Binary thinking and betting: What is a “good bet”?

The way bettors process information is important to their success. What is binary bias? What can YouTube and the Baltimore Ravens tell us about betting psychology? What is a good bet? Read on to find out.

What is binary thinking?

Binary thinking involves sorting information into mutually exclusive options, not unlike the way a computer thinks in binary code. Something is either a 1 or a 0 and those are the only two options. There is no grey area.

Many argue that humans instinctively sort information in this kind of way, naturally jumping into this kind of binary method of thinking.

For primitive humans this made sense. The kind of judgements that needed to be made to survive lent themselves well to such a way of thinking, especially when it came to quick decision-making. Decisions such as whether a rustle heard in the bush is a predator or non-predator were life-or-death ones.

The reward offered by spending valuable time weighing up the information available about the sound (whilst a predator could be preparing to strike) is not worth the risk of being eaten. Simply categorising the rustle in the bush as a predator and fleeing makes much more sense from a risk vs reward perspective.

Richard Dawkins claims such a desire for straight yes-or-no solutions to neatly categorise information is “The tyranny of the discontinuous mind”. He suggests that people seek the reassurance of an either-or classification because it’s much easier for the brain to think in binary, as our distant ancestors did, rather than consider the shades of grey between two conclusions.

This kind of binary decision making is perfectly fine for basic snap decision making, but we now live in a world of nuance. Nowhere is this reflected more acutely than in the world of betting.

Binary bias: caffeine and YouTube ratings

How does binary decision making affect the way we process information?

Fisher and Keil set out to ascertain this in a series of studies on what they called “binary bias”. For these studies, participants were given evidence about a topic, before being asked to summarise the evidence and give a rating that best captured their overall impression of the strength of the argument.

If people are evaluating data from different studies investigating the relationship between caffeine and health, for example, they would quickly categorize data as either showing an effect or not, regardless of the relative strength of the evidence.

Overall they found that: “Across a wide variety of contexts, we show that when summarizing evidence, people exhibit a binary bias: a tendency to impose categorical distinctions on continuous data. Evidence is compressed into discrete bins, and the difference between categories forms the summary judgment.”

In other words the participants tended to ignore the relative strength of the evidence presented to them, instead favouring categorising them into discrete categories and looking at the sum total of evidence within those categories.

This stripped out all the continuous data. As a result, a conclusion with a 25% likelihood in one direction was simply bucketed with all the conclusions that leaned in that direction regardless of their strength. This made the data easier to process for the test subjects but meant that the value of the information diminished.

YouTube discovered this whilst trying to refine their rating system for videos. Their star ratings proved to be ineffective since the vast majority of votes were either for one star or five star.

This was a consequence of binary decision making. If the user likes the video they categorise it as a five, whilst if they didn’t like the video then they categorised it as a one. All of the information in the middle of these two discrete categories was lost. This resulted in YouTube switching to a simpler thumbs up/down system.

Outcome bias

As shown above, humans prefer to sort information into two distinct categories where possible. This is also the case within betting.

To an inexperienced bettor, a good bet is simply one that wins. A bad bet is one that loses. Those two buckets are easy to grasp and make intuitive sense to somebody without a good grasp of the nuances behind betting.

This however, is completely false. A winning bet can be a terrible bet whilst the best bet ever placed may have turned out to be a loser. By categorising bets in such a simple way, all of the useful information gets stripped away.

This desire to attribute a data point into a “good” or “bad” category due to the outcome of an event was shown during the debate around the Baltimore Ravens’ failed two point conversion attempt from the 2019 NFL season.

Mathematically, the decision to go for the two point conversion was the correct one by the Ravens. However, because the attempt failed, some pundits categorised the call into the “bad decision” bucket.

The extra information given by the analytics behind such a play was removed for these pundits due to a mixture of outcome bias (a failed attempt must have been caused by a poor decision) and binary bias (the need to place the play into a distinct category). Had the play proved succesful their opinions would, in all likelihood, have been different.

What is a good bet? Thinking like a bettor

In order to get into a successful betting mind-set the bettor must learn to avoid such biases. The grey area between win and lose is what distinguishes a good bet from a bad one.

Bettors work in percentages. If the bettor’s percentage is more accurate than that of the bookmaker’s he will win in the long run. But is it even possible to ascertain whether the bettor’s percentages are even accurate?

Without a large sample size it is almost impossible to answer that question definitively.

Take one famous percentage figure as an example. Statistics website FiveThirtyEight gave Donald Trump a 30% chance of winning the 2016 US presidential election. Of course, Trump went on to become president.

The reaction to this prediction from some quarters was to label it as “wrong”. Given the binary approach people take to such things, you can see why it would be tempting to do so. As the work on binary bias done by Fisher and Keil showed, people removed the weakened strength of the prediction (Trump being awarded 30% chance instead of 0% chance) to place the prediction in the “wrong” category they are comfortable with.

But this is obviously nonsense. According to the prediction, Trump should win three times in ten. The fact the scenario played out to become one in which Trump won shows us nothing new about the accuracy of the prediction.

The sample size would need to be extended to a meaningful level by running the same election repeatedly (which is of course impossible). Only then could we see how close FiveThirtyEight’s prediction of 30% Trump wins was to reality.

Controlling the chaos

This is understandably disconcerting. It goes against our instincts to say that we actually don’t know and may never know whether an individual prediction was a good one.

There have certainly been bets I have placed where I intuitively felt the percentages were in my favour, but outside of a model run across a large sample of similar events, there is no way to definitively say that I was correct.

As bettors we are operating in that grey area between the “good” and “bad” bet buckets. To be successful you have to step away from easy classifications and embrace the percentages on an individual bet for what they are. Simply attempts to create a “good” bet with the knowledge that we may never truly know whether we can ever classifiy them as such.

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