The Fallacy Of Conjunction

I wanted to do a quick article on something that I've been pondering for a while, it is a particular cognitive bias called the, conjunction fallacy. 

The conjunction fallacy is a cognitive bias whereby the brain gives two outcomes a greater statistical likelihood than a single outcome. Generally the conjunction fallacy will not play a significant enough part in our day to day lives for us to notice.

But when we are attempting to profit by trading sports on Betfair, then this cognitive bias has the potential to ruin your long term profits and that is enough of a reason to understand what it is and how to recognise when you're experiencing it.

Let's look at a scenario where  conjunction fallacy can rear its ugly head; consider Barcelona and Lionel Messi. In the 2014/2015 season Messi scored 45 goals in 38 games and 10 Champions League goals in 13 matches; in the last 5 seasons, Lionel Messi has scored 198 goals in 190 games.

In the following scenario, using the information above, put in order the most likely outcome as number 1 and the least likely as number 3:

It is the following season and Barcelona are just about to play Atletico Madrid at home*

 You can't lose with this bet; right?

You can't lose with this bet; right?

1. Barcelona will win the game and Messi will score
2. Barcelona will win the game
3. Messi will score
4. Barcelona will lose the game and Messi will score

OK, so you should have put 

1. Barcelona will win the game
2. Messi will score
3. Barcelona will win the game and Messi will score
4. Barcelona will lose the game and Messi will score

At this point you might say hang on, Barcelona lose so few games and Messi's goal ratio over the previous 5 seasons was better than one goal per game. So surely, Barcelona winning and Messi scoring are the most likely thing that should happen on that list.

Unfortunately you'd be wrong, because even though all those things are true,  Messi scored 198 goals in 190 La Liga games, stretching back 5 seasons. However, he still failed to score in 45 of those matches, which is almost 25%. 

On the flip side, Barcelona only lost 22 games in that same 190 game period, which is of course just under half the amount that Messi fails to score in. In other words, it is twice as likely that Messi will not score, than Barcelona will lose. Or to put it a simpler way, it is more likely that Barcelona will win than Messi will score.

High street and online bookmakers take advantage of the  conjunction fallacy all the time; how many times have you walked past a bookmaker's shop window, or seen a new customer offer from an online bookmaker, offering you a great odds deal! On Team A to score and Top Scorer to score at any time?

Or Team A to win by 2 goals and both teams to score?

There are many, many examples of bookmakers taking advantage of the  conjunction fallacy and the clue is in the name, it's a fallacy in thinking, because any time two events can happen independently of each other, then the statistical likelihood of them happening together is always less than them happening independently.

So now you know what  conjunction fallacy is; how do you know when you are experiencing it and not just identifying two likely outcomes in an event?

Well in any given trade, whereby you want to trade on two outcomes or more; ask yourself, how connected are these outcomes to each other?

So outcomes in an event are either dependent on each other, or have what we can call an interpersonal connection, or a weak interpersonal connection.

Imagine we are looking at a cup final between Barcelona and Bayern Munich, below are 3 examples of connections between outcomes.

Dependent connection –  The final result of the game and the winner of the cup – These two things are inextricably linked. If a cup game ends 2-0 to Team B then Team B wins the cup. You may have bet on Team B to win the cup earlier on in the season and then you decide to bet on Team B once the cup final starts.

Betfair Trading Tip – You are not suffering from conjunction fallacy if you bet on these two things, because the statistical likelihood of the outcome of the two events are linked. However, you may be suffering from a basket too full with eggs if you have made two bets like this, but that's another story.

Interpersonal connection – The team of the top scorer winning and the top scorer scoring a goal at any time.

Betfair Trading Tip – This is a classic conjunction fallacy bet, the two things are mutually exclusive, but of course other factors come to play such as, how well the team is playing at the time of asking and what sort of form the top scorer is on. You can make two individual trades like above, but never, I repeat never, do the above as a double.

Weak Interpersonal Connection – A particular team winning and the top scorer scoring the first goal

Betfair Trading Tip – This example is the ultimate conjunction fallacy bet, if you ever take this bet as a double or two singles, slap yourself really hard across the face. The only time you should take a bet like this is never, I don't care if you're being offered 100/1, just walk away

So we see that in the first example, the winner of the cup is completely dependent on the result of the game, if you lose the game, you lose the cup, if you win you win, simple.

The second example the two occurrences have an interpersonal connection, in that one may influence the other. If Barcelona are playing well and go 1 or 2 nil up, then their top scorer (at the time of writing, Luis Suarez) may well score and indeed, if Suarez does score, that will have a positive effect on Barcelona and may lead them to win. However, importantly, they are not dependent on each other, one can happen and the other not.

Lastly, we have a weak interpersonal connection in one team winning and the top scorer scoring the first goal, this as I have said above, is a sucker bet, don't ever take it, or you're being a sucker.

So whether it's Leicester City to win Premier League and Jamie Vardy to be top scorer, or Tottenham to win and Harry Kane to score first goal, or even Roger Federer to win without dropping a set, make sure you are aware that the statistical likelihood for any of those outcomes is lower than for the single event to happen on its own.

Suarez conjunction fallacy bet.jpg

If you are uncertain of conjunction fallacy bets, then just check out the double bet offers that are around and you will start to become more aware of these bets and ultimately avoid them.

*By the way, Barcelona won the game 2-1, Suarez scored, Messi didn't...

As ever, good luck and happy trading.

The Zen Trader