In a comment on Overlawyered, Ted Frank points to his draft paper (with Marie Gryphon), Negotiating in the Shadow of ‘Bad Faith’ Refusal to Settle: A Game Theory Model of Medical Malpractice Pre-Trial Settlements and Insurance Limits:

Recent empirical studies of Texas data by Hyman et al, Zeiler et al, and Silver et al suggest that insurance limits affect settlements of medical malpractice cases. Writing separately, Silver argues that insurance limits act as a de facto cap on malpractice payouts, that plaintiffs are being underpaid as a result, and that therefore legislative caps on damages are unnecessary. But this hypothesis is inconsistent with the data, which indicates that forty-seven percent of cases in which plaintiffs obtain verdicts above policy limits are subsequently settled above policy limits. We propose to reconcile the data by accounting for the effects that third-party causes of action for alleged bad-faith refusal to settle — known in Texas as a Stowers action — have on pretrial settlement negotiations. If an insurer in Texas is presented with a settlement offer within insurance limits, refuses to settle, and the plaintiff wins an award greater than insurance limits, the plaintiff is entitled to sue the insurer for the full damages amount, plus punitive damages, for refusal to settle. In this paper, we explore the game theory of medical malpractice settlement negotiations in the shadow of Stowers.

Based on their (admittedly, and necessarily, simplistic) model of malpractice settlements, they run a Monte Carlo simulation.

It’s not a bad idea, but they’ve missed one of the most important factors in settlement — the willingness and ability of the plaintiff to fight through years of risky litigation, trials, appeals and bankruptcy, where they must succeed 100% of the time to recover — and haven’t shown why the existence of third-party bad faith lawsuits (i.e., those brought by the plaintiff against the defendant’s insurer) contribute more towards settlement than the existence of first-party bad faith lawsuits (i.e., those brought by the defendant against their insurer).

Let’s start with the biggest missing element from their model:

Silver, et al. suggests that there are polite reasons not to seek more than [the insurance policy limits]. But this hypothesis contradicts both what we know about the incentives of attorneys and the empirical data. Are we to believe that trial lawyers, out of the goodness of their heart, refuse to seek more than [insurance policy limits]? This seems improbable: the insured doctor is likely to have substantial assets, trusts provide limited protection, and the plaintiff attorney’s fiduciary duty to her client requires her to zealously pursue the doctor’s assets.

There are indeed "goodness of heart" considerations: it’s psychologically easier to take an insurance company’s reserves — which have been collected and maintained for the purpose of compensating injured plaintiffs — than to take an individual’s personal assets.

But let’s put that aside and focus on the money. Keep in mind that, in most circumstances, the insurer can’t just pay their policy limits and wave goodbye to the defendant while the plaintiff goes after the defendant’s assets. If the defendant doesn’t want to pay any of their own money, then the insurance company will keep defending them to a full and final conclusion, without paying the plaintiff a dime in the meantime.

Most often, the settlement of an above-policy-limits claim at policy-limits is not due to the goodness of anyone’s heart: it’s the rational choice between either settling at insurance policy limits and walking away with the money now, or refusing the insurance money and then chasing the doctor’s assets for years (with five-or-six figure additional costs) through trial, appeals, re-trials, bankruptcy, bankruptcy appeals, and bankruptcy discharge, which often pays unsecured creditors a fraction of their claim’s value. And don’t forget: the plaintiff has to be successful in each and every one of those proceedings.

If the insurer actually tenders their full policy limits, then my "fiduciary duty" to the client typically compels me to recommend the client take the policy limits now, rather than starve themselves for years and endure the substantial risks of running the entire civil legal gauntlet — where they must succeed 100% of the time to recover anything — for a theoretical shot at more.

To their credit, the authors admit at the end that they haven’t included these factors:

This is still a relatively simple model: it assumes instantaneous and frictionless rulings, rather than an expensive process that may take several years with substantial fees for attorneys and medical expert witnesses. We assume that the trial court’s judgment is 100% accurate, and that there will be no appeal. We therefore do not consider the issue of post-trial settlement. In real life, the risk that a favorable judgment will be struck on appeal one reason why so many large judgments are settled so seemingly favorably, but it is impossible to estimate the size of this effect without qualitative data that the Hyman “haircut” study does not have.

Trials take years. We make no effort to compare the value of a settlement in the hand with a judgment several years in the future that is stayed by appeal. On the other hand, Texas has relatively generous post-judgment interest rates with a floor of 5%. Expanding the model to consider the time-value of money from early settlement would be useful in adjudging the merits and effects of the so-called “early offers” reform. As Zeiler notes, such time-value can also result in settlements below policy limits by virtue of aggressive negotiating by insurers.

Those two economic issues — the risk of losing on appeal (and/or retrial) and the time value of money — create a massive disincentive against attempting to pursue assets beyond the insurance policy limits. Post-judgment interest is generally irrelevant in the context of cases with damages/judgments larger than insurance proceeds: unless the plaintiff wants to go all the way through appeals, retrials, judgment execution, and bankruptcy, then, regardless of any post-judgment interest, the plaintiff’s recovery is still effectively capped at the insurance policy limits.

