The trend toward passive investing has been inexorable, although slow, for the past 20 years, with roughly 1% of active investors abandoning the game of active management annually. Perhaps we have reached what might be called the tipping point, with the trend now accelerating. Consider that in the first 10 months of 2015, the four fund families with the largest growth in assets under management are all either best known for their passive investments or exclusively offer passive funds.

According to Barron’s, the Vanguard Group — the largest provider of index mutual funds — was on pace to pull in more money last year than any other asset manager in history, having added $191 billion in new assets through October 2015. At that rate, the firm was on course to bring in about $230 billion last year, well ahead of its record $216 billion in 2014.

In second place, at least as of November 2015, was BlackRock, the largest provider of index ETFs. Their iShares ETFs had $1 trillion in assets as of September. In third place was WisdomTree Investments, another provider of passively managed ETFs. In fourth place appeared Dimensional Fund Advisors (DFA), a leading provider of nonindexed, passively managed mutual funds. (Full disclosure: My firm, Buckingham, recommends DFA funds in constructing client portfolios.)

To answer the question of whether the trend toward passive investing will help or hinder actively managed funds in their quest for alpha, we can start by engaging in a simple thought experiment. Consider two groups of investors, each of which have been using actively managed funds. The first group, Group A, has been generating positive alphas (outperforming appropriate risk-adjusted benchmarks), while Group B has been underperforming (generating negative alphas). Fund families that have been generating positive alpha will almost certainly attribute their success to skill — either their skill at picking stocks, or the skill of the fund managers they chose and their skill in selecting them. It’s highly unlikely they’ll attribute their success to luck.

Thus, they will continue to play the active game. It’s the losers from Group B, those with either less skill or bad luck, who will abandon active management in favor of passive strategies. We can then conclude that the remaining players in the pursuit of alpha are more than likely to be the ones with the most skill. After all, if an investor’s outperformance was based on good luck, the good luck will eventually disappear and they will join the losers in Group B and eventually abandon the game. As less-skilled investors abandon active strategies, the level of competition among the remaining participants will increase.

The following example from my book, “The Incredible Shrinking Alpha,” which I co-authored with Andrew Berkin, comes from game theory. It helps to explain why the level of competition is likely to continue to increase, persistently raising the hurdles for successful active management.

Imagine the following scenario: You are an NBA player. The league is holding a free-throw shooting contest open to all players. Each participating player is allowed to take 100 shots, receiving $1,000 for each shot made.

You are given a choice to play or not to play the game. If you don’t play, you will get paid based on the average score of all the players who do decide to participate. The best free-throw shooter in the league shoots about 90%, while the average player shoots just 73%, and you shoot 83%. Should you compete, or accept the average score of those who participate?

Since you shoot an above-average percentage, it seems like you should play. However, the fact that you are above average is irrelevant because all the players with a below-average shooting percentage should choose not to play. And, anticipating this occurrence, all the players with above-average scores should decide not to play as well. Logically, only the player with the best percentage should choose to compete, and everyone now has an expected return of $90,000.

What does this scenario have to do with investing? As we have discussed, it seems likely that those abandoning active management in favor of passive strategies will be investors who have had poor experiences with active investing. As less-skilled investors flee active strategies, the level of competition among the remaining players will increase.

What so many people fail to comprehend is that in many forms of competition, such as chess, poker or investing, the relative level of skill plays the much more important role in determining outcomes rather than the absolute level. What is referred to as the “paradox of skill” means that even as skill level rises, luck can become more important in determining outcomes if the level of competition is also rising.

Charles Ellis, one of the most respected people in the investment industry, noted the following in a recent issue of Financial Analysts Journal. He wrote that, “Over the past 50 years, increasing numbers of highly talented young investment professionals have entered the competition…They have more-advanced training than their predecessors, better analytical tools, and faster access to more information.”

Legendary hedge funds, such as Renaissance Technology, SAC Capital Advisors and D.E. Shaw, hire Ph.D. scientists, mathematicians and computer scientists. MBAs from top schools, such as Chicago, Wharton and MIT, flock to investment management armed with powerful computers and massive databases.

For example, Eduardo Repetto, the co-CEO of DFA, holds a Ph.D. from Caltech and worked there as a research scientist, and DFA’s co-CIO Gerard O’Reilly also has a Caltech Ph.D. in aeronautics and applied mathematics. And my co-author, Andrew Berkin, the director of research at Bridgeway Capital Management, has a Caltech B.S. and University of Texas Ph.D. in physics and is a winner of the NASA Software of the Year award. According to Ellis, the “unsurprising result” of this increase in skill is that, “The increasing efficiency of modern stock markets makes it harder to match them and much harder to beat them, particularly after covering costs and fees.”

Analogous examples are seen in the sports world. For instance, from the advent of the modern baseball era in 1903, seven players achieved a batting average over .400 a total of 12 times. But the last to do so was Ted Williams, who hit .406 in 1941, more than 70 years ago. Yet, today’s players are superior athletes — they are demonstrably bigger, faster and stronger, use superior training techniques and have better diets.

However, all players have these advantages. The result is that as average skill increases, it becomes more difficult to outperform by large margins — the standard deviation of outcomes narrows. In the first 20 years of the modern era (1903-1921), the average hitter batted about .250-.260. During that period, the .400 mark was reached four times. Since 1950, batting averages have been fairly stable in that same .250-.260 range. Yet no one has hit .400. Why? While batting averages were the same in the two eras, the standard deviation has dropped dramatically, from 40.6 points in 1921 to 26.1 points in 2003. Batting .400 is now a more than five standard deviation event, with a probability of less than one in a thousand in a given year. In other words, no one hits .400 anymore because the average baseball player of today is far better than the average player of a hundred years ago.

The paradox of skill means that while today’s athletes are more skillful, they are not likely to produce the kind of outlier results that the legends of yesteryear achieved. We see the same phenomenon in the game of active management, where the quest for alpha has become ever more frustrating as the level of skill among competitors rises.

The bottom line is that as more and more investors learn about the evidence against active management as the winning strategy, as well as “benefit” from their own experiences with actively managed mutual funds, I expect to hear questions about what will happen to the odds of active management outperformance as the trend to passive investing persists with increasing frequency. And the answer will be the same — the odds of success are getting smaller and smaller, asymptotically approaching zero.