Challenging the flaw of averages

By Enda Keane

Have you ever heard the sorry tale of the statistician who drowned while crossing a river that was, on average, only three feet deep? A mathematical fact with enormous practical consequences.

This funny anecdote is applicable in many industries where the law of averages is used as a means for making key decisions.

As an example, a number of years ago I read an interesting article about how a U.S. air force lieutenant Gilbert Daniels challenged and overcame this flawed average figure.

In the 1940’s the air force was concerned with the high level of crashes which was attributed primarily to pilot error. At that time, the airplane cockpit was designed for the average pilot. Daniels however worked out that there was a huge flaw in the design because there were in fact no pilots that met these average dimensions. This cockpit design was responsible for many crashes. To their credit, the Air Force did take action and started to design cockpits to fit the intended pilots, leading to much better results.

The Flaw of the Standard Tree

Many foresters around the globe use the average tree as a key parameter for the estimation of the value of a forest.

From our experience of measuring many forest types in many parts of the world, given the natural variation of tree size, this is a very flawed metric for assessing the value of a forest. The challenge with forest measurement is the fact that the tree size varies greatly throughout a forest. However, many of today’s forest managers still cling to “flat earth” belief that the average tree is a good indicator.

Having collected millions of tree profiles from trees felled by harvesting machines across the world, we started to clearly see that this method was in most cases very flawed. We firmly believe that foresters need to abandon the average tree measurement and face up to the fact that they need to act on a range or distribution of tree measurements rather than a single average tree.

To address this problem, Treemetrics developed a software solution called Forest HQ which was recently demonstrated for the first time at the Elmia Wood show in Sweden. The software platform has a simulation tool which allows foresters to analyse a distribution of tree sizes for a sample representing the full range of tree sizes measured in the forest. A virtual harvesting simulation module within Forest HQ creates tree taper profiles that allow the forester to simulate the cutting of the measured trees into log products. The simulator also allows the user to also predict the level of waste by analysing quality data recorded by visual assessment or a 3D laser assessment (see figure 2 below). The resultant simulations provides an estimate of the log product volumes standing in the forest i.e. a detailed estimate of the potential timber production for a given set of desired products. From this point the forester can easily calculate the market value of a forest using the current market value of the specific log products.

Figure 2: ForestHQ stem simulator viewer showing log product potential and waste

Summary
Why was the U.S. air force willing to make such a radical change so quickly? Because changing the system was not a difficult intellectual exercise — it was a practical solution to an urgent problem. Hence the modern car has adjustable seats, steering wheels and mirrors.

Foresters need to reflect and assess the practical consequence of poorly estimating the value of the forest. To properly measure the forest, you have to ensure that a good representation of tree size variation is collected when measuring the forest. The resultant analysis needs to show the range of trees size variation to ensure a more accurate prediction of the value of the forest.

To simplify the measurement challenge we have a simple statement: Small trees that are under represented are the enemy of the buyer and big trees that are under represented are the enemy of the owner.

To find out more about our Forest HQ technology and in particular, the forest simulation element, click here.

 

Reference:
https://www.thestar.com/news/insight/2016/01/16/when-us-air-force-discovered-the-flaw-of-averages.html

http://www.harpercollins.ca/9780062358363/the-end-of-average

http://flawofaverages.com/