The reality of dollar-cost averaging

The notion of dollar cost averaging has its share of critics. It doesn't take a great deal of insight to see that investing later will reduce one's returns, so I agree that anyone with a big lump of cash to invest should invest it as soon as possible. However, most of us don't have a huge lump of cash waiting to be invested, and instead invest biweekly or monthly anyway.

The question that interests me is: what is the effect of spreading out one large investment into many smaller investments? I specifically want to exclude the effect of investing earlier or later, as that will naturally have predictable results.

To answer this question, I started with the daily closing values of the S&P 500 over the last 50 years. I simulated a series of investment strategies, each of which involves investing N dollars every N trading days, then looking at the total investment value after waiting for N/2 trading days. A year has about 250 trading days, so the time horizon I used was 256 days, and the N values were all powers of 2 ranging from 1 to 256. Every dollar in any of these schemes is invested for an average of 128 days, which means no scheme has the money invested any longer than any other scheme. Each day for the last 50 years, I computed the value that each scheme would produce over the prior "year" (where a year is 256+N/2 trading days).

So, with a total $256 investment over a year, each scheme produces the following results:

N (days)  Average  Std deviation
    1     $266.73      8.4%
    2     $266.77      8.4%
    4     $266.77      8.4%
    8     $266.77      8.4%
   16     $266.77      8.4%
   32     $266.77      8.5%
   64     $266.77      8.6%
  128     $266.77      8.9%
  256     $266.65     10.3%

So on average, it seems spreading out your investments over the course of the year has very little effect. I wasn't expecting that. I guess you learn something every day.

According to these results, there's no point at all in investing more often than once per month. With a single lump sum invested for a year, your standard deviation is only 30% more than it would be with daily investments.

Is dollar-cost averaging a myth? What other conclusion could I draw?