Wednesday, 17 October 2007

The rule of three

Whether it's in the financial markets or on the football pitch, most people believe in runs or streaks of luck. We tend to think that if a stock has risen for several successive days, or if a team has put together a string of wins, then the chances of a future good outcome are increased. However this belief is often a fallacy because streaks are a natural part of any random sequence (and see here).

Now Kurt Carlson and Suzanne Shu report that the key moment we perceive a streak as having occurred is after three repeats – what they call the 'rule of three'. In other words, we don't read meaning into a repeat of two, and we don't read any additional meaning into streaks of more than three.

In one study, students were asked to decide how much fictional inheritance to invest in a stock. After hearing the stock had risen for one day or for two consecutive days, there was little increase in the amount they chose to invest. The largest jump in the students' investment decision came after they learned the stock had risen for three consecutive days. By contrast, hearing that the stock had risen for four, five or even six consecutive days didn't make any further impact on their decision making.

Other support for the rule of three came from an analysis of basketball data and of how streaks are discussed in sports journalism.

Carlson and Shu say the 'rule of three' has implications in real life. For example, in sports gambling, a team that has won three games in a row will be overpriced by the bookies (because most punters will have acted as though the team has an increased chance of winning), while a team that has lost three in a row will be under-priced. “A savvy gambler (who is aware of the rule of three) might do well to bet against teams that have won three games in a row and bet for teams that have lost three games in a row,” they said.

Carlson, K.A. & Shu, S.B. (2007). The rule of three: How the third event signals the emergence of a streak. Organisational Behaviour and Human Decision Processes, 104, 113-121.

Post written by Christian Jarrett (@psych_writer) for the BPS Research Digest.


  1. Anonymous12:48 pm

    Why a the results of sports fixtures to be considered random? Surely if a team has won many games in a row, it is because they are a good team and are therefore more likely to win the next game?

    I think this piece of 'research' is a little bit simplistic as you have reported it.

  2. Statistically speaking, streaks can be very unlikely. Just how unlikely depends on the signal to noise ratio of the system being studied. Quite how noisy investment markets are is open to debate, but broadly if a fund returns unexpectedly positively, say, five times in a row, then it's unlikely to have happened by chance.

    Of course, there are a lot of funds in the world, so even if it is unlikely, there's a fairly good chance that *some* of them will exhibit this "lucky streak" by chance.

  3. By the way, I was assuming I was talking about annual returns in that last comment. Obviously the chance of having five good consecutive days are likely to happen by chance, but not five years.

  4. Anonymous3:42 pm

    The poster who wonders why "results of sports fixtures ... considered random" misses the rationale I think

    The bookies set their odds in accordance with the available information, you can't beat the odds by knowing that Liverpool is a better football team than Wycombe Wanderers, because the bookies know that too.

    However if the bookies are consciously or unconsciously influenced by the "rule of three" which has no basis in fact then you can beat them by playing against this rule. You need have no regard to the relative strength of the teams because that's already factored into the odds given.

  5. Would I be completely out of line in thinking this research adds some support to the idea of a "three time convincer" (i.e. you have to demonstrate a proposition three times before most people find it convincing), as used by some sales people, trainers and speakers?