How Expected Value Can Help You Make Good Decisions (Part 2)
Learning to take calculated risks when the outcome is uncertain is a matter of skill and intelligent calculation. Get-It-Done Guy explains how to make any uncertain decision.
In Part 1 of this series, we looked at using expected value as a tool for decision-making under uncertainty. It’s a way to make sure you’re taking enough risks, and the right risks. Instead of comparing best case and worst case scenarios when making a decision, look at the expected value, which is the probability of an event times the payoff from that event.
Check out Part 1 of this series for a detailed explanation of what expected value is and how to derive it for any decision you’re making.
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Do Research to Estimate Probabilities
Calculating expected values requires estimating probabilities and figuring out what the payoff is for each branch of the decision.
For example, Melvin saw what seemed to be an amazing deal—a 2-year-old Toyota Corolla for $5,000 on Craigslist, “Priced to move by a desperate seller.” He planned to buy it and sell it at a high price in a more leisurely time frame. The seller wouldn’t let him see the car or get a mechanic’s report prior to purchase. And he must wire the payment directly to a bank account in Nigeria.
Melvin figures there’s a 5% chance the ad is a fraud and worth $0, and a 95% chance it’s worth $125,000. He calculated the expected value at 5% times $0 plus 95% times $125,000 or $118,750, minus the $5,000 purchase price, or $113,750. Who could pass up that expected value?
You and I should pass that up. Melvin’s gut feel is wrong, both for the probabilities and the car value. Even with expected value, making better decisions requires research.
Estimate Probabilities Intelligently
To estimate probabilities, you can often find publicly available statistics. If you’re estimating the chances that a new company will survive its first 5 years, for example, you can use the statistic that roughly 55% of all businesses fail by year 5, which means that there’s a 45% chance of 5-year survival.
You can look also for more specific data. If you’re considering starting a real estate business, 5-year survival rates are higher, at 58%. You could also spend time researching your geographic area to get statistics that are more representative of the business you’re starting.
For Craigslist, Googling “fraud on Craigslist” doesn’t give stats, but it does give 6 million hits. A quick trip to the Craigslist Scams page shows that the ad Melvin got so excited about fits several warning signs for a scam. We won’t reject it out of hand (maybe it really is an overlooked opportunity) but we’ll adjust our expected value percentages, and say there’s a 97% chance of the car being a fraud, and 3% chance of it not.
Estimate Values Intelligently
Research also helps figure out the values of the different outcomes. If you’re deciding whether or not to go to college, you can figure out a dollar value of a college education by Googling “How higher education affects lifetime salary.” Use those numbers to put a specific dollar value on the payoff of a college education.
Melvin says that the non-fraud outcome of the Craigslist purchase is worth $125,000. A quick visit to the Kelly Blue Book web site shows that a 2-year old Corolla sells between $11,000 and $14,000, not $125,000. Plus, Kelly Blue Book gives 4 prices depending on the car’s condition, and the percentages of cars that they see in each condition. That’s enough information to make each car condition a separate branch of the expected value calculation.
Making decisions using expected value calculations is a way of life.
I’d use that information to calculate the expected value using the range of conditions and stats from the Blue Book site. For the sake of simplicity right now, let’s just assume the car is worth $12,000. The expected value of the Craigslist ad is 97% x $0 + 3% x $12,000 or $360. Now we subtract the $5,000 purchase price for a final expected value of -$4,640.
A little research showed that Melvin’s $118,000 opportunity was really an expected loss of $4,640. Melvin used his gut for both the values and probabilites. His gut was wrong. You and I do our research, however, and realize this is not a positive expected value situation.
Remember to Factor Up Front Costs into the Expected Value
When you’re calculating expected value, remember you’re not just looking at payoffs or losses, but also the money you’ll have to put in up front. In Melvin’s Craigslist example, that’s the $5,000 he has to pay, regardless of whether the car is a clunker.
In real estate, closing costs, inspection fees, etc. are your up-front costs. You’re deciding to buy a new house, for which you must pay $2,000 in closing costs. You think there’s a 20% chance the house will gain $15,000 in value while you own it. There’s a 60% chance it will remain unchanged. And there’s a 20% chance it will lose $10,000 in value.
The expected profit on the house is 20% x $15,000 + 60% x 0 + 20% x ($–10,000) = $3,000 + $0 – $2,000 = $1,000.
At first glance, that looks like a positive expected value. But remember: No matter how it turns out, you always have to pay $2,000 in closing costs. So you subtract $2,000 from the expected profit, bringing the expected profit to -$1,000. This is a negative expected value transaction.
Use Positive Expected Value Consistently
Expected value decision-making isn’t a one-time thing. It’s a way of life. Expected values are based on probability. It only makes sense to use EV calculations if you use them consistently enough for the odds to even out. Making just a single decision based on EV doesn’t give you enough exposure to upside and downside outcomes for the odds to even out in your favor.
Don’t Die! Limit Your Bets
In order for you to make enough positive expected value decisions for the odds to work in your favor over time, you have to be able to stay in the game. That means being consicous of how much you can afford to lose.
Even if you always make only positive expected value bets, sometimes you’ll go through a dry spell where the odds just don’t work in your favor. You need to have enough of a cushion to make it through those times.
If you’re down to your last $1,000, making a $1,000 bet—even with a positive expected value—might not be wise. If you win, you clean up big. But if you lose, you’ve lost all the resources you have available to make other bets in the future. There’s no firm guideline as to how much of your remaining money to put into an uncertain decision, so you’ll have to use your judgment about how close to the edge you want to play.
This is one reason, by the way, that a rich person who thinks in terms of positive expected value can really clean up. They have the resources to make many positive expected value bets at once, so at any given moment, chances are that one or many of their projects are paying off.
Process, Not Outcome
As Billy Murphy puts it, contrary to how most of us think in business, outcomes don’t matter. Obesssing about success or failure isn’t useful. Obsessing about good processes in deciding where to put your time and energy is useful.
As long as you’re making positive expected value investments, you should expect some losses. But over the long term, you’ll win. Any one outcome isn’t as important as making decisions based on solid, simple math. Spend your time getting better at estimating outcomes and probabilities, make consistently positive expected value investments, and avoid risk of ruin, and you’ll find yourself on a steady path to greater and greater success.
Remember to check out my interview with expected value guru Billy Murphy at getitdoneguy billymurphy.
I’m Stever Robbins. I help high achievers accelerate or change careers. If you want to know more, visit SteverRobbins.com.
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