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Anyone have any idea how much better 52 purchases is relative to 6 or 12?

Assuming you are investing a set dollar amount over the year, because of what is called "regression to the mean" the more often you invest the more likely you are to exactly match the actual return of a market. That is, you will achieve the average.

For example suppose you want to invest $3600 a year. I'm using a 360 day calendar here for ease of explanation.

If you invest $10 a day every day for 360 days you'll will exactly match the market for the year. You'll get the average for the year.

If you invest all $3600 at once you have a 1 in 360 chance of picking the best day of the year to invest and a 1 in 360 of picking the worst. Also you have a 50% chance of picking a below average day and 50% chance of picking an above average day to invest

If you're investing 12 x $300 times in the year you'll have more chances of being on the high side but equal chances of being low but you chances of picking the overall worst day will be offset by more chances at picking better days. The off setting of chances causes the likelihood of achieving "average" increases with more frequent investments. As we tend to believe the market rises overtime frequent investments to get this "average" is viewed as a good thing.

The laws of average say you are most likely to pick 6 good days and 6 bad days to get average. You might also pick 7 good and 5 bad or vice versa etc. But even though it's possible it's less likely you'll pick 12 good or 12 bad days only.

So the short answer is the more often you invest the more likely you'll match the yearly performance of the stock.

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