What reserve holds nineteen years out of twenty?
Reserving the average across forty matters covers you about half the time. This table shows what each extra thousand a matter buys, and where it stops buying anything.
Words on this sheet
- Standard deviation: How far a typical reading sits from the average, in the same units as the readings.
- Sample variance: Spread, squared: the standard deviation multiplied by itself.
Legal Intermediate Data Table free
After you install, this is the model to open.
How Much Should We Reserve Per Matter?
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
The answer
- Reserve the average
- 52% cover at $30,000 a matter, a coin flip
- Nineteen in twenty
- $38,000 a matter holds 95.4% of the time
- Expected shortfall
- $3,763 at $38,000, down from $73,549 at the average
- The last $4,000
- $160,000 of cash removes only $3,365 more shortfall
Two questions get confused in every reserving conversation. What does a matter cost on average, and what does the book cost if things go badly. The expected cost of one matter answers the first: 62% of $48,000 is $29,760, and forty of them cost $1,190,400. But an average matter also has a standard deviation of $31,015, driven mostly by the fact that a matter either pays or it does not, and forty of those give the book a standard deviation of $196,157.
That last step is the one worth understanding: the book's variability grows with the square root of forty rather than with forty, so the more matters you carry the smaller your relative uncertainty gets, which is exactly why a book is easier to reserve than a case. The sheet opens at $30,000 a matter, a whisker above the average. Click Run and the table sweeps the reserve from $26,000 to $42,000.
At $30,000 the reserve holds in 52 of every 100 runs and the expected shortfall is $73,549. That is the headline and it should be uncomfortable: reserving the average is a coin flip, because the average is the middle of the distribution and half of everything lands above the middle. At $34,000 the reserve holds in 81 of every 100 runs (80.6%) with an expected shortfall of $21,011.
At $38,000 it holds 95.4% with $3,763. At $42,000 it holds 99.4% with $398. So the reserve that holds nineteen years in twenty is $38,000, about 28% above what a matter costs on average, and the last $4,000 a matter, which is $160,000 of cash across the book, removes $3,365 of expected shortfall. That is the point where prudence stops being prudence and starts being idle money, and the table lets you see it rather than argue about it.
Run it again with the matters in the book changed from 40 to 120 and the same 95% confidence needs only about $34,400 a matter, because a bigger book is a more predictable book, which is the strongest argument there is for reserving at the book level rather than matter by matter. The model assumes matters are independent, which fails badly if several arise from the same event or the same court, and it uses a normal approximation that is reasonable at forty matters and poor at five.
Put your own closed-matter history into the payout chance, the average payment and its standard deviation, and your live matter count into the matters in the book.
The model
It arrives on a tab called Template: Reserve Per Matter, carrying these columns:
- Try reserve per matter ($)
with the model computed beside the data:
| Expected cost of one matter ($) | 29,760 |
| Second moment of one matter | 1,847,600,000 |
| Variance of one matter ($ squared) | 961,942,400 |
| Standard deviation of one matter ($) | 31,015.2 |
| Expected cost of the book ($) | 1,190,400 |
| Standard deviation of the book ($) | 196,157.3 |
| Total reserved ($) | 1,200,000 |
| How far above expected (std deviations) | 0.04894 |
| Chance the reserve covers the book | 0.5195 |
| Standard normal density at that point | 0.3985 |
| Expected shortfall ($) | 73,549.1 |
| Reserve above the expected cost ($) | 9,600 |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
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