In 1976, Vanguard launched its 500 Index Fund, making it the first index mutual fund available to non-institutional investors. The creation of an index fund intended for individual investors was an important salvo in the now long-running battle over which investing approach—active or passive—is superior.

This is a 35-year-old fight (at least) that I certainly don’t think I can settle. But in discussions of the issue over the years, I’ve found that a few points are really critical, and often not appreciated by more casual participants.

Zero-sum. You don’t need to believe in efficient markets, rational behavior, economics, or the tooth fairy to establish that a portfolio that holds all the securities in a capitalization-weighted market index (i.e., an index weighted like the S&P 500 and other common indexes, but containing all the securities in the market) will, after costs, outperform the average dollar invested in the market if active management costs more than cap-weighted indexing, which it generally does. You do have to believe in basic arithmetic. (And the index must be cap-weighted, as this wouldn’t necessarily be true for other indexing methods.) But the result is purely mathematical from there, and is based only on the definition of the word “average”—not on fancy/complicated theories that require any additional assumptions.

Importantly, this basic math applies regardless of the market, or the so-called efficiency of the market. Market inefficiency means only that there is a lot of private information about values that is not immediately reflected in prevailing market prices. This in turn means only that there is significant scope for investors either to take advantage of private information that they have, or to be taken advantage of by others who have better information.

The upshot is that in inefficient markets (think small-cap stocks or emerging markets), you tend to get much wider dispersion in manager results. There are lots of home runs, and lots of strikeouts (or worse). But it’s still the case that, regardless of which investors beat the average and which fall below, the performance of the average dollar in an inefficient market is equal to the performance of a cap-weighted index of that inefficient market—but only before costs. If the cost to invest is higher in active funds than in a cap-weighted index fund, then the after-cost performance of the average dollar in active funds must lag that of the index fund.

“Active” is not an investment. Hiring an active manager means believing that a specific manager or managers have an edge over others in the same market. You can’t buy active management—only the services of specific managers. This means that comparisons of whether the average active fund beat the indexes are not as relevant as they may seem; you can’t buy the average active fund. The choice you have is whether to invest with specific managers, or to invest in a cap-weighted index fund. If you choose specific managers, your experience can, and typically will, vary from that of the average active fund. From the very practical point of view of someone with money to invest, the debate isn’t really about whether active is better than passive—it’s about whether you can pick winners.

There’s a lot of noise. We know from the “zero-sum” discussion above that in terms of the overall market, cap-weighted indexing always beats the average of all active managers, after costs. Academic tests of whether fund managers add value are trying to determine whether the average active mutual fund manager—just one type of active investor—is better than the cap-weighted index/average of all active investors in the market. These tests have generally found no evidence that the average fund manager can reliably beat passive investment strategies. So we are back to the above point: getting outperformance from an active mutual fund manager is all about choosing a better-than-average manager.

A very significant challenge to this is that objectively determining whether a manager is better than average, based on real-world data alone, is very hard. Even with many years of data, in most cases formal statistical tests are merely going to reveal that the data we have are not inconsistent with the notion that the manager adds no value. That is, given the amount of noise in the data, we very often just can’t say whether any outperformance or underperformance is due to luck or skill. The issue of “noise” is more severe in inefficient markets, where prices and manager performance tend to be more volatile. Sure, there are some managers/investors who will frequently end up on the upside of wild swings, but there are also those who frequently end up on the downside. In such an environment, it’s generally harder to distinguish who is really adding value or subtracting it, given the additional background noise.

So, what does it all mean?

I’d say first and foremost, my takeaway is that cap-weighted indexing is the right place for investors to consider as a start. If you aren’t satisfied with the potential for slightly-better-than-average net performance that goes along with that approach, and want to try your hand at choosing active funds, do so with care. Acknowledge the zero-sum math above, and accept that by investing actively you are betting that Manager X is better than the bottom half of all other active investors—and that given the noise out there, it’s very possible that you could be wrong and end up on the other side of the index results (regardless of where the average active manager ends up).

Finally, the one thing you can know for sure when investing is what your manager’s pay rate is. Higher expenses set up a higher hurdle for him or her to overcome in order to add value for you. In a world where you can’t ever be sure how good a manager is, low investment costs provide a strong, systematic advantage out of the gate.

Note: All investments are subject to risk. Past performance is no guarantee of future results. Stocks of companies in emerging markets are generally more risky than stocks of companies in developed countries. Prices of mid- and small-cap stocks often fluctuate more than those of large-company stocks.