Investing a fixed amount on a fixed schedule produces an average cost per unit below the average of the prices encountered. The effect is arithmetic rather than a matter of timing skill.
A fixed sum buys a variable quantity
Committing the same amount each period means the number of units purchased moves inversely with the price at that moment.
More units are acquired when the price is low and fewer when it is high, without any decision being made about whether the price is attractive.
The portfolio therefore accumulates a larger share of its total holding at the cheaper prices, which is what shifts the weighted average downward.
The averages differ because one is weighted
The simple average of the prices paid treats every purchase equally, regardless of how many units it bought.
Average cost per unit weights each price by the quantity acquired at it, so the low-price purchases carry more influence.
Except in the case where the price never moves, the weighted figure is always the lower of the two, which is a mathematical property rather than a market observation.
The comparison with lump-sum investing is separate
Spreading a sum already in hand across several months is a different question from investing income as it arrives.
Because markets rise more often than they fall over long periods, holding money back to invest later means spending more time out of the market than in it.
Investing available cash immediately therefore tends to produce higher expected outcomes, while staging it reduces the consequence of committing everything just before a decline.
Regular contributions are the natural application
Money arriving with each paycheck cannot be invested as a lump sum, since it does not exist yet, so the schedule is imposed by the income rather than chosen.
A retirement plan contribution is dollar cost averaging by construction, which is why most people practise it without ever selecting it.
The automation matters as much as the arithmetic, because a contribution that requires no decision continues through the periods when deciding would be hardest.
The behavioural effect is the durable one
A fixed schedule removes the question of whether now is a good moment, which is the question that most often stops people investing at all.
It also means purchases continue during declines, when a discretionary investor is most likely to pause and least likely to resume promptly.
The price advantage is real but modest; the reliability of continuing to invest through unpleasant periods is where most of the benefit accumulates.