### Introduction

Markets change; they shift, they grow, they shrink. Think of change as a curve over time. What shape curve best represents changes in Big Law service delivery?

Service delivery here means how law firms – and law departments – deliver legal advice. That includes the mix of labor, the use of budgets and project plans, self-serve options, technology that improves efficiency + effectiveness, and frequency of communicating with clients.

Graphing service delivery changes requires metrics. Too bad we lack metrics. But a thought experiment can help us understand changes in service delivery. (My other posts about service delivery are here.)

### Types of Growth Curves

Mathematics describes many curve types. Examples include linear, logarithmic, exponential, hyperbolic, or quadratic. These shapes describe the past and can help predict the future. A Google search (20 Mar 2019 – 06:04PM EDT) shows many growth curve examples:

A Sampling of Growth Curves from a Simple Google Image Search

For our thought experiment, let’s focus on common curves:

1. Flat – no change over time.
2. Linear – the unit changes by the same absolute amount each year.
3. Hockey stick – the unit changes by the same absolute amount each year but starting suddenly, the line gets steeper. (In the illustration above, the bold red line in the 3rd row illustrates this.)
4. Constant growth – the unit changes by the same percentage each year.
5. Exponential – the unit of time is the exponent (power) of the year number.

The two Excel-created graphs below show each curve type in mythical “service delivery units” over time, which we’ll call years. Note that the first one excludes exponential and includes growth rates of 9% and 25%:

Five Growth Scenarios

The next chart is the same except it includes exponential growth – the Y value (service delivery units) is the square of the X value (time). Exponential growth dwarfs the other curves, to the point that scale compression makes it hard to estimate end values (except for he exponential):

Six Growth Scenarios, Including Exponential

### Speculation on the Shape of Service Delivery Curve

If we had to characterize changes in lawyers’ service delivery, which line would you choose? Many commentators imply rapid growth, a hockey stick, or a discontinuity.

Where I have seen the most and fastest change in service delivery is in law firm pricing and matter budgeting. Until about one-half dozen years ago, there were only a handful of law firm pricing professionals. Now, the main pricing conference, P3, has some 500 attendees. A decade ago, budgets were rare. Now, many partners budget matters. If we had good data for these, I suspect the curves for both would have some initial steep growth, then a relatively modest growth rate.

What about legal tech? Uptake of machine learning systems for due diligence reviews has been rapid. Again, my market observation suggests initial steep growth followed by more modest continuous but perhaps lumpy growth.

I visualize growth of these with the graph below: initially rapid penetration, followed by steadier growth. If we imagine not individual lawyers but rather the Am Law 200, consider where my assumptions leave the market after 10 years and ask yourself how many products / ideas / processes achieve 85% penetration (172 of 200) in 10 years.

Rapid Initial Stepwise-Growth Followed by Continuous Growth

### Concluding Thoughts on Service Delivery

I emphasize again that everything above is a thought experiment. We lack good metrics but we can think about patterns of growth. If we do, and apply the bit of rigor implied here, would that change the nature of discussion about the speed of change in service delivery?