The statistical revolutions that have overtaken sports, business and markets have bred suspicion of any observation or assertion not backed up by hard numbers.

This is a good thing in most respects. Yet experts who study these complex realms surely have ideas about how they work based on their long experience that can’t be firmly proven quantitatively. Now that fancy stats have become the dominant means we use to understand and explain patterns and performance, we almost need to coax softer, “gut feel” tenets from the sharpest commentators.

So I did.

Inspired by an exercise undertaken by baseball writers and advanced-statistics devotees Ken Arneson and Rob Neyer, I asked a handful of astute professional investors in the Yahoo Finance Contributors Network what they believe about markets that they are unable to prove quantitatively.

Here are some of their responses:

Josh Brown, Ritholtz Wealth Management, @ReformedBroker:

One thing I’m absolutely sure of that cannot be proven statistically (that I’m aware of) is that some people are born to be good investors, some people are born to be terrible investors and maybe 90% of the population are somewhere in between. I don’t think people in the bottom 95% accept that they are there, and I also don’t think most can ‘learn’ to become good. Lots of the brokerage biz is based on the idea that this is possible, though. Americans don’t accept that some people are what they are, or the concept of elitism in general.

How could we ever know if this is true?

Ben Carlson, A Wealth of Common Sense blog, @awealthofcs

-My first thought would be that most mom & pop investors aren’t as bad as most assume. Obviously there are terrible ones, but most are probably mediocre or average. Everyone gets lumped in with the mutual fund flow data, but it’s small in the context of total investable assets. I’d venture to guess the behavior gap isn’t all that different between professional and individual investors.

-Supremely intelligent investors are well suited to run a fund but not an entire portfolio. I’d rather have an Ivy Leaguer run a hedge fund for me than a portfolio. Portfolio management is more about common sense than intelligence.

David Merkel, The Aleph Blog, @AlephBlog:

In a strict sense, almost everything that I believe about investing can’t be proven mathematically. There are several reasons for this:

-If we apply the best statistical techniques to the analysis, as opposed to the normal distribution, the volatility level is so wild that we can’t prove almost anything with 95% certainty. That is what infinite volatility does, which we can never calculate, but, my, don’t we get a lot of 6, 10, 12, 18, 21-sigma events?

-When new ideas get published, they get pursued often eliminating their prospective strength, until the idea is “forgotten” and it regains strength.

-Many techniques have power for an era off of some unique macroeconomic/financial setup, but when it is gone, it is gone.

-Data for some phenomena have only been measured for 5, 10, 20, 40, etc. years, in certain countries, etc. Many studies can’t capture the regime-dependence of the study.

-Eras often produce the seeds of the next anti-era, etc. Regulators fight the last battle, which recurs in way no one anticipates.

So, I have a simple one-word answer for you: everything.

I say this as a quantitative investor who uses all manner of ideas from research. But truly proving it is impossible. Much as I think Buffett is a genius, and many other value investors as well, there aren’t enough data points to prove that the luck component isn’t dominant. I still do value investing because it is consistent with what intelligent businessmen do operationally.

Peter Kenny, Clearpool Group, http://peterckenny.tumblr.com

Markets, broadly speaking, have crowd sourced intelligence that has the ability to deliver performance that defies the most intelligent, sophisticated and well prepared individual or team more often times than not. For all the capital invested by “smart” institutions or hedge funds in order to ensure an enlightened view, the number of them closing their doors every year as a result of poor relative performance to indices at any point in a year is astounding - year in and year out.

Despite that track record, there is no end to the number of new funds opening up. This is a healthy and dynamic sign because it speaks to a drive for outperformance that investors want and reward. That is why there will always be a demand for discipline and outstanding research. Based on my years in the business there are not many funds able to compete with the intelligence of the crowd represented in the broader market.

The key for me is balance or strategic humility. Have exposure to broad market measures of performance for a portion of the portfolio so as to capture the crowd intelligence and returns while potentially homogenizing catastrophic downside risk. Additionally, keep enough of an allotment of capital focused on unique alpha generating ideas. The unearthing of alpha is the differentiator - the degree of outperformance that merits income generation.

Let me know what you believe strongly about the markets but don’t have the math to prove it.