Falling Victim to the Whims of Chance

I did an analysis of my Vancouver photographs looking at streaks of outings with no first-rate photographs.  The streaks were longer than I expected, but that can be attributed to the whims of chance.  My analysis of streaks re-enforced for me the importance of continuing to take photographs even if there has been a prolonged period of disappointing results.

For more information on methodology see my post on Photography Analytics.

I analyzed 101 Vancouver outings.  There were 30 outings with one or more first-rate photographs for a probability of 0.3 (30/101).  That's consistent with what I expected.  Before doing the analysis, I estimated 1 in 3 outings resulted in at least one first-rate photograph.  

The number of first rate photographs on any given day depends on chance.  It’s like flipping a coin.  I know I’ll get heads or tails on each flip.  I also know that I might get several heads or several tails in a row.  With the photographs, I know there’s a 1 in 3 chance I’ll get 1 or more first-rate photographs on any outing.  There will be streaks of consecutive outings with first rate photographs.  There will also be streaks where there are no first-rate photographs for several outings in a row.

Our intuition often fails us when it comes to randomness:

People tend to think that streaks in random sequential events are rare and remarkable. When they actually encounter streaks, they tend to consider the underlying process as non-random.

from http://www.ncbi.nlm.nih.gov/pubmed/20728080

This psychological expectation can play havoc with my confidence.  Based on my estimate of 1 in 3, I accept not every outing will be successful and that unsuccessful outings will outnumber the successful ones by 2:1.  It’s natural to expect luck to be evenly distributed.  That is, there will be a successful outing followed by a couple of unsuccessful ones followed by another successful one and so on.

Chance - randomness - doesn’t work that way.  Rather than being the exception, streaks are the norm.  

Even knowing this, I still expect - or at least hope - my luck will be fairly evenly distributed.  I start to feel a little hard done by if there are more than two days in a row without any first-rate photographs.  If the streak extends to three days or more, it begins to feel like a mounting crisis.  On the other hand, sometimes the wins come more frequently.  Rather than attributing this to good luck, I start to believe I have somehow “levelled up” and will now continue to produce at a higher rate.  It’s an emotional see-saw.

Here are my streaks of consecutive outings where I had no first-rate photographs.  A streak-length of zero means I had one or more first-rate photographs in back-to-back outings.

101 outings, length of streaks with no first rate photographs

My streak lengths have a median value of 2 and 75% of the streaks are three or less outings in length.  But 25% of the streaks are 4 or more outings in length and I went on one streak lasting 8 outings in a row!   That can seem like an eternity.  If you're only going out once a week that two month stretch might be enough to convince you to pack it in.  (it feels a little less painful when I'm shooting more frequently than that.)

It's tempting to think I must have been doing "something wrong" during those streaks.  However, this distribution looks similar to randomly generated streaks.

I built a simulation of 101 streaks where the probability of 1 or more first-rate photographs in an outing is 0.3.  Here's the results from three different simulations:

The streaks vary considerably with every simulation.  

It turns out a streak of length 8 or more is quite likely.  I ran the simulation 10,000 time recording the longest streak of each simulation.  Using these simulation results, I calculated the probability of a simulation having at least one streak greater than a given length.   

10,000 simulations of 101 outings with probability of one or more first-rate photographs in an outing = 0.3

100% of the simulations had a streak at least 4 outings long and 69% of the simulations had a streak of 8 outings or longer.  Rather than being an exception, a streak of 8 is to be expected. 

The expected length of streaks is dependent on the percentage of outings with one or more first-rate photographs.  For example, here's what the simulation looks like if the probability increases to 0.5.

10,000 simulations of 101 outings with probability of one or more first-rate photographs in an outing = 0.5

Even if the odds are 50/50 of getting a first-rate photograph on an outing, there is a greater than 50% chance of having at least 5 outings in a row with no first-rate photographs.  Ouch.

I conclude that despite my best efforts, streaks will happen.  Rather than getting discourage I just need to accept it and carry on.  

The photograph that preceded the streak of 8 consecutive outings without any first-rate photographs.