That’s the first problem: the failure to consider the effect of the willingness and ability of the plaintiff to fight through years of risky litigation on settlement.

Here’s the second problem: the authors "add a Stowers factor S, which is equal to expected Stowers recovery given a victory at the underlying medical malpractice trial" but don’t say how they calculate S. More importantly, though, they don’t explain why a third-party bad faith recovery would be expected to be any larger than the first-party bad faith claim available to the doctor if she believes the insurer did not handle the case properly.

When an insurer worries about a potential bad faith claim, they’re not just worried about the plaintiff suing them. Indeed, they’re usually more worried about the defendant suing them.

Like Dr. Woo:

Robert C. Woo is a Seattle-area dentist. An online guide praises his "first-class service" and "painless procedures." It is likely that Tina Alberts, his former assistant, disagrees.

Alberts cared for pot-bellied pigs, a frequent topic for office banter. Dr. Woo enjoyed taunting her with accounts of his boar-hunting trips, and a picture of a skinned pig hanging from a hook. He predicted a similar fate for Walter, her beloved pet pig. Dr. Woo informs us that this was all part of a "friendly working environment."

When Alberts required surgery to replace two teeth, Dr. Woo saw an opportunity to cement this self-impression of bonhomie. Once she was completely sedated, he halted the agreed procedure, and began a new one. Replacing her teeth required the temporary installation of standard false teeth. Dr. Woo had secretly ordered a second set of temporary teeth, shaped like boar tusks. Removing her oxygen mask, he inserted the tusks and – we must assume this was part of the friendly working environment – took photographs of her with her eyes and mouth pried open. Returning at last to his professional duties, he removed the tusks and inserted the correct temporary teeth.

A month later, Dr. Woo’s staff presented Alberts with the pictures at her birthday party. The fun-loving Woo described them as a "trophy" to take home. Home she went, never to return. Instead, she sued Dr. Woo for battery, invasion of privacy, medical malpractice, and a host of related claims.

Dr. Woo’s insurance company refused to defend him in Alberts’ lawsuit. Dr. Woo settled the case on his own for $250,000, then sued his insurance company.

And won:

Because his insurer should have defended him, Dr. Woo recovered the $250,000 he had paid Alberts. But he also claimed emotional distress due to his insurer’s abandonment. Despite "the absence of any medical, psychiatric or expert testimony" attesting these injuries, a jury awarded him $750,000, which suggests the rather even quality of justice throughout the judicial system of Washington State. And naturally, Fireman’s had to pay for Dr. Woo’s legal costs.

The end result was exactly what Ted Frank and Marie Gryphon’s paper is supposed to focus on: a situation in which an insurance company was forced to pay more than the policy limits for a malpractice claim. Yet, in Dr. Woo’s case, the third-party Stowers action had nothing to do with it — it was a purely first-party claim brought by the doctor. 

I hope there’s more study down this field; the world of litigation and defense & indemnity insurance is ripe for rigorous game theory analysis. But it needs to be as thorough and rigorous as the study of any other economic situation.

  • I read through the Frank-Gryphon article and looked at their model. Since it’s a draft, I’ll try to respect their request not to quote or cite them. Here’s what jumps out at me:
    – Models with or without Stowers adjustments conclude that non-economic damage caps hurt plaintiffs with strong cases more than those with frivolous ones. Shouldn’t we thus throw out the entire malpractice-cap system?
    – As you said, the reasons to not seek more than policy limits are not “polite,” they are pragmatic. Frank and Gryphon silently assume risk-neutral plaintiffs, which is absurd. Individuals tend to be extremely risk-averse relative to insurance companies!
    Consider the following offer: you load two bullets into a six-chamber .22 revolver, spin the cylinder, aim the barrel at your gut, and pull the trigger. If it doesn’t fire, you win $3 million. If you refuse, you “settle” for $500,000. The expectation value of accepting is +1.5 million, so only a strongly risk-averse person would refuse. The problem with this offer, obviously, is that the consequences of failure are catastrophic.
    Now imagine you are a permanently disabled plaintiff with a strong case: both parties agree you are 67% likely to win. If you don’t win, you’ll be disabled and broke. Your lawyer and the insurance company (somehow) know that your case is worth $3 million if you win. Win or lose, you will spend years in court awaiting a verdict while medical bills bankrupt you. The company offers to settle for $500,000. What would you do? F&G’s model assumes you will nearly always go to trial because the expectation value is positive and you are risk-neutral.
    Insurance companies don’t like losing a trial, but they can afford it. You can’t. In game theory terms, insurance companies are much less risk-averse than individuals. In poker terms, you’re playing at limits above your bankroll; insurers are not.
    – It does seem perverse that Stowers claims make moderately-strong cases more valuable than strong cases. One solution is to remove the Stowers factor. The other solution is to extend the Stowers factor to cases with claims above insurance limits. The authors quietly ignore this solution, though it removes the conflict of interest they mention.