Legal Risk Evaluation Services
Using Decision Tree Analysis
L AW
from a business point of view.®
An Introduction to Legal Risk Evaluation
Using Decision Tree Analysis
We first used decision trees to evaluate legal risks in the early 1980’s,
applying the techniques learned from Marc Victor who created
Litigation Risk Analysis™. Since then, we have introduced these
techniques to clients and in-house counsel. We have also served as
consultants to lawyers in other firms and have used decision tree
analysis (DTA) in a variety of litigation related contexts.
The first section in this brochure gives a summary explanation of DTA
and addresses some of the common “challenges and responses” we
have encountered in discussing why lawyers and their clients should
use decision analysis. The remaining sections explain the mechanics
of DTA and its use to value a case and make strategic decisions. The
brochure also serves as an introduction to the software that has
simplified the mechanical processes while allowing for much more
sophisticated analyses.
The brochure is not an in depth explanation of DTA, nor does it
illustrate all of its many uses. It should, however, give you a good
taste of what DTA is and what it can and cannot do. DTA will not tell
you the result in any given case. Properly used, however, it enhances
dispute management by allowing for a more rigorous and methodical
application of the judgment that good lawyers have always used to
assess the strengths and weaknesses of their cases and to make the
most cost-effective uses of their client’s resources.
Decision analysis has its limitations (GIGO – Garbage In, Garbage
Out – is perhaps the best example) but it also has the readily
apparent benefits that are best summarized in this quote from a
piece by Marc Victor and co-authored by the general counsel and
deputy general counsel of Chevron Phillips Chemical Company LP,
ConocoPhillips and Phillips Petroleum Company:
Businesses have long valued risky situations
by weighting the potential outcomes by their
probabilities of occurring, and then selecting
the strategy with the highest positive (or
lowest negative) “probability-weighted”
average [the “expected value”]. At least two
industries owe their long existences to the
soundness of making decisions based on
probability-weighted averages: the insurance
industry and the gambling industry. And while
a mathematician could prove that continually
making decisions based on expected values
will maximize one’s wealth (or minimize one’s
losses) over time, Damon Runyan (18801946) said it best: “It may be that the race is
not always to the swift, nor the battle to the
strong – but that is the way to bet.”
Evaluating Legal Risks and Costs with Decision Tree Analysis in
SUCCESSFUL PARTNERING BETWEEN INSIDE AND OUTSIDE
COUNSEL (Chapter 12) West Group & ACCA, 2000-2004, Marc
Victor, et. al.
i
Lewis and Roca LLP Legal Risk Evaluation Services
TABLE OF CONTENTS
Why Decision Tree Analysis?
E xplanation of Decision Tree Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Challenges and Responses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
The Coin Flip
Decision Tree Analysis for Litigation—How a Tree Works. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
The “Solved” Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Determining Probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
Sample Decision Tree Analysis: Smith v. Jones
Unsolved Tree with Variable Definitions Hidden & Shown
Explanation of Unsolved Tree—Definitions Hidden. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unsolved Tree with Variable Definitions Hidden. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Explanation of Unsolved Tree—Definitions Shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unsolved Tree with Variable Definitions Shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-2
3-3
3-4
3-5
The Variables Report
Explanation of Variables Report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
Variables Report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3
The Solved Tree
Explanation of Solved Tree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2
Solved Tree With Only Essential Terminal Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3
Solved Tree With Terminal Columns Showing Components of Judgment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4
Node Comments and The Win/Lose Analysis
How Scientific is Decision Tree Analysis?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Decision Tree With Flags Denoting Location of Node Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Win/Lose Comment For Choice of Law Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Expanded Win/Lose Comment For Choice of Law Issue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probability Wheel For Choice of Law Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-2
6-3
6-4
6-5
6-6
ii
Lewis and Roca LLP Legal Risk Evaluation Services
TABLE OF CONTENTS
Continuation of Sample Decision Tree Analysis: Smith v. Jones
Probability Distribution Charts
Explanation of Probability Distribution Charts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2
Probability Distribution Chart Created Using TreeAge Pro™ Excel Add-in Module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3
Probability Distribution Chart Created In TreeAge Pro™. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4
Sensitivity Analyses
Explanation of Sensitivity Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sensitivity Analysis On Causation Issue Created Using TreeAge Pro™ Excel Add-in Module. . . . . . . . . . . . . . . . . . . . . .
Sensitivity Analysis On Causation Issue Created In TreeAge Pro™ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Strategy Graph On Causation Issue Created In TreeAge Pro™. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiple Variable Sensitivity Analysis Created Using TreeAge Pro™ Excel Add-in Module. . . . . . . . . . . . . . . . . . . . . . . .
Tornado Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8-2
8-3
8-4
8-5
8-6
8-7
Professional Biographies
ouglas L. Irish. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-2
D
José A. Cárdenas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-5
iii
Why Decision Tree Analysis?
1-1
Explanation of Decision Tree Analysis
Coping with uncertainties in a reasoned way is essential to effective dispute management. Documenting your decisions is essential to defending
your due diligence in making them. A decision tree puts multiple uncertainties into perspective, taking into account all potential outcomes. It is your
tool for making good decisions, retaining a record of how you reached them, and improving your chances of obtaining a good outcome.
Decision analysis rests on the idea of expected value. In shorthand terms, “expected value” is the value of a potential outcome, multiplied by the
probability of its happening. In the multiple uncertainty world of dispute management, it is the weighted average value of all potential outcomes.
Business Decision Makers Can Use This Tool in Managing Their Disputes
Decision makers and their lawyers involved in dispute management must make decisions with incomplete information. Questions arise such as:
•
•
•
•
•
Will the judge admit this document into evidence?
Will the jury believe the design met the state of the art defense?
Is it worth spending $10,000 for expert witness A to help us prove this point?
What impact will a favorable ruling on choice of law have on the case?
Will the jury’s damage award run in the high, medium or low range?
Lawyers tend to express their opinions in qualitative, not quantitative, terms, e.g., “It is probable that ….;” “It is more likely that ….;” “There is a
good chance that ….” However a lawyer’s “probable” may mean 55 % to her, but 85% to you. On a million-dollar decision, that can be a $300,000
misunderstanding. We need a language that is both common and measurable.
Probabilities expressed in percentages provide the essential qualitative ingredient as shown in this example:
Question: “The plaintiff has offered to settle for $60K. My best estimate is that I have a 40% likelihood of being held liable. If I am held
liable, there is about a 25% probability the verdict would be in the $225K range, a 50% probability of being in the $100K range, and a
25% probability of being in the $35K range. Should I accept the offer?” Answer: If you are risk neutral, not at that price. But you might
consider settling it in the $46K range. Here’s why:
(.4 x .25 = .10): 10% likelihood of a $225K verdict, so its expected value is $22.5K
(.4 x .5 = .20): 20% likelihood of a $100K verdict, so its expected value is $20K
(.4 x .25 = .10): 10% likelihood of a $35K verdict, so its expected value is $3.5K
The sum of the expected values (the weighted average) of all liability scenarios (22.5+20+3.5) is $46K. This is a simple example, easily analyzed on
the back of an envelope. But when there are several variables, the human mind has difficulty structuring, keeping in mind, and analyzing all their
possible permutations and combinations of outcomes. It needs a tool, and a Decision Tree is ideally suited to the job.
The pages that follow will give you further insights into decision tree analysis and how we use it to conduct a legal risk evaluation. You will also see
examples of some, but by no means all, of the information and analyses we can provide using powerful decision tree software.
1-2
Challenges and Responses
Challenge: I can’t be precise or objective about uncertainties, so how could I assign them “percentages” of probability?
