Most litigators who have benefitted from participating as counsel in a few trials can assess, with reasonable confidence, whether their client has a “strong” or a “weak” case. However, if one asked them whether they could frame their forecasts as a range of likelihoods of an acquittal, a fine range, or the length of incarceration, probation, or a suspension, most litigators demur from making such a forecast. Yet, increasingly, sophisticated parties demand these forecasts. Insurers ask for realistic estimates rather than “worst case” estimates of reserves they need to set aside. Litigation finance must assess the likelihood of recovering a sum of damages that reflects the risks of loss. Our trade publications are rife with articles about clients who demand greater transparency into how litigators develop their forecasts.

The Role of Decision Analysis

Decision analysis is a discipline with universal use in other fields such as operations research, finance, project management, among many others. Whenever a person needs to forecast an event that depends on a chain of events, each link of the chain having a range of likelihood of occurrence, those professionals will employ decision analysis tools. A wonder that lawyers, whose stock and trade is in the analysis of uncertain events, have not embraced these techniques. It’s high time we did.

The Decision Tree

A decision tree is a model of event points having a range of potential outcomes. Lawyers have defined “decision points” for generations. For example, with a prosecution of a business contrary to section 6(1) of the Environmental Management Act, the Crown must prove beyond a reasonable doubt that: (1) the accused “introduce, cause, or allow” waste to be introduced into the environment; (2) the accused introduced “waste”; (3) the waste introduced into the “environment”; (4) the accused engaged in a “prescribed industry, trade of business”; and (5) the accused failed to execute due diligence to prevent the contravention.

Knowing the evidence, lawyers can identify the likelihood that each element can be proven. With that capability, each question becomes a point in a decision tree.

Here is an example of such a tree:

In this example, each node on the tree represents an element of the Crown’s case.

But you may say, “It’s impossible to be so precise in putting a number at each of those nodes! It’s more like a range of probabilities!” Decision analysis allows for this: the Monte Carlo simulation — a technique developed by theoretical physicists trying to develop the atomic bomb. The word “Monte Carlo” refers to the codename that US government scientists gave to the technique rather than to the suggestion that the technique results in random results or is a form of gambling. The lawyer assigns to each node a range of reasonable outcomes for that node. Usually, a node represents a discrete and often binary condition: “Yes” or “No”. As in, did the Plaintiff prove that the Defendant owed the Plaintiff a duty of care: “Yes” or “No” — unlike lawyers, a judge does not have the luxury of “Maybe”. In our example, the lawyer has defined the likelihood that a judge will decide that the Defendant owes the Plaintiff a duty of care as being 70% plus or minus 20%.

In this model, we establish probability ranges for each node of the tree, recognizing that we are uncertain how a court will rule on each point along the analysis. For example, we have modelled whether the Crown can prove the accused’s actions caused the introduction of waste into the environment with this probability range:

Just what does this figure mean? One way of putting it is that if we ran this trial in front of 100 judges, 70 judges would likely assess the issue as having a 75% chance of proving that element. We can predict 20 judges will make this finding 90% of the time and 10 judges will make the finding 95% of the time. This is a form of legal realism and not formalism. We are recognizing that judges are human and are prone to seeing cases differently from each other.

The Monte Carlo Simulation

Now, we run the Monte Carlo simulation. We recalculate the results while we change all the percentages for each node simultaneously. Running this exercise meaningfully requires thousands of iterations. This exercise cannot feasibly be done by hand. But, thanks to computers, we can run this simulation in a few seconds. But to reach a point where we had “stability” — that is where the result repeated themselves — the computer had to run 3400 iterations of this example model. Here are the results:

There is a pattern to the results, one readily discernible to clients, insurance professionals, and financial managers. The chart shows an average result of 54% chance of conviction.

There is a chart for each node that allows us to verify that the computer used random inputs into our model:

The input chart reflects the functions we created for each node. If one can imagine, we believed, based on our assessment of the evidence, that the Crown had between a 75% to 95% chance of proving that the accused introduced waste into the environment, where that distribution was skewed upwards. We assumed a wider range of risk whether the Crown could prove the accused operated in a prescribed industry. Despite the relatively high confidence the Crown could establish these elements, the final result shows the cumulative effects of uncertainty and risk in whether the Crown can prove its case. The analysis demonstrates the Crown is more likely to obtain a conviction, but the Crown has risk, and a plea arrangement with some favourable terms for the accused ought to be pursued.

This following chart presents the effect one node has on the result. The longer bars illustrate variables with a greater effect on the outcome. We use this graph to help recommend to the client where to focus a limited litigation budget (hint: after spending enough resources to satisfy that we can disprove, minimally, all elements, we focus remaining budget on disproving those elements with the greater impact on the result). Here, if the client had a limited budget (and which client does not), the chart suggests we ought to focus our efforts on fighting whether our client operates in a prescribed industry since that is the variable that creates the most variability in the result and creates the most opportunity to cause a likelihood where the Crown fails to prove its case beyond a reasonable doubt.

This note scratches the surface of how this technique is used and its power. We have used these techniques in helping clients understand whether to pursue litigation, helping accused persons know where to best deploy their defence budget to attack the Crown’s case, to formulate plea and defence positions, and to justify legal budgets with professional funders. After having used these techniques for several years, we can attest to their power not only in helping us make more rigorous and disciplined decisions, but its power to help clients see our work.

These techniques are commonplace in many areas of advanced business. Executives responsible for selecting major capital projects, sending people to space, deploying major population-wide health programs routinely procure these studies to inform their decisions. In all cases, these executives are seeking to forecast risk and opportunity. Lawyers are forecasters of risk and opportunity. We can mitigate risk and maximize the opportunity for our clients with legal tools. We should adopt these tested techniques pioneered and used in many other industries.