Pat,

"Someone withdrawing capital is using a total return approach.  What does someone using an income approach do?"

Good question, two options (without going to the TR approach).

Option 1 - Increase the yield of the portfolio.  Move some low yield money (e.g., 2% dividend yield equity money) into higher yield assets (e.g., 5% interest yield debt).  Or some high yield money (e.g., 5% intermediate term debt money) into long term debt assets (e.g., 6% interest yield).  Or some high yield money (6% long term quality debt) to higher yield assets (8% intermediate term high yield debt).  Or move 0.5% yield growth equity money to 3% value equity assets.

Option 2 - This is for the specific case where you are withdrawing less then the yield (a point missed by Vanguard).  For example, you are withdrawing 4% from a 5% yield portfolio, reinvesting 1%.  Simply reinvest less.  That is, if inflation is 3%, then a 4% withdrawal becomes a 4.12% withdrawal, so you would reinvest only 0.88%.

"Vanguard's belief is based on data provided by Lipper."

I don't believe the Lipper data, or any OTHER TR data, for that matter, will show that the yield portion of total return is more volatile then the capital change portion, which is based on share price volatility.  Do YOU have some?

"Excuse the repeition . . . ."

You're excused.  Now, excuse MY repitition: " Here are a few questions to ponder.  First, how much better is an 85% probability of success compared to a 75% probability of success?  Remember, those probabilities refer to the chance that you'll run out of money before you run out of life.  And do you want to take a chance that a decision you make, on day zero of your retirement, will negatively affect you 15-30 years down the road, with no reasonable way to recover?

One 'feature' of the income approach is that you know exactly how much money you can spend each year.  It's what shows up in your money market account (you take all dividends and interest in cash).  With the TR approach, you need to spend MORE then what shows up there, so you have to spend capital."

"If it is data mining only when the analysis shows that non-dividend payers had total returns greater than dividend payers, is it also data mining when the analysis shows the opposite?"

The data is what it is.  Mathguy2 provided the modern historical record (from 1929, 'ifn I remember) that showed the TR for the dividend payers of the S&P500 was consistently higher then that of the non-dividend payers.  He also showed that, as the dividend yield increased, the TR also increased, at least up through the 9th. decile.  The last decile (the highest yielders in the index) provided slightly lower TRs then the 9th. decile.

There is a theoritical basis for this (related to market valuations), and the FF3F also showed a value effect (dividend payers are typically value orientated).

"Over time, there is no guarantee that the yield amount from a portfolio will be greater than an inflation adjusted amount."

No there isn't a guarantee.  What IS guaranteed is that, if you never spend capital, you won't run out of it!  Your confusing the risk of portfolio survivability (running out of capital) with the risk of having a non-inflation adjusted income stream.

"Turns out that the period of time, starting around 1965, was particularly bad in terms of a TR based withdrawal strategy, as defined in the Vanguard paper.  Withdrawing 5% (of the 1965 value of a retirees portfolio, increasing the amount withdrawn with inflation each year) depleted the portfolio well before 30 years."

This period of time is reflected in the Vanguard table, but it's also discussed quite extensively in a Bill Bernstein paper on withdrawals (The Retirement Calculator from Hell).  That paper showed that ANY allocation (from 100/0 to 0/100) ran out of money, at a 5% withdrawal, before 30 years.

"It appears people using the term income approach have a mindest that the income each year will be greater than the inflation adjusted inital income."

Most income approach mindsets that I am familiar with don't withdraw a fixed X% of the initial value of their portfolio each and every year, increasing it with inflation.  Most withdraw a percentage of the CURRENT value of their portfolio instead.

"but my question, to you, is how would someone know, in 1965, that the 5.25% withdrawal case was going to be a disaster, while that same person, in another year, would know it would be a success?

"There is no way to know."

There is no way to know what PERCENTAGE yields will do, from one year to the next.  Percentages depend on share and bond prices.  But you EXPECT the DOLLAR amount of the yield to be fairly steady.