Response: Your combined knowledge, experience and good judgment are all that is needed. Adding these to known facts and recognized
uncertainties, your opinion expressed as percentages of probability will convey your degree of uncertainty and allow you to draw sound
conclusions upon which to make good business, and legal, decisions about strategy, case value, etc.
Challenge: I can’t give a precise probability percentage. My estimates must be plus-or-minus 5% to 10% in either direction on some issues.
Response: That’s fine. This is a computerized tool. We can easily run “sensitivity analyses” that will show how the overall expected value of
the case may be affected as an uncertainty’s probability moves along the scale of 0% to 100%.
Challenge: Do decision trees show the outcome of my case?
Response: No. Any given trial could come out in a number of ways. A Decision Tree Analysis takes into account all the possible outcomes to
ensure that good decisions will improve the likelihood of a good outcome in this case.
Challenge: Why should I spend the time and money on Decision Tree Analysis?
Response: Early and ongoing case assessment can lead to earlier disposition based on good business judgment, saving time, money and
disruption of your business. It will help you explain and defend your decisions. Moreover, if you aren’t working on a strategy based on a full risk/
benefit analysis, how much effort and money are you expending on topics that may not have much effect on the outcome of a case?
Challenge: Will this tool help me make strategic cost/benefit decisions for allocating resources?
Response: Yes. If you estimate how much a proposed step will cost, you can estimate how success in taking that step will improve the
probability of an uncertainty coming out favorably. A sensitivity analysis on how a change in that probability would affect the expected value of
the entire case will tell you whether it is worth taking the step.
Challenge: Why should I pay Lewis and Roca to do this? I can have my own people trained to do it.
Response: You can and we have trained both in-house and outside counsel and we will gladly train your employees. But when we work with
you, we bring a fresh set of eyes to your dispute and our own litigation experience. Moreover, while the learning curve is fairly short, it is also
fairly steep and doing risk analysis well requires regular practice. As a result, people who do not use it often tend not to use it at all.
Lewis and Roca offers this service to clients, non-clients and law firms where we are not counsel of record. So, while we and others can train you,
and will do so if you wish, on balance we believe we can perform the analysis more efficiently and effectively, thus providing the best value to you
and your company.
1-3
The Coin Flip
2-1
Decision Tree Analysis for Litigation—How a Tree Works
This “unsolved tree” values the risks and opportunities of the chance to win $100 by flipping a coin just three times and getting heads each time.
Nodes: The square “node” is a decision node, representing the choice between keeping this opportunity and selling it. In a lawsuit, the choice is
typically between litigating and settling. The circle nodes are chance nodes and represent the significant uncertainties in the litigation or, here, in
the game. The triangles are terminal nodes that represent the outcome of any particular series of events or scenarios.
Variables: For such a simple tree, we could use numbers for probabilities and for outcomes instead of variables such as “p_Heads” (for the
probability of getting heads on any individual flip) and for the outcomes (“Win/Lose”).
• Variables and formulas (which are discussed in the Smith v. Jones tree), however, allow us to make changes easily, which is important in more
complex trees.
• They also permit sensitivity analyses to assess the impact of changes in various assumptions, which is particularly important where, for
example, there are differences of opinion as to the probability of a particular event’s occurrence.
2-2
The “Solved” Tree
The “solved” tree shows the value of this opportunity is $12.50, i.e., it is the mathematical probability of getting heads 3 times in a row (.5 x .5 x
.5 = .125 or 12.5%) times $100, which gives an “expected value” of $12.50.
Play
Coin Flip
Play : $12.50
Sell Opportunity
Heads
0.5000
$12.50
Tails
0.5000
Heads
0.5000
$25.00
Tails
0.5000
Heads
0.5000
$50.00
Tails
0.5000
Scenario Outcome Probability
1
$100.00
12.5%
2
$0.00
12.5%
3
$0.00
25.0%
4
$0.00
50.0%
5
$10.00
Expected Value is not an actual outcome. You either win $100 or get nothing. It does mean that if you play the game often enough, the weighted
average outcome of all the games will be $12.50.
• If you are risk neutral, you would turn down the proposed sales price of $10 and accept any offer greater than $12.50.
• If you were risk averse, e.g., you need the money, you might accept that $10 offer.
• In the litigation context, a defendant might pay more than the expected value to settle a case even though the risk of a high punitive damages
award is exceedingly small because the company cannot afford the costs or the bad publicity or both.
The dollar figures in the boxes to the right of each chance node reflect the expected value at that point in the tree, e.g., if the first flip was heads,
the value of this opportunity increases to $25. These are called “Intermediate Expected Values,” which are useful in settlement negotiations
and in planning strategy, as explained in the Smith v. Jones discussion below.
A note on the software: There are several software packages available. We use TreeAge Pro™. You can get additional information at the
TreeAge Pro™ website, www.treeage.com, where you will also find links to basic decision tree and legal model demos.
2-3
Determining Probabilities
The Probability Wheel: As the authors of the TreeAge Pro™ software manual point out, “A frequent problem encountered in decision
analysis is the assignment of subjective probability assessments to chance events. Many people find it easier to use a graphical aid in assigning
probabilities.” Our experience is that the best way to determine probabilities is to use a “probability wheel,” either a paper one or the one that
comes with the TreeAge Pro™ software. The wheel is not a substitute for an attorney’s judgment. It is simply a tool to ensure that the lawyers
making the assessment are speaking the same language when, for example, one says winning an issue is a “slam dunk” and another says the odds
are “better than even.”
We agree with Marc Victor, who developed Litigation Risk Analysis™ years ago, that “people provide more realistic assessments when they
can visualize probability and compare their chances of winning (or losing) an issue to the chance of a spinner landing in the darker region of
the wheel.” Evaluating Legal Risks and Costs with Decision Tree Analysis in SUCCESSFUL PARTNERING BETWEEN INSIDE AND OUTSIDE
COUNSEL (Chapter 12) West Group & ACCA, 2000-2004.
The image below comes from the TreeAge Pro™ manual. It has three different color areas, instead of the two you would normally find at a
chance node because this particular chance node has three possible outcomes representing high, medium and low damages.
2-4
Unsolved Tree With
Variable Definitions
Hidden & Shown
3-1
Smith v. Jones Decision Tree Analysis:
Explanation of Unsolved Tree—Definitions Hidden
The Smith v. Jones tree used to illustrate the mechanics and processes
of decision tree analysis is very loosely based on elements from
several different actual decision tree analyses.
For illustration purposes and to keep the display to one page, this
tree is simpler than the originals and than most actual trees. There
are, however, various ways in which the essential aspects of very
complicated trees with hundreds of scenarios can be displayed on
one or two pages. These techniques include the use of “clones”
and “hidden subtrees” as well as separate subtrees that are used
to calculate the probability of winning a particular issue or subset
of issues. The resulting value is then plugged into the main tree,
automatically or manually.
There are different ways to display the unsolved tree. In this
version, we have “hidden” the definitions for the variables in the
tree. Displaying them, as shown on the pages that follow, provides
useful information, but also consumes a lot of space and sometimes
makes the tree look cluttered.
Whether to hide or display definitions is simply a matter of selecting
the appropriate options in the preferences settings dialog provided
by TreeAge.
The software also allows you to insert notes providing further
explanations of the tree. This can be useful in making presentations
to decision makers.
The tree below is an “unsolved tree.” It shows the tree structure,
but it does not show the actual outcomes for each scenario or the
expected value of the tree, i.e., the probability weighted average of
those outcomes. That information is shown on the “solved tree” at
page 5-3.
