Why you Fail after you Win

Maths! Photo "Amherst63-012" by NealeA, Flickr, CC-By-2.0
Maths! Photo “Amherst63-012” by NealeA, Flickr, CC-By-2.0

In mathematics and statistics, Mean is one method to represent a data set with a single number. When we talk about “Average” we often refer to the “Mean.” The Mean is calculated by diving the sum of data points by that number of data points:

Add Data Points: 4 + 8 + 15 + 16 + 23 + 42 = 108

Sum of 108, Divided by 6 data points = 108/6 = Mean of 18

Mean is easiest to calculate with numbers and quantifiable data, such as your average (mean) nightly hours of sleep, or your mean cost of lunch. For example, the “Average Human” is either calculated from measurements, or it’s a general term people use without accuracy.

By calculation, the mean result tries to represent the data with a single number. This calculation puts the mean somewhere near the middle of the data — not necessarily right in the middle (that’s the median).

In our example above, the Mean of 18 has 4 numbers below it and 2 above it. It’s near the middle but not exact.

Numbers that are wildly different from the rest of the data set are frequently excluded from statistical calculations. These “outliers” don’t well represent the data set (or perhaps they’re intentionally excluded to create specific outcomes with the calculations). Future results will be unlike the outliers, will be closer to the data set, and therefor will remain closer to the mean.

So why is a big win often followed by a big loss? Regression.

Regression to the Mean requires that any result far from that mean is, by definition, not really average. Future results will skew back towards that average. By calculation, some future results must fall below that mean, to maintain the mean.

Big wins pull the average up. To keep that average, something must pull it down again.

We see this with sports teams, where a winning streak may be followed by a losing streak (or vice versa). Right now (May 24th, 2018) the Minnesota Twins have 21 wins and 24 losses this year. They’re currently averaging 43% wins. Of their last 10 games, they had a losing streak of 3 games followed by a winning streak of 3 games.

While the Minnesota Twins current average is 43%, their average average so far this year is 48% (calculated by adding the season’s averages after the last 45 games and dividing by that 45). Based on this, I expect the Twins to win their next two games to regress towards their average average. (I’ll update this post after those two games against Seattle on the 25th and 26th — UPDATE: They lost those two games. This isn’t exact, it’s prediction using averages.)

Minnesota Twins mean and mean of the mean, 45 games into 2018 baseball season.
Minnesota Twins mean and mean of the mean, 45 games into 2018 baseball season.

(Of course, the Twins are playing a different team and all kinds of other factor come into play. Remember the Law of Small Numbers (data sets) — Small Numbers act nothing like Large Numbers. Also I’m not a sports statistician. Do not place bets based on this post!)

We see Regression in the stock market. Stocks that rally often fall again after their name is no longer being hyped for some new business practice or other reasons for being in the news.

Once we know about Regression to the Mean, we can see it everywhere — including in ourselves.

Over-confidence itself can cause our performance to drop below our average performance. We don’t try as hard when we think we’re in first.

The more data being measured (Large Numbers), the harder it is to move that mean upwards (or downwards). It requires considerable performance improvements to pull your mean performance upwards.

Understanding that under-performing will be a part of the process is essential to keeping a positive mindset and confidence in your skills. It’s also a statistical way to help predict what might come next.

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