Favorite-longshot bias is one of the most reliable behavior patterns in all of sports gambling. It applies to markets, too, which means most investors are impacted by it — including you and me.
This doesn’t have to be a bad thing though. If you understand the concept of favorite-longshot bias and the key thing that makes it a costly error, you can take steps to adjust the odds. This lets you put favorite-longshot bias in your favor, instead of having it work against you.
The favorite-longshot bias is basically what it sounds like: A tendency to overbet “longshots” relative to their likelihood of paying off, while under-betting the favorites.
This means that, as a general rule, sports gamblers will weight the high-odds favorite with a lower probability than deserved, and weight long-odds plays with a higher probability than deserved.
References to favorite-longshot bias date back to the 1940s. It was first noticed at the racetrack, but has since been documented in all kinds of sports betting, from football to tennis to track-and-field and more.
An in-depth study of S&P 500 and FTSE 100 index futures options, using pricing data for a 17-year period from 1985 to 2002, showed that the favorite-longshot bias is present in financial markets, too.
If the favorite-longshot bias is a human psychology phenomenon, which certainly seems to be the case, it would make sense that it shows up everywhere.
In the options market, favorite-longshot bias shows up as a heavier weighting towards out-of-the-money call or put options than rational likelihood would indicate. Investors consistently pay up more than they should for wild or extreme pricing scenarios.
Bookmakers and options market makers earn a bread-and-butter living from the favorite-longshot bias. A tendency to overpay for lower likelihood outcomes on a constant widespread basis over and over again puts a steady stream of cash in their pockets.
In 2010, two university economists named Erik Snowberg and Justin Wolfers — one at CalTech and the other at Wharton — posed an interesting question: Is the common nature of the favorite-longshot bias due to a “love of risk” on the part of those making the error, or is it rooted in a misperception of probabilities?
In other words, are sports gamblers and option-buying investors overpaying for longshots because they like the thrill, or are they simply getting the probabilities wrong?
In their National Bureau of Economic Research (NBER) research paper, Explaining the Favorite-Longshot Bias: Is it Risk-Love or Misperceptions?, Snowberg and Wolfers argue that misperception of probabilities — getting the math wrong — is the main driver.
They pointed out that, based on numerous cognitive psychology studies, “people are systematically poor at discerning between small and tiny probabilities, and hence price both similarly.”
The difference between “small and tiny probabilities” is the key thing. Getting those mixed up is often the difference between a logical wager and a worthless wager.
A longshot with a small probability of a sufficiently large payoff can be a rational investment, whereas a longshot with a tiny or microscopic probability is almost never worth it. For example:
- Imagine a bag with 100 marbles, 98 red and 2 green.
- If you draw a green marble, you win $150.
- If you draw a red marble, you get nothing.
- The opportunity to draw costs $1.
Would you pay a dollar for a chance to draw with those odds, expecting to lose 98 times out of 100? The rational answer would be yes. Not only would it make sense to pay the $1, you should take as many draws as you need to get the two green marbles.
Because even though the odds of drawing a green marble are only 2% — remember there are two green marbles out of a hundred — the expected value of the wager is a solid profit.
A 2% probability is small, but not tiny, so the large potential return made the bet worth it. Mega-millions lottery tickets, on the other hand, have a probability that is not just tiny but infinitesimal.
For example, if you pay $2 for a 1-in-300 million chance to win $50 million after taxes, you are in the same boat as someone who paid $2 for a 1-in-300 chance to win 50 bucks. The expected value here is negative, which makes it a bad deal for the buyer and a great one for the seller.
In psychological terms, we would argue favorite-longshot bias is widespread because of optimism. Sports gamblers are inherently optimistic about the wagers they are making, and investors are inherently optimistic about the options or stocks they buy.
But the optimism part isn’t the problem. Without an optimistic outlook, entrepreneurs wouldn’t build new companies and investors wouldn’t take smart calculated risks.
The problem is the misreading of odds, and this is where understanding the favorite-longshot bias can make a difference. If you learn to discern between “small” probabilities and tiny ones, you can get in the habit of only making longshot investments with a positive expected value.
The simplest definition of expected value, in case you don’t have it handy, comes from the most rational value investor of them all, Warren Buffett:
“Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect but that’s what it’s all about.”
There are whole industries that focus on positive expectation longshots — and make money doing so.
Take venture capital for example, where the VC firm expects to lose money or barely break even on the majority of its startup investments — but also expects a small handful of startup investments to do extremely well, with big returns on the winners producing a healthy return overall.
The mechanical trend-following discipline practiced by commodity trading advisors (CTAs), who collectively manage hundreds of billions of dollars in futures markets, follows a similar logic.
Mechanical trend followers typically expect to be wrong and lose money on a majority of their trades. They will also have a significant number of trades that break even or only make a small amount. Then a handful of big winners — the strong outlier trends — keep the lights on and produce a favorable net return. This is, once again, a longshot focus — but one with positive expected value over time.
The key here is to be aware of the odds and to know the difference between “small” and “tiny.” You can do this by running a basic expected value calculation: Take the payoff from winning multiplied by the probability of winning, then subtract the cost of loss multiplied by the probability of loss.
If you do this, you will find that highly aggressive bets can sometimes make sense, even if the odds of winning are less (sometimes far less) than 50%.
The next step from this point is to size the investments properly in your portfolio — don’t make them so large you can’t sleep at night — and then go about putting as many factors in your favor as possible.
TradeStops can help you with the “putting factors in your favor” part. For example, say there is a volatile and aggressive small-cap stock you are following. You might believe this stock can deliver a 200% return, or even a 1,000% return, if the company executes well and things go just right.
If that’s the case, why not wait for the stock to move into an uptrend (as determined by TradeStops indicators) before buying? Then, when you are ready to buy, TradeStops can help you size the position properly, so that you don’t overload your portfolio with volatile and risky positions.
With these tools and others, you can become more comfortable and profitable in your aggressive “longshot” investments.
Once you’ve determined that the odds are in your favor — avoiding the pitfalls of confusing “small” with “tiny” — you can then put further elements in your favor and position size correctly with TradeStops.
Richard Smith, Ph.D.
CEO & Founder, TradeSmith