Expected Value: How to Play the Odds and Come Out Ahead

This article is a reprint of Wise Bread's contribution to OPEN Forum from American Express -- where small business owners can get advice from experts and share tips with each other.

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People are afraid of all kinds of things: death, public speaking, the dark, snakes…you name it. Many of our deepest fears can be lumped together under one umbrella: "the unknown." The unknown is perhaps mankind's deepest and most universal fear.

Yet while others spend a substantial portion of their time and money trying to avoid the unknown, we entrepreneurs embrace it. It's our playground. For us, the unknown isn't the realm of fear, but the realm of possibility.

You're going to make mistakes. You're going to have some failures, whether they be small (not getting a client deal you've been working on) or large (your company goes bankrupt). It's often said that successful entrepreneurs are simply those who have gotten up once more than they've fallen down. That can be a great source of encouragement when you've experienced one of those devastating failures, but it's hardly a sustainable model for a successful business.

As an entrepreneur, you're frequently going to be dealing with the issue of how best to allocate limited resources. By understanding the expected value concept, and making realistic assessments of your odds of success, you can make better decisions about how to allocate those resources.

Expected value can be expressed very simply:

Outcome Value x Odds of Success = Expected Value

And, simply put, those opportunities in which the expected value exceeds the cost are good investments (and the greater the difference, the better the investment). Those in which the cost exceeds the expected value are bad investments.

Let's use various gambling scenarios to illustrate the concept:

Coin toss: You and I both bet a dollar. Whoever wins gets the two dollars. Your odds are 50-50. Two dollars times fifty percent = one dollar, the same as your investment. It's a wash, no matter how many times you flip the coin.

Roulette: You bet on red or black, or even or odd. The payout is 1:1. However, your odds, because of the 0 and 00 on the board, in which the house wins, aren't actually 50-50, but rather 18/38, or 0.47. Your expected value is 0.47 times $2, or $0.94, while your investment is $1. It's a sucker's bet.

Lottery: Now this is an interesting case. I won't run through the exact details of the math, because you have to factor in things like the possibility of multiple winners and it gets kind of complicated, but what happens is that in the first week of a typical 6 out of 49 lottery, the expected value of a $1 lottery ticket is about $0.25. As the jackpot increases from week to week when there are no winners, the number of people purchasing tickets increases as well, but not as much as the jackpot increases. As a result, the expected value increase, until eventually — when the jackpot hits a little over $150 million — the expected value of a ticket actually exceeds its cost.

In one famous example, a businessman named Stefan Klincewicz and his associates bought up almost all of the 1,947,792 combinations available on theIrish lottery. They paid less than a million Irish pounds, while the jackpot stood at £1.7 million. While Klincewicz ended up splitting the jackpot with two other winning ticket holders, with the numerous "Match 4" and "Match 5" prizes, they made a small profit overall.

Applying Expected Value in Your Business

As business owners, the concept of expected value is an essential part of both your forecasting and your decision-making.

One common application is sales forecasting spreadsheets. For each potential deal, you list the odds of successfully closing the deal and the total value of the sale. Multiply these two values together and you get the expected value of each deal. Add them all up and you have the expected value of your sales pipeline.

However, what many forget to do is to consider the cost of the sale, as well. What's the cost of your sales and support staff's time, travel, web conferences, etc.? What's going to be your cost of delivery after the sale is made?

Let's say deal #1 has a 50% chance to close on a $10,000 sale, and the estimated cost of the sale, factoring in all the time to both close the deal, deliver and support it, is $5,000. Your expected value is also $5,000.1.0. It's a break-even proposition.

Deal #2 has a 25% chance to close on a $5,000 sale, but the estimated cost to close it is only $1,000.Your expected return is $1,250.Your return ratio is $1,250 / $1,000, or 1.25. It's a better use of your time.

Too many entrepreneurs are, frankly, compulsive gamblers. They'll look at this and merely think that the 50% odds on a $10,000 sale is a better use of their time than the 25% odds on the $5,000 sale, ignoring the cost factor. Don't let yourself be fooled by the thrill of a big return without fully considering the costs.

Factoring in Risk

On average, if you choose to invest your time and resources in those activities with the highest return ratios, you will be more successful. However, this always has to be tempered by your risk tolerance.

Deal #1 has a 50% chance to close on a $100,000 deal. The cost to make the sale is, let's say, $20,000 (including the majority of your sales resources' time for a couple of weeks). $50K/$20K — that's a 2.5 return ratio.

Four other small deals valued at $25,000 each also have a 50% chance to close, with a cost per sale of $6,250. The expected value is again $50K, but the cost is $25K — that's a 2.0 ratio.

On paper, if you have to choose, it seems like deal #1 is the better choice. On average, over time, if you had to make this decision repeatedly, it probably would be. However, consider this: In deal #1, your odds of getting nothing — losing everything — are 50%. In the multi-deal scenario, your odds of getting nothing are only 1 in 16, or 6.25%. Your chance of making at least one sale, and therefore at least breaking even, is 93.75%.

No matter how great the expected value, you have to always consider whether it has an acceptable level of risk. As the old saying goes, "Don't bet more than you're willing to lose."

Factoring in Optimism

Entrepreneurs are optimists. We have to be. If we looked at the expected value of starting a business, considering the statistics, we'd all realize that we should probably just go get a full-time job! We don't, though, because a) we consider the reward worth the risk, and b) we all think that we can beat the odds — that we can be the ones who pull the average up, not down.

Unfortunately, it's not as easy to calculate the odds on our business initiatives as it is in games of chance. Companies with highly repeatable business processes can, over time, accumulate enough data on which to reasonably base predictive models. They know their expected closing ratios and can fairly accurately calculate things like the lifetime value of a customer. But if your business is fairly new, or if your deals are truly unique, your estimations are based on some combination of experience and gut feel.

Know yourself, and factor in your optimism when estimating odds of success. Personally, I discount all of my odds estimates by about 20%. If you don't have someone on your team who's "the voice of reason," you may have to be your own.

In the end, expected value and return ratios are only one element of the process for making big strategic decisions. You also have to include factors such as cash flow, strategic value, and yes, gut feel. It should, however, be an essential part of your forecasting and planning. Do it well, consistently, and odds are you'll come out ahead.

This is a guest post by Scott “Social Media” Allen, a 25-year veteran technology entrepreneur, executive and consultant. He’s coauthor of The Virtual Handshake: Opening Doors and Closing Deals Online, the first book on the business use of social media, and The Emergence of The Relationship Economy.