3-2
Smith v. Jones
Get High
Damages
Jones Breached
Duty
(Exculpation
Clause
Inapplicable)
Prove
Causation
p_Win_Cause
p_Hi_Dams
Get Low
Damages
#
p_Win_Br
Get Tax
Gross Up
(1) Judgment
p_Get_GU
No Gross Up
#
Get Tax
Gross Up
p_Get_GU
No Gross Up
#
Release Not
A Defense
No Causation
(3) Judgment
(4) Judgment
(5) Judgment
#
p_Win_Rel
(2) Judgment
Jones Did Not
Breach
Arizona Law
Applies
(6) Judgment
#
p_Win_Law
Release Is A
Defense
(7) Judgment
#
Get High
Damages
Jones Breached
Duty
(Exculpation
Clause
Inapplicable)
Litigate
Prove
Causation
p_Win_Cause
p_Hi_Dams
Get Low
Damages
#
p_Win_Br
Smith v Jones
Get Tax
Gross Up
p_Get_GU
No Gross Up
#
Get Tax
Gross Up
p_Get_GU
No Gross Up
#
Release Not
A Defense
No Causation
p_Win_Rel_2
#
(8) Judgment
(9) Judgment
(10) Judgment
(11) Judgment
(12) Judgment
Jones Did Not
Breach
Lose Choice
of Law
(13) Judgment
#
#
Release Is A
Defense
(14) Judgment
#
Settle
(15) Settlement
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
3-3
Smith v. Jones Decision Tree Analysis:
Explanation of Unsolved Tree—Definitions Shown
The page below shows the variable definitions, i.e., the information
inside the boxes, used for the tree. (The “variables report” below
(page 4-3) provides some of the same definitions information.) It is
a bit cluttered and we would not normally use this version in, for
example, a meeting with a mediator, but it is helpful here to explain
exactly how a tree works.
Most variables are defined at the root, which is why we have the
big box at the far left side of page. Some variables have different
definitions at different points in the tree. For example, we have
defined the outcome in this case, i.e., a “Judgment,” as the sum
of “Damages+GrossUp+PreJ_Int [prejudgment interest].” Typically,
the variables that are components of the “Judgment” formula are
defined at the root node as zero.
This tree first analyzes the choice of law issue. We use a variable
– p_Win_Law – to represent the probability of Smith winning that
issue. The probability of winning the next issue, whether Smith is
bound by a release, is higher (p_Win_Rel = .7) where Arizona law
applies, and lower (p_Win_Rel_2 = .4) where Smith has lost the
choice of law issue.
That is because the computer searches from right to left for
definitions. Thus, if it gets all the way back to the root node before
finding a definition for “Damages,” it will assign it a value of zero,
which is what happens on every losing scenario. Conversely, where
damages are awarded, e.g., on scenarios 1 and 2, it will quickly find
Damages defined as equaling “High_Damages,” which, in turn, is
defined at the root node as equaling $29 million.
Under either scenario, if Smith loses the release issue, it loses the
case. If Smith gets past the release and other preliminary issues
(breach of duty and proof of causation), Smith gets to the issues of
damages, and the question of whether damages will be grossed up
to deal with tax consequences.
3-4
Smith v. Jones
Prove
Causation
Jones Breached
Duty
(Exculpation
Clause
Inapplicable)
Get Tax
Gross Up
Get High
Damages
*Judgment Components:
*Gross Up:
Tax_GrossUp=.61
*Judgment Components:
*Damages:
Damages=High_Damages
p_Get_GU
No Gross Up
*Judgment Components:
*Pre Judgment Interest:
PreJ_Int=Damages*PJI
p_Win_Cause
p_Win_Br
Release Not
A Defense
(2) Judgment
#
p_Hi_Dams
Get Tax
Gross Up
(3) Judgment
Get Low
Damages
*Judgment Components:
*Gross Up:
Tax_GrossUp=.61
*Judgment Components:
*Damages:
Damages=Low_Damages
p_Get_GU
No Gross Up
(4) Judgment
#
#
No Causation
p_Win_Rel
(5) Judgment
#
Arizona Law
Applies
(1) Judgment
Jones Did Not
Breach
p_Win_Law
(6) Judgment
#
Release Is A
Defense
(7) Judgment
#
Get Tax
Gross Up
Prove
Causation
Litigate
Jones Breached
Duty
(Exculpation
Clause
Inapplicable)
*Judgment Components:
Judgment=Damages+GrossUp+PreJ_Int
*Damages:
Damages=0.
High_Damages=29000000.
Low_Damages=4000000.
*Gross Up:
GrossUp=Damages*Tax_GrossUp
Tax_GrossUp=0
*Pre Judgment Interest:
PJI=.0675*3.33
PreJ_Int=0
*Probabilities:
p_Get_GU=0.6
p_Hi_Dams=0.7
p_Win_Br=0.75
p_Win_Cause=0.66
p_Win_Law=0.6
p_Win_Rel=0.7
p_Win_Rel_2=0.4
Settlement=2000000.
*Judgment Components:
*Gross Up:
Tax_GrossUp=.61
*Judgment Components:
*Damages:
Damages=High_Damages
p_Get_GU
No Gross Up
*Judgment Components:
*Pre Judgment Interest:
PreJ_Int=Damages*PJI
p_Win_Cause
Release Not
A Defense
Get Tax
Gross Up
Get Low
Damages
*Judgment Components:
*Gross Up:
Tax_GrossUp=.61
*Judgment Components:
*Damages:
Damages=Low_Damages
p_Get_GU
No Gross Up
#
No Causation
p_Win_Rel_2
#
Lose Choice
of Law
(8) Judgment
(9) Judgment
#
p_Hi_Dams
p_Win_Br
Smith v Jones
Get High
Damages
#
(10) Judgment
(11) Judgment
(12) Judgment
Jones Did Not
Breach
#
#
(13) Judgment
Release Is A
Defense
#
Settle
Lewis and Roca LLP
(14) Judgment
(15) Settlement
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
3-5
The Variables Report
4-1
Smith v. Jones Decision Tree Analysis:
Explanation of Variables Report
We use variables instead of numbers because they allow us to make
changes easily in assumptions without making changes at every place
in the tree where that variable occurs. Even in a tree this simple that
can be time consuming and errors can occur if we fail to make all of
the changes. More importantly, we need variables to perform the
sensitivity analyses discussed below.
The “Variables Report” captures most of the information used in
our analysis. It shows the values we assigned to the various variables
along with the formulas used to calculate recoveries in this case and
their likelihood of occurring. It shows much of the same information
as the unsolved tree with definitions showing, but, because it includes
a description of the variable (and a “Comment” section) it is more
informative. The report is also easier to read and allows us to use
the unsolved tree with definitions hidden, which is more compact
and easier to read.
The Judgment formula in other trees might be more or less
complex. In a tort case, for example, it might also include “emotional
distress” and “punitive damages.” We would include a variable for
treble damages where they are available. Attorneys’ fees are also a
common component of the Judgment formula. In short, anything
that impacts the ultimate outcome can be factored into the Judgment
formula.
As noted earlier, the variable components for Judgment usually are
defined as zero unless we tell the computer otherwise. We do so
by telling the computer, for example, that when we are on a branch
where Smith is entitled to the tax gross up, the Tax_GrossUp
variable is .61, otherwise it is zero.
Formulas are very useful, particularly to capture all of the
components of the possible outcomes. Here, the ultimate outcome
is represented by the variable “Judgment,” which in turn is defined
by a formula. It is the sum of every possible award the jury might
make: Damages + GrossUp + PreJ_Int.
