Quantitative Leap: Providing Added Value to Clients Through the Use of Decision Trees

WDC Journal Edition: Summer 2012
By: Patricia A. Stone, McCoy Law Group, S.C.

In today’s legal environment, the vast majority of decisions made with regard to settlement amount to nothing more than a cost-benefit analysis. The choice includes whether to continue to fight the claim, which includes the risk of losing more in the end, or settle at a juncture most beneficial to the client. Towards that end, and as litigation management professionals continue to seek methods to better assess the value of a given claim, they often turn to defense attorneys to provide counsel in that regard. As such, it behooves defense attorneys to utilize methods that help to objectively assess the value of a given case. Decision trees provide such a methodology.

Decision trees in the legal setting have been used and advocated in some circles for the past 30 years.[i]They are, in a nutshell, tree-shaped models that trace the various stages of a claim/litigation and assign a value to each stage. Essentially, decision trees convert a subjective assessment of a case into an objective value. That resulting value can assist a client during settlement discussions at all stages of the litigation.

A successful tree will show all significant stages of the litigation (motions to dismiss, motions for summary judgment, trial, verdict, etc.), and will prescribe a likelihood of success at each stage. Then, the decision tree will assign a value to each stage. Those values will then represent the value of a given claim at the given stage in the litigation.

For a decision tree to be successful, it is critical that a litigator be experienced and knowledgeable enough to provide an accurate estimation of the input numbers. For example, a litigator must have a solid understanding of a likely jury verdict—usually framed in terms of “worst case scenario.” That is the starting point. Then, the lawyer must be able to provide a reasonable estimation of the chances of success, especially as they relate to the probability of various occurrences during the lifespan of a matter in litigation.

For the easiest example, consider the verdict stage. If a litigator believes his client has a 60% likelihood of succeeding at trial, that means that the client also has a 40% likelihood of some degree of failure. One must then take a step further, and define “success.” Is that a zero defense verdict? Is it something slightly more than that? In many cases, a verdict in favor of the plaintiff for some amount is fully expected by both sides (medical specials, for example). However, extensive damages, including pain and suffering, lost wages, etc., may be highly contested at trial. A “win” for the defense in this instance may simply be an award limited to the medical specials, and a “loss” would be an outcome in which punitive damages are awarded, for example. An examination of this sort is but a small component of the analysis involved in creating a decision tree.

I. Growing a Decision Tree

Generally, four steps are required for creating a decision tree. Each step is as critical as the next, and the value of a given decision tree relies heavily on the estimations at each step being thoroughly analyzed and assessed.


A.
Recognize All Relevant Events.

First, the attorney must outline the list of possible events throughout the course of the litigation. An “event” is classified as one that alters the potential liability in a case in a significant manner. Things such as motions to dismiss being granted or a critical motion in limine being denied can significantly alter the value of a claim. Depending on the outcome of these critical stages, your client may be more or less likely to be hit with a sizable verdict. It is critical that each step is identified. Once identified, those possibilities will be arranged in a tree-like formation, moving from left-to-right, with both possibilities (granted/denied, verdict for the defense/plaintiff, etc.) being listed at each step.


B.
Identify the Cost of Each Event.

Next, an analysis of the cost to get to each step, and the gain/loss of that step, must be performed. Keep in mind that, in terms of the objective analysis that the decision tree provides, it makes no difference if $40,000 is paid to the claimant to settle or $40,000 is spent filing and succeeding on a motion for summary judgment. Because of this reality, an accurate computation of legal costs spent at each stage of the litigation must be ascertained.

In addition to a reasonably accurate estimation of legal costs, one must also identify what a potential verdict amount might be. The legal costs and the verdict must be combined to determine the total value of a case.

In terms of identifying possible verdict awards, it is best to assess them in terms of three categories, assuming it is a plaintiff’s verdict: high, medium, and low. The “high verdict” amount might be $500,000, for example. A “high verdict” should be a verdict amount that is above that which a reasonable person would expect it to be. Though unexpected, it is still a possibility. As such, the decision tree will need to take it into account. The “middle verdict” amount might be closer to $100,000, for example. This amount should represent an amount in between what the plaintiff and defendant have valued the case to be, and typically represents the most likely amount. Finally, the “low verdict” amount assumes that, though it was not a complete defense verdict, the result was as favorable as it could be in light of the circumstances.


C.
Ascribe a Reasonable Estimation of Probabilities.

Thirdly, one must estimate the probability of each event. If the events conceived of for a given case include a motion to dismiss, motion for summary judgment, and trial, counsel should be able to provide a fair estimation of the likelihood of success for each event. To do this, it is important that a number is not simply “guessed.” Rather, lawyers should take the time to identify reasons for this estimation. Prior cases, tendencies of the given judge, jury pool, etc., should all frame the probability analysis.

This estimation of probability should ideally be based on: (i) strength of the argument/story; (ii) whether undisputed facts are favorable or detrimental; (iii) venue; (iv) judge; (v) jury pool (in the case of a verdict); (vi) quality of favorable witnesses; and (vii) impeachability of unfavorable witnesses. If counsel is not familiar with the venue, for example, a consultation with local counsel, if available, may be required to create an accurate assessment. This is true for all categories. Each case is different, so attorneys should be mindful of other, potentially significant variables that should be considered, as well as resources if a given allocation is uncertain.

