Gaming the Numb3rs

Last night at the Old Globe here in San Diego I got to see one of my favorite plays, Rosencrantz and Guildenstern are Dead, presented as part of the Globe’s 2013 Shakespeare Festival. Doing so brought the following post to mind in that it uses the play as a springboard for discussing probability and investing. I hope you will enjoy it — or enjoy it again.


Tom Stoppard’s Rosencrantz and Guildenstern are Dead  presents Shakespeare’s Hamlet from the bewildered point of view of two of the Bard’s bit players, the comically indistinguishable nobodies who become headliners in Stoppard’s play.  The play opens before our heroes have even joined the action in Shakespeare’s epic. They have been “sent for” and are marking time by flipping coins and getting heads each time (the opening clip from the movie version is shown above).  Guildenstern keeps tossing coins and Rosencrantz keeps pocketing them. Significantly, Guildenstern is less concerned with his losses than in puzzling out what the defiance of the odds says about chance and fate. “A weaker man might be moved to re-examine his faith, if in nothing else at least in the law of probability.”

The coin tossing streak depicted provides us with a chance to consider these probabilities.  Guildenstern offers among other explanations the one mathematicians and investors should favor —“a spectacular vindication of the principle that each individual coin spin individually is as likely to come down heads as tails and therefore should cause no surprise each individual time it does.”  In other words, past performance is not indicative of future results.

Even so, how unlikely is a streak of this length? Continue reading

Probability, Baseball and the WSJ

TroutAs if we needed further demonstration that we suck at both math and probabilities, The Wall Street Journal foolishly suggests via headline that the Los Angeles Angels’ season is already effectively over because the team had an MLB-worst 10-20 spring training record. This isn’t the first time that the Journal has performed mathematical malpractice, of course.  But it still demonstrates a fundamental misunderstanding of how to use probabilities – whether in sports, gambling, or investments. Continue reading

Data-Driven Difficulties

As my masthead states, I aspire to make my perspectives data-driven.  Too much analysis (in the investment world and beyond) is driven by ideology.  I reject that idea and maintain that every idea and every claim — even ideas and claims I would normally be prone to accept on account of my pre-existing values, beliefs and expectations — should be judged first and foremost by the data and evidence that support (or fails to support) them.   

A major problem with this approach (as I have written before; see here too) is that we all have difficulties engaging with issues mathematically and probabilistically. 

We are all prone to innumeracy, which is “the mathematical counterpart of illiteracy,” according to computer scientist Douglas Hofstadter. It describes “a person’s inability to make sense of the numbers that run their lives.” Although Hofstadter coined the term, mathematician John Allen Paulos popularized the concept with his book, Innumeracy: Mathematical Illiteracy and Its Consequences.  While illiteracy strikes mostly the uneducated, we are all prone to innumeracy. 

For example, most people would consider it an unlikely coincidence if any two people would share the same birthday in a room with 23 people in it. People would generally look at it like this:  since one would need 366 people (in a non-leap year) in a room to be certain of finding two people with the same birthday, then it seems to make sense that there is only a 6.28% chance of that happening with only 23 people in a room (23 divided by 366). However, 99% probability is actually reached with just 57 people in a room and 50% probability exists with only 23 people (more on the “birthday problem” here).

In the investment world, we intuitively tend to think that if we start with $1,000 and suffer a 50 percent loss on Day 1 but make 50% back on Day 2 (day-to-day volatility being exceptionally high, donchaknow), we’re back to even. However, were that to happen, our $1,000 would be reduced to a mere $750 (more on the “arithmetic of loss” here).  Similarly, a sum of money growing at 8 percent simple interest for ten years is the same as 6 percent (6.054 percent to be exact) compounded over that same period. Most of us have trouble thinking in those terms.

These examples are pretty (pardon the pun) simple.  When things get more complicated we can really go off the rails, especially when the answer seems straightforward.  To illustrate, if you have two children and one of them is a boy born on a Tuesday, what is the probability you have two boys?  If you do not answer 13/27 or 0.481 — as opposed to the intuitive 1/2 — you’re wrong (to find out why go here).

The consequences for us as investment professionals should be obvious. As a starting point, we need to be careful to understand the math ourselves.  We also need to use math appropriately and well.  For example, virtually every investment presentation is replete with charts and numbers.  But do these charts really show what they are offered to show (see below)?

Chart sourcesRolling Stone; U.S. Department of Energy (do a bit of research on Boobquake and watch this for other examples of correlation not implying causation and check out this thoughtful post from Interloper about the misuse of charts and more).

Similarly, we need to be careful to check the work (as best we can) of those upon whom we rely — whether economists or other investment professionals.  Finally, we have to communicate investment realities, largely predicated upon math, to our clients carefully, appropriately and meaningfully, even though they may well be severely challenged by innumeracy.  Doing so is much easier said than done.