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# Morrison on Metrics: Graphing solutions for complex data sets

Use inverted axis graphs and double axis graphs to paint a clearer picture

Inverted axis graphs and double axis graphs allow managers of law department data to present data more effectively. Whether budget numbers, compensation changes, or benchmark analyses, these two techniques, described below, add flexibility and insight to your metrics.

We are all accustomed to graphs with the horizontal X axis tracking numbers from low on the left to high on the right. Vertically, the Y axis indicates numbers from low on the bottom to high on the top. The lower left corner of the chart, therefore, typically starts at 0,0. (In another column we will look at changing scales and intervals.).

But with an inverted graph, the numbers on the Y axis decline as you move up the axis. Why is that useful? Perhaps you want to show that your department’s payments to law firms in Japan have tracked the value of the Yen to the U.S. dollar. The payments are shown against the X axis, year after year, and let’s assume they have been trending up. But perhaps that  trend reflects the weakening value of the dollar versus the Yen more than growing needs for local counsel. If the Y axis is inverted, so that the higher you go on the axis, the less the dollar buys in Yen, then the graph will show that your seeming profligacy in that country stems more from the falling dollar than your need for more or costlier legal advice in that country.

The advantage of inverted scales results is that the eye can better see the relationship between two graphed phenomena. Had the rising Yen been reflected on a normal Y axis, the legal spending would have diverged from the exchange rate counterpart. If you invert the Yen conversion, the two track each other and make the point.

A double axis graph serves a different data problem:  when one set of numbers is small in range and another is very large. Double-axis graphs let you show data that has scales of very different magnitudes on the two vertical axes, such as the number of months cases have been pending versus dollars spent, or years out of law school versus base compensation.

Keeping with the theme, a double axis chart comes in handy if you want to show the number of Japanese law firms you retained each year on the X axis matched against two other series. On the left Y axis might be the dollar value of revenue from Japan while right Y axis might show the number of facilities in Japan where you operate. The dollars rise to the tens of millions; the locations don’t reach double digits. If you put both of them on the same Y axis, either the spending would swamp the locations (they wouldn’t register except as a flat line along the bottom) or the spending would have to be severely truncated since the number of locations are so relatively tiny.

To resolve this problem, the left axis can show locations and run from 0 to 16 with intervals of two. The right axis, the double axis, can show dollars, running from zero to \$200 million with intervals of \$50 million. With that solution, the correlation, if there is one, will be clear.

### Rees Morrison

Rees Morrison, Esq. is a partner at Altman Weil, Inc. with countless interests in legal data analytics. He is also the founder of General Counsel Metrics, LLC....

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