It should be noted that your 10, 20, and 30 year charts actually show an advantage to investing in off years; your conclusion that "there is no significant advantage" is mistaken.

On the 30 year chart, the peaks on the 20-50% line are a couple percent above the peaks on the all line. Boosting returns from 7% to 9% over 30 years, or from 12% to 14% over 30 years, results in over 70% more total wealth after compounding. The visual difference is not as striking on the 30 year chart as on the 5 year chart, but that's because you're presenting annualized rather than total returns.

The argument against market timing I've always liked comes from Malkiel's Random Walk:

> During the decade of the 1980s, the Standard & Poor's 500 Index provided a very handsome total return (including dividends and capital changes) of 17.6 percent. But an investor who happened to be out of the market and missed just the ten best days of the decade—out of a total of 2,528 trading days—was up only 12.6 percent. [...] market timers risk missing the infrequent large sprints that are the big contributors to performance.

The "ten best days" argument is a good argument against short-term timing (you could, at random, miss just those 10 days and nothing else if you're trying to guess good and bad days.) But it's not a very good argument against the particular type of long-term timing discussed in this sub-thread. The 10 best days tend to be clustered somewhat, but often interspersed with several bad days; if you're simply looking for a good price and then buying, you're not going to miss the 10 best days without also missing a large number of bad days. Missing both the best and worst 10 days of the decade gives you almost exactly average returns. Furthermore, the 10 best days tend to occur in the "short sprints" that follow a down market; the strategy described above says to buy in to a down market, which means you'd hit most of those 10 best days -- and, quite likely, miss at least a few of the 10 worst days, generating net above-average returns. (The parent post's graphs showed this exact result: buying into the market after a largeish downturn gets you great returns, long term.)

Why is it that no one ever does the same analysis for the 10 worst days?

Here you go: http://www.freemoneyfinance.com/2010/11/the-truth-about-mark...

  Invest in S&P 500 ETF (SPY) starting at inception
  Growth of $100,000 from 1/29/1993-8/30/2010
  Buy and Hold: $324,330.15
  10 Best Days Removed: $156,354.12
  10 Worst Days Removed: $692,693.90
  10 Best and 10 Worst Days Removed: not listed, but very close to Buy and Hold (the green line in the chart)

Rob Bennett's followup comments are quite good, as well.