As discussed above, the lawyer will also need to consider the varying degrees of success (or, failure, depending on perspective) of a verdict. A “high verdict”, as described above, may be unlikely but, nonetheless, possible. As such, one may want to attribute a 3% likelihood to such a verdict. Similarly, a “low verdict” may not be particularly likely, but, given the circumstances, could arise. Perhaps a 15% likelihood is correct in that instance. That leaves the “middle verdict.” Because all plaintiff verdict possibilities must be accounted for, all possibilities must add up to 100%. Therefore, assuming the “high verdict” has a 3% likelihood, and the “low verdict” has a 15% likelihood, then the “middle verdict” must have an 82% likelihood. Similarly, and obviously, in cases where two outcomes are possible (a motion to dismiss, for example), if the likelihood of the motion succeeding is 20%, then the converse likelihood of it failing would be 80%. It is incredibly important in the decision tree making process that these probabilities be as accurate and reasonable as possible. This is not the time for counsel to be overly optimistic about a client’s potential for success in a lawsuit.


D.
Compute the Inputs.

The final step in this process is to perform some basic math (i.e. multiplication and addition). The decision tree should proceed in a left-to-right direction. The first critical step in litigation forms the first branch of the tree, followed by the next branch, and ending with the verdict decision. In performing the math portion of this exercise, one proceeds in the opposite direction (from right-to-left). The math portion begins by multiplying the potential verdict amount by the likelihood of it happening. If the chance of a verdict of $500,000 has a 3% chance of occurring, then that branch would be worth $15,000 ($500,000 X .03). Similarly, where the “middle verdict” has an 82% likelihood of occurring, the value of such a branch would be $82,000 ($100,000 X .82). Lastly, the “low verdict” branch value would be worth $3,000 (where the low verdict value was placed at $20,000 and the likelihood of such a verdict was 15%).

Next, one would total up those three branches ($100,000). That number will represent the value of a plaintiff’s verdict. If, during the probability analysis, it was determined that the probability of a plaintiff’s verdict was 70%, and the chance of a defense verdict was 30%, then those numbers would similarly be multiplied with their respective values. In the case of a defense verdict, the verdict is zero, but the expense leading to that result must be accounted for. If it cost the client $75,000 in legal fees to get to that point, then the likelihood of a defense verdict would be multiplied by those fees. In this case, the value of the defense verdict branch is therefore $22,500. Similarly, if a plaintiff verdict is the result, an equal amount of legal fees were expended as with that of the $0 defense verdict. As such, the branch for the plaintiff verdict would be $175,000 (or, $100,000 for the actual verdict and $75,000 for the legal fees).

To understand the total value of this case at trial, then, one would add the value of a defense verdict (already determined to be $22,500, or $75,000 X .30) with that of the plaintiff verdict ($175,000 X .70, or $122,500). Therefore, the total value of this case to a client, once it gets to trial, is $145,000. In this basic analysis, where a trial is the only significant step, the client would be faced with a relatively easy decision. Should plaintiff demand something under $145,000, the client should be advised that, barring extraneous circumstances, as discussed below, a settlement under $145,000 is a good value. There is, after all, a significant chance that a verdict, along with legal fees, would exceed that amount. There is also a chance that a verdict would be favorable. The figure of $145,000 represents that average outcome of these scenarios.

Should an attorney be adverse to math, as many are, programs are available whereby you simply input the values, resulting in a decision tree being generated. For those with mathematical limitations or, more likely, time constraints, this is a preferred option.

II. Usefulness

As discussed above, the utility of decision trees is that they provide an objective analysis of the cost of a case, rather than a typical subjective analysis wherein the attorney outlines the strengths/weaknesses of a case and a range of verdict possibilities. Decision trees can be helpful as a supplement to these more traditional analyses.

On occasion, especially in large cases, both parties may agree to perform a decision tree analysis jointly. This can aid in ascertaining a reasonable settlement value at that juncture. Such a process, however, is contingent on both parties being agreeable as to the inputs and being honest about the strengths and weaknesses of their case. An opportunity such as this rarely exists.

III. Limitations

Decision trees are, at best, an objective analysis of a case that provides a simple answer to a complicated question: “What is the settlement value of this case?” The answer, if the decision tree is done correctly, is the value indicated by the decision tree at the applicable stage of the litigation. However, as with everything in the legal realm, limitations of such a methodology persist.

First, as all litigators know, the strength of a case can change overnight. Deposition testimony can derail an otherwise strong case. Responses to interrogatories can be unanticipated. A voir dire can provide little in the way of favorable finders of fact. Decision trees hinge on inputs that fairly and accurately represent the likelihood of various outcomes. As such, as litigation proceeds, it is critical that a decision tree is updated to ensure that the inputs represent the true likelihood of a particular event, given the changing dynamics of a case.

Additionally, decision trees represent solely a cost analysis of a given claim. However, other considerations are often present. These include a client’s interest in deterring future, similar lawsuits, as well as a client’s preference to maintain a certain image with the general public. These interests often take precedence over a simple analysis of the right time to settle a claim. Should these forces be present in a case, a decision tree may provide little, if any, value.

IV. Conclusion

Ultimately, the use of a decision tree can provide exceptional value to a client, if done correctly. However, to formulate a useful decision tree takes time, experience, and an objective assessment of the case. Further, decision trees are fraught with their own limitations. However, being able to identify those instances where the information provided by decision trees can be helpful to a client can provide a level of clarity that is typically otherwise unattainable.


[i] A discussion on the pioneer of decision trees' applicability in the legal field (Marc B. Victor) can be found at http://www.litigationrisks.com.