Investing is always a game of probabilities and possible scenarios, and there is no way to be absolutely certain about the outcome of an investment. In the words of renowned fund manager Peter Lynch:

In this business if you're good, you're right six times out of 10. You're never going to be right nine times out of 10. This is not like pure science where you go, "Aha" and you've got the answer.

Even Warren Buffett has made some lousy investment decisions. Buffett's investment holding, Berkshire Hathaway, is named after the textile business he bought in the 1960s that turned out to be a big money loser until it was ultimately shut down. The Oracle of Omaha estimates this huge mistake had a jaw-dropping total cost of more than $200 billion when including opportunity costs over the years.

However, losing tons of money in this particular investment did not stop Buffett from becoming one of the richest men on Earth, as his winning picks outpaced his losers by a wide margin over the years.

Everyone makes mistakes in the market. Nonetheless, as long as you are following a sound strategy and playing the game for the long term, investing in stocks can be one of the most powerful and effective ways to build wealth over time.

On winners and losers
When looking at my investment holdings, the winners are clearly outpacing the losers. Innovative growth companies such as (NASDAQ:BKNG) and Netflix (NASDAQ:NFLX) are particularly profitable positions, as they are respectively disrupting the travel and entertainment industries, while generating tremendous growth over the long term despite short-term volatility.

NFLX Total Return Price Chart

NFLX Total Return Price data by YCharts.

Coach (NYSE:TPR), on the other hand, is clearly out of fashion. The handbags and accessories specialist is materially lagging the S&P 500 over the last five years, as sales are stagnating and the company is losing market share to competitor Michael Kors (NYSE: KORS). Coach is betting on its renewed collection to turn the business around, so I will give management some time and see if has what it takes to reinvigorate the brand.

That said, my position in the company has clearly delivered disappointing returns, especially considering that the stock is down by more than 37% year to date. However, Coach was not my most expensive investment mistake over the last few years.

That delicious burrito I didn't buy
Chipotle Mexican Grill
(NYSE:CMG) is arguably the most explosive growth story in the restaurant business. The company's food with integrity approach to tacos and burritos is a booming success among customers, and this is reflected in mouthwatering financial performance and succulent returns for investors.

I have always loved Chipotle Mexican Grill, both as a customer and as an investor. However, I decided to wait until the valuation came down to more attractive levels before taking a position in the company. I was too slow to pull the trigger when Chipotle dipped in 2012, so I missed the stock completely .

Looking at P/E ratios over the last five years, Chipotle has usually looked more "expensive" than other restaurant chains, be it traditional fast-food giants like McDonald's (NYSE: MCD) and Yum! Brands (NYSE: YUM) or more dynamic growth players such as Buffalo Wild Wings (NASDAQ: BWLD) and Panera Bread (NASDAQ: PNRA).

CMG PE Ratio (TTM) Chart

CMG P/E Ratio (TTM) data by YCharts.

However, this premium valuation did not stop Chipotle from generating exceptional gains for investors over the long term. Unfortunately, while I was waiting for the stock to drop so I could buy in at a lower valuation, Chipotle decided not to wait for me and continued on its way to extraordinary returns.

CMG Total Return Price Chart

CMG Total Return Price data by YCharts.

The lesson
When analyzing our performance in the market, we tend to focus on the gains and losses from positions in our portfolio. However, missed opportunities can be more expensive than disappointing investments.

That's the beauty about mathematics in the stock market: your maximum potential loss can be 100% if the stock goes to zero, but the big winners can multiply your capital fivefold, tenfold, or even more in the long term.

I correctly identified Chipotle as an amazing growth company, but I waited for a better entry point to take a position. French philosopher Voltaire is commonly credited for saying that "perfect is enemy of the good", and by waiting for a perfect time to buy I missed a huge opportunity for profits. 

I should have listened to Warren Buffett instead: "It's far better to buy a wonderful company at a fair price than a fair company at a wonderful price."

Investment mistakes are not only the possible problems with your portfolio -- missed opportunities can have an even bigger negative impact on your overall returns. Valuation is an important factor to consider when making investment decisions, but we need to remain open-minded and flexible here. After all, superior companies deserve a premium valuation.