4-2
Smith v Jones
Variables Report
Smith
v Jones
Variable
Name/Categories
Description
Judgment
Amount of Total Recovery
Variable Name/Categories
Judgment Components
Judgment
Variables Report
Formula
Value at Root Node
Damages+GrossUp+PreJ_Int
Description
Formula
Amount of Total Recovery
Damages+GrossUp+PreJ_Int
Value at Root Node
High_Damages
$0
Amount of Damges If Based upon Death
Benefit
of Life Insurance as of specified date
GrossLow_Damages
Up
GrossUp
Amount of Gross Up
Tax_GrossUp
Multiplier for Tax Gross Up
Tax_GrossUp
$29,000,000
$0
Amount of Damges If Based upon Death
Benefitof Damages if Based Upon Value
Amount
Low_Damages
Gross Up
GrossUp
$0
Comment
$0
Damages
Judgment Components
Damages
Damages
High_Damages
Damages
Comment
$29,000,000
$4,000,000
Amount of Damages if Based Upon Value
of Life Insurance as of specified date
Amount of Gross Up
$4,000,000
Damages*Tax_GrossUp
Damages*Tax_GrossUp
Multiplier for Tax Gross Up
$0
Equals .61 when ABC entitled to
$0
$0 tax
Equals
.61gross
whenup
ABC entitled to
$0 tax gross up
Pre Judgment Interest
Pre Judgment Interest
PreJ_Int
PJI PreJ_Int
PJI
Amount of Prejudment Interest at rate of
Amount
of3.33
Prejudment
6.75%
over
years Interest at rate of
6.75% over Interest
3.33 years
Prejudgment
Prejudgment Interest
.0675*3.33
.0675*3.33
0
0
0.224775
0.224775
Probabilities
Probabilities
p_Get_GU
p_Get_GU
p_Hi_Dams
p_Hi_Dams
p_Win_Br
p_Win_Br
p_Win_Cause
p_Win_Cause
p_Win_Law
p_Win_Law
p_Win_Rel
p_Win_Rel
p_Win_Rel_2
p_Win_Rel_2
Settlement
Settlement
Lewis and Roca LLP
Lewis and Roca LLP
Probability That Smith is Entitled To Gross
Probability That Smith is Entitled To Gross
Up Damages for Tax Effect
Up Damages for Tax Effect
Probability That Jury Decides Smith is
Probability That Jury Decides Smith is
Entitled
totoHigh
Entitled
HighDamages
Damages
Probability
That
Probability
ThatJury
JuryFinds
Finds That
That
Exculpation
and
ExculpationClause
ClauseisisInapplicable
Inapplicable and
that
Jones
that
JonesBreached
BreachedDuty
Duty
Probability
That
Probability
ThatJury
JuryDecides
Decides Jones'
Jones'
Breach
CausedDamages
Damages
Breach
Caused
Probability
WinningChoice
Choice of Law
Probability
ofofWinning
Law
Question
Question
Probability
ThatJury
JuryFinds
Finds the
the Release
Release
Probability
That
Was Not Valid Under Arizona Law
Was
Not Valid Under Arizona Law
Probability of Winning Release Issue
Probability of Winning Release Issue
Where Arizona Law Does Not Apply
Where Arizona Law Does Not Apply
Amount of Settlement Offer
Amount of Settlement Offer
60%
60%
70% 70%
75% 75%
66% 66%
60% 60%
70%
40%
70%
40%
$2,000,000
$2,000,000
Confidential Attorney Work Product and Attorney Client Privileged Information
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
[Date]
4-3
The “Solved” Tree
5-1
Smith v. Jones Decision Tree Analysis:
Explanation of Solved Tree
Actual Outcomes: The first version of the solved tree (page
5-3) shows the actual judgment resulting from each scenario and
its probability of occurring. The second tree (page 5-4) is identical
except that it includes additional columns showing the components
of the judgment. That can be very useful information, but it can
make the tree harder to read.
Expected Values: You will find the expected value for the
tree ($9.8M) on the far left of the tree next to the decision and
litigate nodes. There is no scenario that produces a judgment of
$9.8M. This figure is the probability weighted average of the 14
litigation scenarios. It takes into account those two scenarios (1
and 8) where Smith recovers $53.2 million, the six scenarios where
Smith wins nothing, and the other winning scenarios with outcomes
ranging from $4.9M to $35.5M. If Smith is risk neutral, $9.8M is
the settlement value of the case. (A probability distribution
(see below) contains further information of relevance to Smith’s
assessment.)
The other boxed figures are intermediate expected values and
show the value of the case at that particular point in the tree. We
can use the preferences settings to hide the intermediate values,
which makes the tree more presentable. But intermediate expected
values do provide useful information. They show, for example, that
if Smith wins the choice of law question, the expected value of the
tree goes up from $9.8M to $11.9M. If Smith loses that issue, the
expected value goes down to $6.8M.
This illustrates another benefit of decision tree analysis, i.e., you
do not have to redo the analysis to take into account the results
of, for example in this case, the court’s ruling on a motion in limine
directed to the choice of law question. This can be helpful in
settlement negotiations where the opposing party will argue that
the complexion of a case may change significantly once the court
rules on that pending motion. The tree allows Smith to respond
that it has taken that possibility into consideration in arriving at its
settlement demand, and to point out how much the value of the
case will go up if the ruling goes in Smith’s favor.
Additional Details of Actual Outcomes can be shown by adding
more terminal columns as shown on the second version of the
solved tree (shown on page 5-4). This version of the tree includes
additional columns showing the components of the judgment. Thus
the $53.2M Judgment in scenario 1 is comprised of $29M in damages
plus $17.7M for the Gross Up and $6.5M in Pre Judgment Interest.
You can identify, and change as you wish, the columns you want to
display and the information you want to have in them by using the
preferences settings for the tree.
