What are the Odds? by Kevin McManus
First published in Industrial Engineer magazine October 2002
It usually happens at least twice a year. Whenever the weekly lottery begins to approach the $50 million mark, workplace discussions (and possibly activities) begin to focus on what it will take to become rich this time. People begin to band together to sweeten the pot, and I invariably end up getting asked to participate as well. Each time this occurs, I have to bite my tongue and curb my criticism.
The statistician in me wants to tell them about how the odds of winning really don't increase significantly when you by more than one ticket, and that their odds of ‘winning big' in general (1 in 7 million) are much less than the possibility that they will be killed by lightening on the way home from work today (1 in 2 million). Since I don't want to spoil their fun or shoot holes in their dreams, I keep these thoughts to myself. At the same time, I also wonder about the degree to which we really do dismiss statistical probability as we live our day-to-day lives at and away from work.
Industrial Engineers spend significant curricular time focusing on statistics concepts and applications. While the odds of using a high percentage of these skills in the future are less than the chance of getting killed by a dog (1 in 700,000), their study does provide us with a way of thinking that helps us both understand systems performance and predict the potential output levels of such systems. One of my recent lottery experiences jogged some interesting thoughts in mind about the non-use of statistics at work, and how a shift in perspective really might help ease some longer term pain.
My insights centered around using statistics to project systems output, or more specifically, the probabilities of attaining certain levels of systems output given the current design of the associated processes and procedures. This train of thought progressed to one where I envisioned using statistics to gauge the probability of attaining those lofty performance goals that many of us are just starting to project (or have projected for us) for the coming fiscal year.
In the past, I have more often than not seen managers simply take the current year average and bump it up by a percentage to set next year's goal. This is usually done before (or without ever) considering the degree of systems change that would be required to consistently attain that level of performance. In turn, unrealistic expectations are raised and skepticism about management's understanding of the business is ignited. Imagine what might happen when the desired result is not consistently met?
When I first became an Industrial Engineer, using statistics in such a manner was a time consuming process. Spreadsheet software however now makes conducting such an analysis quite easy. For example, if you have a twelve-month sales history, you can easily obtain a mean and standard deviation for this data, and then use a special formula to determine the probability of hitting certain performance levels if the system is not changed. In other words, you can use statistics to compare process capability to the goals that you are considering for monitoring performance.
The more effective approach involves using statistics to identify the capability of the system as it is currently designed and to measure performance to this capability over time to search for unexpected systems changes. Once we know where our current baseline is, we can analyze the data further to determine which factors are hindering our performance to the greatest degree and possible countermeasures for minimizing or eliminating these factors. Only after doing this should we even begin to think about what levels our performance might improve to if these changes are implemented.
Another point to consider involves system variation. If you have done little to stabilize your processes, the probability of hitting your process average, or close to it, will be notably less. It will be even more difficult to project future system performance. On the other hand, if you do what Dr. Deming (and others) suggest, you will seek to reduce process variation before even attempting to shift the process average up or down.
Because the lottery is a relatively stable process, projecting your potential success against that system is pretty easy to do. Work systems however are inherently less predictable, primarily because the potential for external influences (those outside of your immediate control) is so much greater. This only heightens the need to better understand our systems and processes in a fact-based manner.
More than anything else, you need to be clear on the operational definitions that are being used and the source of your data itself. I have referenced a few mortality odds in this article, but I simply got them off of the Internet. The odds of my using them to make a meaningful decision are about as great as those of being killed by falling out of bed (1 in 2 million). If you don't know where the data comes from, you should not use it to make assumptions or decisions.
If you are projecting performance goals for next year by simply bumping up this year's average, the odds of hitting those goals are probably about as good as being killed by poisoning (1 in 86,000). Of course, I am making some pretty big assumptions in making such a statement, but so are you in terms of setting your goals in the manner that you are. It's like telling me to get to work two minutes faster each day on average, without giving me a car that can't be detected by radar, fewer stop lights, or relief from the train that impedes my progress at least twice a month.
If we have a basic understanding of probability, we will think our people are foolish for buying multiple lottery tickets in a given week. If we have a basic understanding of probability and fail to use those skills as we set performance goals, we are the ones that are being foolish. If we attempt to sell those higher goals to our people without also improving the system involved, they will see us as being a lot worse than foolish.
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“The only thing I know is that I do not know it all.” -- Socrates