 invested. In the Roth IRA, you pay $970.59 more in tax and can then invest the remaining $5500 in the Roth IRA.

In that case, your math* works out to $169,867.10 in both cases at year 20. With the Traditional IRA you then pay $25,480.07 in tax and are left with $144,387. But the Roth IRA you end up with $169,867.10.

So, the Roth IRA actually lets you shelter MORE in a tax sheltered account than the traditional IRA. This is since the traditional IRA caps you at $5500 and the Roth IRA caps you at an effective $5500 / (1 - your tax bracket) which is always more than the traditional IRA's cap. In this example of a 15% tax bracket, the Roth IRA lets you invest the equivalent of $6470.59 a year and the Traditional IRA lets you invest only $5500.

2) The traditional IRA forces you to withdraw each year after a certain age. Thus, you are essentially forced into a specific tax bracket if you only have a traditional IRA. But the Roth IRA doesn't have that restriction. if you have a mix of retirement accounts, you can pick and choose to minimize taxes.

Suppose you had only a traditional IRA, were married, and were forced to withdraw $50,000 a year in 2016 and later. Assuming only the $12,600 standard deduction then your tax bracket would be 15%. You'd pay $4691 in tax each year.

But what if you had half traditional IRA and half Roth IRA. Then you would be forced to withdraw $25,000 a year from the traditional IRA. Assuming only the $12,600 standard deduction then your tax bracket would be

__10%__. You'd pay $1243 in tax each year, well less than half. Or, you could withdraw even more than the minimum, lets say $31,150 so that you maximize the 10% tax bracket. Then all your traditional IRA is at a lower tax bracket AND you will drain it out faster so that you can end your life in the 0% tax bracket.

* Your math is odd. You math seem to have no gains the first year and then you are instantly getting the full gains on a contribution the instant you make them in subsequent years. Instead of using ((Previous Balance) + (New Contriubutions))*1.04, it would be more realistic to do (Previous Balance)*1.04 + (New Contriubutions).