5-2
Smith v. Jones
Get High
Damages
Jones Breached
Duty
(Exculpation
Clause
Inapplicable)
0.75
$22.6M
$34.2M
Get Low
Damages
0.30
0.40
Get Tax
Gross Up
0.60
$6.4M
No Gross Up
No Causation
$16.9M
Judgment
Probability
1
$53.2M
8.73%
2
$35.5M
5.82%
3
$7.3M
3.74%
4
$4.9M
2.49%
0.34
5
$0.0M
10.71%
6
$0.0M
10.50%
7
$0.0M
18.00%
8
$53.2M
3.33%
9
$35.5M
2.22%
10
$7.3M
1.43%
11
$4.9M
0.95%
12
$0.0M
4.08%
13
$0.0M
4.00%
14
$0.0M
24.00%
15
$2.0M
Jones Did Not
Breach
Arizona Law
Applies
0.60
0.66
0.70
0.60
$46.1M
No Gross Up
0.40
Release Not
A Defense
0.70
Prove
Causation
Scenario
Get Tax
Gross Up
$11.9M
0.25
Release Is A
Defense
0.30
Get High
Damages
Litigate
Jones Breached
Duty
(Exculpation
Clause
Inapplicable)
$9.8M
Litigate : $9.8M
0.75
0.40
$22.6M
$34.2M
Get Low
Damages
0.30
0.40
Get Tax
Gross Up
0.60
$6.4M
No Gross Up
No Causation
$16.9M
0.34
Jones Did Not
Breach
Lose Choice
of Law
0.40
0.66
0.70
0.60
$46.1M
No Gross Up
0.40
Release Not
A Defense
Smith v Jones
Prove
Causation
Get Tax
Gross Up
$6.8M
0.25
Release Is A
Defense
0.60
Settle
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
5-3
Smith v. Jones
Get High
Damages
Jones Breached
Duty
(Exculpation
Clause
Inapplicable)
0.75
Release Not
A Defense
0.70
Arizona Law
Applies
0.60
$11.9M
Litigate
0.75
0.25
Release
ReleaseNot
Is A
ADefense
Defense
0.70
0.30
Arizona Law
Applies
0.60
Jones Breached
Duty
$16.9M
(Exculpation
Clause
Jones Did Not
Inapplicable)
Breach
0.30
Litigate : $9.8M
Release Not
A Defense
$9.8M
Smith v Jones
0.40
Litigate : $9.8M
Lose Choice
of Law
0.40
Settle
0.40
0.66
0.34
$22.6M
0.40
0.60
$6.8M
Get Low
Get
High
Damages
Damages
0.30
0.70
$34.2M
Get Low
Damages
0.30
0.60
$6.4M
No Gross Up
0.40
0.34
Jones Breached
Duty
(Exculpation
Clause
Inapplicable)
Jones Breached
Duty
$16.9M
(Exculpation
Clause
Jones Did Not
Inapplicable)
Breach
0.75
0.25
Release
ReleaseNot
Is A
ADefense
Defense
Lose Choice
of Law
Prove
Causation
No Causation
Jones Did Not
Breach
$6.8M
Smith v Jones
$22.6M
$34.2M
0.40
Get Tax
Get
TaxUp
Gross
Gross Up
0.60
$6.4M 0.60
No Gross Up
$46.1M
No Gross Up
0.40
0.40
Get Tax
Gross Up
No Causation
0.75
Litigate
0.66
Get High
Damages
0.25
Release Is A
Defense
0.70
0.60
$46.1M
No Gross Up
Smith v. Jones
$16.9M
$11.9M
$9.8M
Prove
Causation
Prove
Causation
0.66
$22.6M
Prove
Causation
No Causation
0.66
0.34
$22.6M
0.25
Get Low
Get
High
Damages
Damages
0.30
0.70
$34.2M
Get Low
Damages
Get Tax
Gross Up
0.60
$46.1M
No Gross Up
0.40
Get Tax
Get
Tax
Gross Up
Gross Up
0.60
$6.4M 0.60
No Gross Up
$46.1M
No Gross Up
0.40
0.40
Get Tax
Gross Up
0.60
$6.4M
No Gross Up
0.40
0.34
Jones Did Not
Breach
$34.2M
0.30
No Causation
$16.9M
0.70
Scenario
Judgment
Damages
Gross Up
PreJ Interest
Probability
1
$53.2M
$29.0M
$17.7M
$6.5M
8.73%
Get Tax
Gross Up
2
$35.5M
$29.0M
$0.0M
$6.5M
5.82%
Scenario
Judgment
Damages
Gross Up
PreJ Interest
Probability
3
1
$7.3M
$53.2M
$4.0M
$29.0M
$2.4M
$17.7M
$0.9M
$6.5M
3.74%
8.73%
4
2
$4.9M
$35.5M
$4.0M
$29.0M
$0.0M
$0.0M
$0.9M
$6.5M
2.49%
5.82%
5
$0.0M
$0.0M
$0.0M
$0.0M
10.71%
3
$7.3M
$4.0M
$2.4M
$0.9M
3.74%
6
4
$0.0M
$4.9M
$0.0M
$4.0M
$0.0M
$0.0M
$0.0M
$0.9M
10.50%
2.49%
57
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
10.71%
18.00%
68
$0.0M
$53.2M
$0.0M
$29.0M
$0.0M
$17.7M
$0.0M
$6.5M
10.50%
3.33%
9
7
$35.5M
$0.0M
$29.0M
$0.0M
$0.0M
$0.0M
$6.5M
$0.0M
2.22%
18.00%
10
8
$7.3M
$53.2M
$4.0M
$29.0M
$2.4M
$17.7M
$0.9M
$6.5M
1.43%
3.33%
11
9
$4.9M
$35.5M
$4.0M
$29.0M
$0.0M
$0.0M
$0.9M
$6.5M
0.95%
2.22%
12
$0.0M
$0.0M
$0.0M
$0.0M
4.08%
10
$7.3M
$4.0M
$2.4M
$0.9M
1.43%
13
11
$0.0M
$4.9M
$0.0M
$4.0M
$0.0M
$0.0M
$0.0M
$0.9M
4.00%
0.95%
12
14
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
4.08%
24.00%
15
13
$2.0M
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
$0.0M
4.00%
14
$0.0M
$0.0M
$0.0M
$0.0M
24.00%
15
$2.0M
$0.0M
$0.0M
$0.0M
Release Is A
Defense
0.60
Settle
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
5-4
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
Node Comments and the
“Win/Lose” Analysis
6-1
Decision Tree Analysis With Its Trees, Values and Numbers
May Look Very Scientific, But It Is Not
It is instead a disciplined way to capture the best judgments of
counsel, which in turn depend upon reasoned, thoughtful analysis.
GIGO (garbage in; garbage out) applies to decision tree analysis in
the same way it applies to every kind of analysis.
The process of identifying the critical uncertainties and of determining
why you can still lose a case even if you have won an important issue,
and vice versa, is more important than the numbers. It helps you
make better judgments and it helps you identify areas where you
need more factual investigation or legal research.
When we prepare a legal risk evaluation, we keep lists of the reasons
why we, or the lawyers we are working with, think an issue will
be won or lost. We typically display the completed lists when we
determine the probabilities of prevailing on an issue. The lists can
also be printed out and shared with clients to explain why counsel
handling the case felt strongly about winning an issue or were
pessimistic about the outcome.
The “node comment” feature of TreeAge Pro™ provides an easy
way to record reasons for winning or losing an issue. The flags that
denote the presence of the node comments do not show up when
the tree is printed, so on the page below, and the three that follow,
we used the print screen feature to show how the flags and the
node comments appear on the computer screen.
The tree below (page 6-3) shows the flags on the litigate node
and several other nodes that indicate the presence of hidden node
comments.
As the second picture (page 6-4) shows, the flags indicate node
comments for the issue that is immediately to the right of the
highlighted node. Here the highlighted node is the Litigate node and
the node comment box that is opened is for the choice of law issue
to the right of the Litigate node. Some sample reasons for winning
and losing the choice of law question are listed. Typically the first
few items represent anticipated responses to the points made in the
other column – a sort of point, counterpoint.
The node comment box can be resized, as shown at page 6-5,
to make it easier to read. Node comments can also be printed,
but additional formatting is required to display them as opposing
columns.
Once the lists are exhausted, we determine the probabilities of
winning or losing the particular issue. Page 6-6 shows the probability
wheel for the choice of law question. The size of the darker area
reflects our assessment that the probability of winning the issue is
60%.
6-2
6-3
6-4
6-5
6-6
Probability Distribution Charts
7-1
Smith v. Jones Decision Tree Analysis:
Explanation of Probability Distribution Charts
Even a relatively simple tree is often too large to show all possible
outcomes and their probability of occurrence. A probability
distribution chart captures all of that information and does so in a
more digestible and informative manner.
produced the chart and tables seen below. The basic Excel chart
also does not include the middle set of outcomes shown here. We,
however, have found it helpful to rank outcomes by amount as well
as by scenario.
Here we have two probability distribution charts for our tree.
The one below (page 7-3) was generated using the TreeAge Pro™
add-in for Excel. The chart on page 7-4 was generated directly in
TreeAge Pro™. It is a bit easier to read, but does not contain as
much information as the Excel version. While there are ways to
enhance the look of the graph, they are fairly limited, which is why
we normally generate Excel charts instead.
The cumulative probability columns on the far right can be
particularly useful. Here they show that the six “zero” outcomes
have a cumulative probability of 71%. Plaintiff Smith might find this
information, i.e., most of the time it loses, more useful in making a
settlement decision than the $9.8 million expected value.
The basic information generated using Excel includes both the chart
and some of the tables shown here, though without the format and
other changes that we make to provide a more useful chart. These
include headings, use of currency and percentage formats, use of
color, changes to the range scales, etc. These and other changes
Conversely, Jones might be willing to pay more than $9.8 million
rather than run the 20% risk of a judgment in the $36 million to $53
million range.
