## Statistically Estimating Project Timelines by Walter McIntyre

## Statistics

Why is it that projects more often than not come in behind schedule and over budget? This question drives business executives crazy. Why shouldn’t there be an even split between on time project delivery and late project delivery? These are valid questions.

The answer lies in statistics and human nature. Let’s deal with statistics first. When events are independent, like in rolling a pair of dice, all possible results are independent of each other. For example if I roll a set of two dice 20 times, I will get 20 results that range from two to twelve. If I plot these results in a frequency plot, I will get a normal distribution (a bell curve for you non-statistical types). If I roll the dice another 100 times, I will get the same distribution. Why? Because the probability of getting a pair of 2’s on roll one of the dice is exactly the same as the probability of getting a pair of 2’s on rolls two, three, four, etc. I could bore you with a discussion of the central limit theorem at this point, but let’s not.

Instead, let’s change the rules of dice rolling and magnetize the die so that if die one comes up 2, die number two will come up 2 also. Now the result of each roll of the dice is no longer independent. Instead the resulting sum is dependent upon whether one of the die comes up two or not. The resulting distribution of 100 rolls will be skewed instead of normal. What does this have to do with projects meeting time and budget goals? Let me explain.

If you look at a project map, a Gantt chart for example, you will see that the tasks in the project are not independent. They depend upon each other. For example, let’s say that task three cannot start until task one and task two are finished. This means that task three’s start time is not independent. It is dependent upon the finish time of tasks one and two. So, a delay in either task one or two will result in a late start of task three. Since there is dependency between the successful on time delivery of these tasks, the central limit theorem does not apply. Additionally, the dependency tends to push the time line to the right (late delivery). If we were to run through tasks one, two and three 100 times, the distribution would be skewed to the right (late delivery).

The reason dependency, in this case, skews the timeline to the right is related to human nature. Estimators tend to over promise to satisfy the requirement of a bid process (work is rarely awarded to the bidder with the longest delivery time). Workers tend to wait until the exact start date to begin work rather than start early. Surprises in the task schedule nearly always delay the completion of a task or schedule (how many times have you observed an unforeseen problem shorten the delivery time in a project?).

## Practical Approach

So what is an executive supposed to do? Most look at a schedule and apply a 70% efficiency factor to it. In other words, assume the time line will be 30 % longer and more expensive than planned. Of course the more you know about a project, its customers, and the quality of your delivery processes, the better you can estimate.

## Another Approach

Another approach for estimating a project timeline is using a tribal knowledge calculation.

(most ambitious completion time + (4 x the most probable completion time) + the worst case completion time)/6

I find this method to actually work pretty good. Typically you will get each of these completion time estimates from different groups. It is also easy to sell. One additional plus is the ability to give the results as a date range instead of a specific date.

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