### Statistics and the Flat Fee Part 3: The Control Chart

In part one I went over the theory, and in part two I showed you the numbers and showed you the formula. In this last part of this three part series, I’ll walk you through the Control Chart, and how to use it in your law practice.

How to read a control chart is a discussion in itself, but the key points are to look for trends. Trends over time increasing or decreasing the accuracy of the prediction. If the predictions are starting to be high, maybe efficiency has increased. If a single point is above the UCL or below the LCL, it is a red flag that something outside of statistical normalcy has occurred which means someone should figure out why the prediction was so far off the mark. As long as the points are between the UCL and LCL, there is statistically no reason to think the method of prediction is not working appropriately.

Once we can show the absolute difference predicting to prediction, and the relative variation by percentages, we get a good view of the effectiveness of current prediction methods. For each point out of control, we can determine what went wrong by looking at the particular legal service rendered in combination with the method of prediction. Also, if the variation is (or mostly) under control in the control chart, but there is a significant difference between the total average y and total average y’, “recalibrate” your formula by adding the difference between those two numbers to centralize your predicted costs. However, that simply helps center the predictions, not control variation in those predictions. Does y1 refer to the first equation, and y2 the second equation? That is not clear.

Additionally, you use this Individual Control Chart to determine if there is a real affect from attempted process improvement. If the formula that inputs into the control chart stays the same, but there is a shift in the control chart centerline that predicts more time/money than on average from the time after the process improvement was made, you have evidence of process improvement. However, if under prediction occurs, then you know the process has made things worse. The key is that the chart shows you things that would otherwise be unobservable by the naked eye.

A concern with this method is that it takes the absolute difference between predicted and actual costs, not the proportional difference. So, being $1,000 off a $2,000 prediction would appear the same on the control chart as $1,000 off of a $30 Million prediction. Clearly being off by $1,000 of a $30 Million prediction is less of a concern than the first example. However, this can be solved by using a different control chart that is calculated based on the proportional difference, instead of the difference in absolute value.

Another variant of a control chart that can be used is V= (y’-y)/y where y is predicted costs from the function, and y’ is actual costs. This shows percentage deviation from predicted, which is useful when dealing with a wider range of predicted costs. However, both charts have uses and I recommend using both to get a larger view of what is happening in your firm.

I fully admit that this is a tad complex but the math really isn’t too complicated if you can get your head around which numbers you are measuring. But the real benefits, in a true statistical fashion, determine variation in your flat fee calculations as well as create a true baseline to determine if your process has improved.

Try it, and let me know how it works for you.

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