7-2
Smith v Jones
Probability Distribution
Probability Distribution at
Litigate
100%
90%
80%
Probability
70%
60%
50%
Probablity
40%
30%
20%
10%
0
0
00
00
$5
4,
00
0,
0
$3
9,
00
0,
0
00
00
6,
00
0,
0
0,
00
3,
$3
0
00
0,
00
0,
$3
0
00
0,
00
7,
$3
0
00
0,
00
4,
$2
$2
0
00
00
$2
1,
00
0,
0
8,
00
0,
0
00
0,
00
5,
$1
$1
00
00
,0
0,
$1
2,
00
00
,0
00
$9
,0
00
00
,0
$6
$3
,0
00
,0
$0
0%
Value
Outcomes Ranked by Scenario
Scenario
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Lewis and Roca LLP
Outcome Probability
$53,208,475
8.73%
$35,518,475
5.82%
$7,339,100
3.74%
$4,899,100
2.49%
$0
10.71%
$0
10.50%
$0
18.00%
$53,208,475
3.33%
$35,518,475
2.22%
$7,339,100
1.43%
$4,899,100
0.95%
$0
4.08%
$0
4.00%
$0
24.00%
Outcomes Ranked by
Amount
Outcome
Probability
$0
10.71%
$0
10.50%
$0
18.00%
$0
4.08%
$0
4.00%
$0
24.00%
$4,899,100
2.49%
$4,899,100
0.95%
$7,339,100
3.74%
$7,339,100
1.43%
$35,518,475
5.82%
$35,518,475
2.22%
$53,208,475
8.73%
$53,208,475
3.33%
Cumulative Probability of Outcomes by Ranges
Value
$0
$3,000,000
$6,000,000
$9,000,000
$12,000,000
$15,000,000
$18,000,000
$21,000,000
$24,000,000
$27,000,000
$30,000,000
$33,000,000
$36,000,000
$39,000,000
$54,000,000
Frequency Probablity
6
71.29%
0
0.00%
2
3.45%
2
5.17%
0
0.00%
0
0.00%
0
0.00%
0
0.00%
0
0.00%
0
0.00%
0
0.00%
0
0.00%
2
8.04%
0
0.00%
2
12.06%
Confidential Attorney Work Product and Attorney Client Privileged Information
Cumulative
Probablity
71.29%
71.29%
74.74%
79.90%
79.90%
79.90%
79.90%
79.90%
79.90%
79.90%
79.90%
79.90%
87.94%
87.94%
100.00%
[Date]
7-3
Smith v Jones
Probability Distribution at
Litigate
0.80
0.75
0.70
0.65
0.60
0.55
Probability
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
$0M
$10M
$20M
$30M
$40M
$50M
$60M
Value
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
7-4
Sensitivity Analyses
8-1
Smith v. Jones Decision Tree Analysis:
Explanation of Sensitivity Analysis
A sensitivity analysis allows you to determine the impact that
changes in a particular variable, here the probability of winning the
causation issue, have on the expected value of the case. This has
many benefits:
1. It allows you to assess the significance of differences in opinion
regarding the probability of a particular occurrence without
having to rerun the tree using different assumptions. This
can be helpful for assessing differences amongst the litigation
team.
2. Differences with opposing counsel on the odds of prevailing
on a particular issue can sometimes be resolved by sharing
a sensitivity analysis showing that even at counsel’s higher
probability the case is still worth less than that lawyer’s client
is demanding.
3. Strategic decisions are also better made using a sensitivity
analysis. They can help you decide which issues should be
the focus of your efforts. You can also weigh the benefits of
improving your odds of prevailing on a particular issue, by, for
example, hiring an expert, against the costs of doing so.
The sensitivity analysis immediately below (page 8-3) is a “one-way”
sensitivity analysis, i.e., it analyzes only one variable at a time. You can
perform two-way and three-way sensitivity analyses, but, because
they can easily be misinterpreted, they are not frequently used in
litigation. (You can, however, merge several sensitivity analyses to
display them on a single graph as discussed below.)
The first three charts below focus on the probability of proving
causation. The first sensitivity analysis (page 8-3) was created by
using the Excel add-in feature of TreeAge Pro™. It provides more
information (and offers greater formatting flexibility) than the same
chart generated by TreeAge Pro™ alone (as shown on page 8-4).
The latter, however, can also be converted to a “strategy graph,” as
shown on page 8-5.
The last two charts are different ways of looking at several
different sensitivity analyses at the same time. The first (page 8-6)
is essentially a combination of several complete one-way sensitivity
analyses, created using the Excel Add-in module. The last chart (page
8-7) illustrates another way to do this by creating what is called a
“Tornado Diagram.” The key difference is that it is usually based
on a more limited range. Thus, instead of measuring the impact of
each variable on the expected value as the variable ranges from
0% to 100%, the Tornado Diagram shows the impact for each of
the variables in the chart over a range that is 10 percentage points
below to 10 percentage points above the values assigned in the tree.
The width of the bar is related to the potential impact that variable
has on the tree’s expected value.
8-2
Smith v Jones
Sensitivity Analysis
Smith v Jones
Sensitivity Analysis
Sensitivity Analysis on
Probability That Jury Decides Jones' Breach Caused Damages
ExpectedExpected
Value Value
Millions
$16
$14
$12
Millions
$10
$16
$8
$14
$6
$12
$4
$10
$2
$8
$0
$6
$4 0%
$2
$0
0%
Probability
0%
10%
20%
Probability
30%
0%
40%
10%
50%
20%
60%
30%
70%
40%
80%
50%
90%
60%
100%
70%
80%
90%
100%
Sensitivity Analysis on
Probability That Jury Decides Jones' Breach Caused Damages
Litigate
Settle
Litigate
Settle
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
90%
100%
Probability That Jury Decides Jones' Breach Caused Damages
10%
20%
30%
40%
50%
60%
70%
80%
Probability
That Jury Decides Jones' Breach Caused Damages
Settle
Litigate
$0
$1,487,772
$2,975,545
Litigate
$4,463,317
$0
$5,951,089
$1,487,772
$7,438,862
$2,975,545
$8,926,634
$4,463,317
$10,414,406
$5,951,089
$11,902,179
$7,438,862
$13,389,951
$8,926,634
$14,877,723
$10,414,406
$11,902,179
$13,389,951
$14,877,723
$2,000,000
$2,000,000
$2,000,000
Settle
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
Threshold Values: Probability That Jury Decides Jones' Breach
Caused Damages = 13% at Expected Value of $2M (i.e., settlement
offer)
Threshold Values: Probability That Jury Decides Jones' Breach
Caused Damages = 13% at Expected Value of $2M (i.e., settlement
offer)
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
8-3
Smith v. Jones
Sensitivity Analysis on
Probability That Jury Decides XYZ's Breach Caused Damages
$15M
Litigate
Expected Value
$13M
$11M
Settle
Threshold Values:
Probability That Jury Decides XYZ's Breach Caused Damages = 0.13
EV = $2M
$9M
$7M
$5M
$3M
$1M
0.00 0.20 0.40 0.60 0.80 1.00
Probability That Jury Decides XYZ's Breach Caused Damages
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
8-4
Strategy Graph Generated by TreeAge Pro™
The cross hatched area (in blue) represents the 13% and below probabilities that generate an expected value of $2M or less, in which case settling
is a better strategy than litigating.
8-5
Smith v Jones
Multiple Sensitivity Analyses
Smith v Jones
Multiple Sensitivity Analyses
Multiple Sensitivity Analyses: On Issues of Causation, Choice of Law and Breach of Duty
Millions
Expected Value
Expected Value
$16
Multiple Sensitivity Analyses: On Issues of Causation, Choice of Law and Breach of Duty
$14
Millions
$12
$16
$10
$14
$8
$12
$6
$10
$4
$8
$2
$6
$0
$40%
Litigate as a Function of Causation
Litigate as a Function of Choice of Law
Litigate as a Function of Breach of Duty
Settle
Litigate as a Function of Causation
Litigate as a Function of Choice of Law
Litigate as a Function of Breach of Duty
Settle
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Probability
$2
$0
0%
10%
20%
30%
Probability
0%
10%
20%
30%
40%
Probability
50%
0%
60%
10%
70%
20%
80%
30%
90%
40%
100%
50%
60%
70%
80%
90%
100%
40%
70%
80%
Litigate as50%
a Function60%
of
Litigate
as a Function
Causation
of Choice of Law
Probability
$0
$6,771,929
$1,487,772
$7,279,824
$2,975,545
$7,787,719
$4,463,317
Litigate as a Function
of
Litigate as a$8,295,613
Function
$5,951,089
Causation
of Choice$8,803,508
of Law
$7,438,862
$9,311,403
$0
$6,771,929
$8,926,634
$9,890,000
$1,487,772
$7,279,824
$10,414,406
$10,327,192
$2,975,545
$7,787,719
$11,902,179
$10,835,087
$4,463,317
$8,295,613
$13,389,951
$11,342,981
$5,951,089
$8,803,508
$14,877,723
$11,850,876
$7,438,862
$9,311,403
$8,926,634
$10,414,406
$11,902,179
$13,389,951
$14,877,723
$9,890,000
$10,327,192
$10,835,087
$11,342,981
$11,850,876
90% as a Function
100%
Litigate
of Breach of Duty
$0
$1,309,240
$2,618,479
Litigate as a$3,927,719
Function
of Breach$5,236,959
of Duty
$6,546,198
$0
$7,855,438
$1,309,240
$9,164,677
$2,618,479
$10,473,917
$3,927,719
$11,783,157
$5,236,959
$13,092,396
$6,546,198
Settle
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
Settle
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$7,855,438
$9,164,677
$10,473,917
$11,783,157
$13,092,396
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
8-6
Smith v Jones
Probability That Jury Decides Jones' Breach Caused Damages: .56 to .76
Probability That Jury Finds that Jones Breached Duty: .65 to .85
Tornado Diagram
Probability of Winning Choice of Law Question: .50 to .70
A “Tornado Diagram” is another way of looking at several sensitivity analyses at the same time. The difference between the diagram below and the
multiple sensitivity analyses above is that the range of values is constricted (to allow more meaningful analysis).
Here, the diagram compares the three specified probabilities as they vary 10 percentage points below and above the values used in the tree. The
vertical dashed line represents the expected value of the case using the original assumptions. The widest bars have the greatest impact on the
expected value. This can be helpful in deciding where to focus your resources.
$8.3M
$9.3M
$10.3M $11.3M
Expected Value
Lewis and Roca LLP
Confidential Attorney Work Product and Attorney Client Privileged Information
[Date]
8-7
Professional Biographies
9-1
PROFESSIONAL BIOGRAPHY
Douglas L. Irish
About Mr. Irish:
Mr. Irish is a senior trial lawyer, and was the firm’s Managing Partner from 1987 to 1992. His experience includes trials, appeals and
litigation management in Montana, Texas, Colorado, Louisiana, New Mexico, Nevada, and Arizona, of complex and national/regional
cases involving: corporate, business and commercial disputes; class action defense; engineering/scientific products; pharmaceuticals;
and medical devices.
In 1996 E.I. du Pont de Nemours & Co. presented Mr. Irish with its Gold Eagle Award, the highest honor given by DuPont, and only the second time in
the company’s history that the award had been given to outside counsel. The award was for his outstanding achievement as co-leader of the company’s
National Counsel Team, and as leader of a regional team, in the defense of one of the largest mass tort product liability matters in the company’s history,
resulting in 55 trial and appellate decisions in a row ruling in favor of DuPont, and the adoption of provisions in Restatement of Torts: Products Liability
(1997) exonerating raw materials suppliers from liability for finished product performance.
For nearly 20 years Mr. Irish has also used, and taught others to use, decision tree analysis techniques in the business-oriented management, strategy,
evaluations and settlement of major and complex disputes.
Representative Cases:
Products Liability
•
Mr. Irish defended Westinghouse and General Electric in litigation over foreign object damage to steam turbines used in electric power production.
He established in both cases that the cause of the damage was not the manufacturer’s but was the fault of the owner’s employees. He has defended
Westinghouse against design defect claims with respect to high-voltage circuit breakers and against claims that computerized controls systems used
to start, operate, control and stop gas turbines were defectively and negligently designed.
•
Mr. Irish has successfully defended Blood Systems in more than 125 cases across the country against claims that transfusion recipients contracted
hepatitis or venereal disease. Mr. Irish also successfully defended Blood Systems in the first national AIDS-related transfusion case to go to jury
verdict.
•
Mr. Irish has successfully defended Zimmer Manufacturing Co. against claims that Zimmer’s orthopedic implant used to repair a fractured hip joint
was either defectively designed or defectively manufactured.
•
Mr. Irish successfully defended Smith & Wesson on several claims including claims mistakenly asserting that a design defect in a revolver and semiautomatic pistol discharged without the triggers having been pulled. In both cases, Mr. Irish established that there was no defect in the firearm, but
that it had been misused. In another case, Mr. Irish established that the cause of a destructive explosion in a revolver cylinder was not because of a
defect in the firearm, but because the shooter had hand-loaded the ammunition with the wrong kind of powder.
9-2
PROFESSIONAL BIOGRAPHY
Douglas L. Irish
Corporate, Class Action and Commercial Litigation
•
Mr. Irish successfully defended The Greyhound Corporation and its senior managment in two shareholder derivative lawsuits stemming from a fraud
practiced on the corporation by lower-level employees.
• Mr. Irish successfully defended Group W Broadcasting in a CATV financing dispute involving the evaluation of “stair-stepped” capital leasing.
He also won a wrongful death claim brought against the company on grounds that its program camera crews’ presence at a police incident
influenced the officers to use excessive force, resulting in the shooting death of a suspect they were trying to arrest.
• Mr. Irish defended Genesys, Inc., a specialized telephony software vendor/subcontractor, against claims by the general contractor to the
Maricopa County, Arizona government for a major telephone switch. The general contractor alleged the client’s module did not work and
delayed installation and acceptance of the switch. Following technical and contract-formation discovery, Mr. Irish used Decision Tree Analysis
in the mediation to achieve a settlement satisfactory to the client.
• Mr. Irish represented Motorola in the defense of a claim that an employee had orally committed it to sell a service portion of the company to
an outside entity. It involved counter-allegations that the outside entity had improperly corrupted Motorola’s employee into participating in a
scheme to defraud the company. Mr. Irish used Decision Tree Analysis in the mediation of the case. The case was settled several months after
the mediation.
• Mr. Irish has represented Farmers Insurance in two class actions. One involved alleged underpayment of “med-pay” benefits to first party
claimants. The second involved assertions by the company’s claims adjusters that they were entitled to overtime pay.
• Mr. Irish represented United Nuclear, the owner of a uranium mill in northern New Mexico when the dam on the mill tailings pond failed,
releasing several million gallons of acid and radioactive fluids into the river running through Indian Territory. The case was settled for a nominal
amount. Mr. Irish also successfully defended Foote Mineral against claims by former uranium miners and their families that they had contracted
diseases as a result of exposure to radon gas in the mines.
• Mr. Irish successfully defended claims against Employers Insurance of Wausau by, and pursued affirmative claims against, a professional employers’
organization in a complex case involving premiums and reimbursement of expenses on multiple workers’ compensation policies.
Representative Use of Decision Tree Analytical Skills
• In settlement negotiations with multiple tiers of insurance policy adjusters, Mr. Irish used Decision Tree Analysis and computer modeling to
achieve a satisfactory settlement of claims against a major reclamation project for flood-caused property and business losses. The Decision
Tree helped the insurers understand that the project would likely be held to the duties of a flood control district, and that if the project had
begun releasing water from its reservoirs when in an impending major snow melt, the peak of the flood would have been below damage-causing
levels.
9-3
PROFESSIONAL BIOGRAPHY
Douglas L. Irish
• Assisted the firm’s construction lawyers who were defending the design engineers against claims involving 23 separate design error allegations
for a major water treatment plant in Tucson, Arizona. Using Decision Tree Analysis, Mr. Irish was able to help the lawyers evaluate each claim,
and interrelate their effect on each other. This model was used to ensure mediation which resulted in a satisfactory settlement.
• In a multi-million dollar equitable adjustment claim by the Firm’s general contractor client against the city airport authority regarding a terminal
expansion project, Mr. Irish’s use of Decision Tree Analysis assisted the client’s corporate decision makers in evaluating their company’s claims
to appropriately target a settlement value. The case settled in mediation at the client’s evaluation.
• Mr. Irish has used Decision Tree Analysis in most of his representative cases to conduct ongoing case assessment, make strategic recommendations,
and assist clients in settlement evaluations.
Professional Activities:
Mr. Irish serves annually on the faculty, at both the basic and Master Advocate levels, of the National Institute for Trial Advocacy’s national and
regional programs, teaching primarily direct and cross-examination skills.
He has more than 25 years experience in mediation and arbitration of major disputes, both as an advocate and as a neutral. Mr. Irish is a member
of the American Arbitration Association’s National Panel of Arbitrators and its “Large Complex Case Panel,” and has been appointed by FEMA as
an arbitrator in the New Mexico fire dispute resolution process.
Mr. Irish leads the firm’s pro-bono practice group that advocates the rights of victims of crime. In addition, Mr. Irish has been Co-Chair of the State
Bar of Arizona’s Law Practice Management Committee, and served as Chancellor (general counsel) of The Episcopal Church in Arizona, 19771992.
Court Admissions:
Mr. Irish is admitted to practice in the State and Federal Courts in Arizona and Colorado, and in the 5th, 9th and 10th Circuit Courts of Appeal.
Education:
University of Colorado School of Law, LL.B., 1963
9-4
PROFESSIONAL BIOGRAPHY
José A. Cárdenas
About Mr. Cárdenas
Mr. Cárdenas is the Chair of the firm and a partner in the Commercial Litigation Practice Group. He focuses his practice primarily
on commercial litigation matters.
Prior to joining the firm in 1978, Mr. Cárdenas was Law Clerk to The Honorable Robert F. Peckham, Chief Judge of the U.S. District
Court for the Northern District of California.
Representative Cases:
•
Extensive experience defending insurance companies in life insurance sales practice litigation involving hundreds of plaintiffs in Arizona and New
Mexico.
•
Represented a plaintiff in recouping a substantial portion of a $200 million claim following a leveraged buyout.
•
Represented the plaintiffs in the recovery of a substantial portion of a $125 million fraudulent conveyance claim.
•
Represented the State of Arizona in a variety of complex litigation matters.
Decision Tree Analysis:
Mr. Cárdenas has used decision tree analysis throughout his career as a litigator, both in connection with cases he has handled and as a consultant to other
lawyers both within and outside the firm. In addition to doing so in several of the cases identified above, other representative examples of Mr. Cárdenas’
use of Decision Tree Analysis include matters where he or other lawyers in the firm were representing:
•
Plaintiff businesses in lawsuits arising out of 100 year floods;
•
The general contractor and the bonding company in litigation arising out of the construction of a major resort hotel;
•
Defendants in mass tort litigation arising out of a uranium mill tailings dam spill;
•
Insurers in disability bad faith litigation cases;
•
The plaintiff in a sexual harassment lawsuit;
•
The general contractor in a case arising out of a major airport renovation project;
•
The litigating trustee in claims against the professional advisors of a now bankrupt national restaurant chain;
•
A medical device manufacturer in a breach of contract case that included antitrust claims;
•
Trust beneficiaries pursuing breach of fiduciary duty claims;
•
The trustees in claims against the former owners of major sports venues.
9-5
PROFESSIONAL BIOGRAPHY
José A. Cárdenas
Mr. Cárdenas has also used decision tree analysis in a variety of other contexts including:
•
As a retained consultant, to evaluate the value of a claim for purposes of settling a dispute with the Internal Revenue Service;
•
To analyze the value of claims in large commercial contingent fee cases as part of the firm’s intake evaluation process;
•
The development of decision tree analysis templates that allowed a major employer to analyze the value of hundreds of individual employee claims
that might arise following a reduction in force.
Community and Professional Activities:
Mr. Cárdenas has recently been appointed by Governor Napolitano to serve on the board of the Arizona Economic Resource Organization (AERO). He
is Chairman of the Board of the International Translational Genomics Research Institute (TGen). He also serves as Vice Chairman of Arizona’s Commerce
and Economic Development Commission (CEDC). Mr. Cárdenas is a member of the Council on Foreign Relations.
Mr. Cárdenas is a board member and immediate past Chairman of Greater Phoenix Leadership (GPL), a non-profit organization comprised of presidents
and CEOs of corporations throughout the Phoenix metropolitan area. He also serves on the board of the Greater Phoenix Economic Council.
Mr. Cárdenas is a Fellow of the American Bar Foundation and a member of the Maricopa County, Arizona and American Bar Associations, as well as the
American Law Institute, the Hispanic National Bar Association, Los Abogados Hispanic Bar Association, and the St. Thomas More Society. He is also
admitted to practice law in California.
Other Current and Past Community Activities:
Mr. Cárdenas is a board member of Chicanos Por La Causa and Xico, Inc. He is a Trustee of the Virginia G. Piper Charitable Trust and a member
of the ASU Minority Advisory Council.
Mr. Cárdenas is a past chairman of the board of Valley of the Sun United Way. He also hosts a weekly PBS public affairs program called Horizonte, which
explores “Arizona issues through a Hispanic lens.”
Special Recognitions:
In 2007, Mr. Cárdenas received the University of Arizona Law School Alumni Association’s Professional Achievement Award. He is also listed in the 2007
and 2008 editions of Southwest Super Lawyers in the category Business Litigation. Mr. Cárdenas also received the Valley of the Sun United Way’s Spirit
of Caring Award in 2003.
In 2000, Mr. Cárdenas received the Mexican government’s Ohtli award given to U.S. residents of Mexican descent in recognition of their service to
Mexican communities in the United States. He also received the Valley Leadership 2000 Man of the Year Award and the Leaders of Distinction award
presented by the Anti-Defamation League.
Education:
Stanford Law School, J.D., 1977
University of Nevada, Las Vegas, B.A., 1974
9-6
L AW
from a business point of view. ®
phoenix
40 north central avenue
suite 1900
phoenix, arizona 85004
602.262.5311
albuquerque
las vegas
tucson
3993 howard hughes parkway
suite 600
las vegas, nevada 89169
702.949.8200
reno
50 west liberty street
suite 410
reno, nevada 89501
775.823.2900
one south church avenue
suite 700
tucson, arizona 85701
520.622.2090
www.LRLaw.com
201 third street nw
suite 1950
albuquerque, new mexico 87102
505.764.5400