Why Are Public Defenders So Good?

In my last post, I provided a graph suggesting public defenders have above average win-rates. Most people find this surprising. Actually, this fits neatly into a model of the LSM where defense attorneys are profit maximizers and public defenders are sentence minimizers. Profit maximization does not imply sentence minimization. Instead, defense attorneys focus on “Win-Stay” and “Lose-Stay” outcomes. To see what I mean, consider Bayes’ Rule


All of this means that the probability of A conditional on B equals the probability of B conditional on A multiplied by the probability you assign to A, over the probability of B conditional on A multiplied by the probability you assign to A plus the probability of B conditional on not-A multiplied by the probability you assign to not-A. If the above isn’t clear, check out Bryan Caplan’s excellent lecture notes or this post at Econlog.

Here’s an example relevant to the defense attorney profit maximization problem:

P(A|B) = P(Attorney is Optimal|Bad Case Outcome)
P(B|A)=  P(Bad Case Outcome|Attorney is Optimal)
P(A) = Probability Attorney is Optimal
P(~A)= Probability Attorney is not Optimal

The profit maximizing attorney wants to persuade clients with bad outcomes that their attorney was still the correct choice. This way, the attorney still has access to that client’s network (and of course for future cases with the same client). In order to do this, attorneys should focus on increasing their clients’ subjectively held belief that they are high quality and increasing the clients’ belief that bad outcomes with high quality attorneys are common. For simplicity, let’s assume that the attorney’s clients will stay with them or recommend them to others if the attorney wins their case.

These incentives create a potential agent-principal problem in the attorney-defendant relationship. If an hour of signaling “I have a great win-rate” does more to increase the probability of Lose-Stay outcomes than an hour of work increasing the probability of winning, the attorney will invest too little (from the defendant’s perspective) in actually winning.

Public defenders, as sentence minimizers, don’t have this problem. Basically – and this can be seen in the data – the average public defender is a better agent than the average private defense attorney. Of course public defenders have obvious weaknesses – essentially zero budget for non-procedural trial inputs, for example. But with respect to procedural inputs, they should behave as if they have been given infinitely large budgets.



The Randazza Critique: An Objection

From commenter marcorandazza on a review of a firm in Massachusetts that apparently profiles attorney win-loss records:

This is utterly moronic.

When I hear of a lawyer who “never lost a case,” I hear “this lawyer sucks.”

Any idiot can pick winners. The real skill comes when you take a hard case. Take a dozen hard cases in a row, and lose them all. I’ve certainly taken my share of cases where I had to tell the client “you have a really low chance of winning, but your case is important” or just “you’re in deep shit, but I’ll do my best.”

I’m proud of many of my “losses.” I brag about them. In fact, one of the best things that ever happened to my career was losing a case 0-7 in the Florida Supreme Court. Ever since that case, I’ve handled lots of cases that hang on its logic. And, when my adversary inevitably makes the argument I made in that case, I say “your honor, I love my adversary’s argument. In fact, I wish that it were the law. However, I made the exact same argument to the Florida Supreme Court and the court ruled against me 0-7”


These two dipshits should just go backpack around Europe. Their idea is trash.

I frequently encounter two chief criticisms to attorney win-rate analysis:

  • Trial inputs and output are highly heterogeneous and classifying outcomes as wins or losses is extremely complicated.
  • Many attorneys select their case portfolios for easy cases to give themselves an artificially high win-rate.

I think (1) is a better criticism and I’ve addressed it briefly before (I’ll write about it later as well). Basically, I think the argument that heterogeneous trial inputs and outputs is a serious impediment to win-rate analysis is overrated. It’s technically complicated but theoretically straightforward to consider different types of trial outcomes (e.g. accounting for plea bargains) and analyze sentence quality controlling for relevant variables.

Criticism (2) seems to me much weaker but oddly more commonly voiced. The most important theoretical objection:

Win-rates are not commonly analyzed so I’m not sure why attorneys would be aggressively pursuing high win-rates at the expense of income from potential clients.

The most important empirical objection:

Public defenders are the least likely of all criminal defense attorneys to select their cases and they tend to have win-rates above the median. If attorneys were biasing their win-rates by heavily selecting their client portfolios, we would definitely not expect to see something like this:


Should Public Defender Caseloads Matter for Indigent Defense Outcomes?

Unsurprisingly, I believe the answer is yes; surprisingly, I expect heavy caseloads should improve defense outcomes. My reasoning:

  • Public defenders (PDs) behave as if they are not budget constrained (with respect to trial inputs they supply themselves).
  • Heavy caseloads should increase the probability of seeing any given case continued on a given day.
  • The average indigent defendant is more likely than the average wealthy defendant to have a prior criminal record, and the marginal disutility of additional criminal charges is probably strongly diminishing. In other words, prosecutors quickly lose (or often lack) the ability to tempt indigent defendants with plea bargains that offer features like amended charges with better labor market signaling. Indigent defendants have more taste for trials, which are costly to prosecutors.

(1) strongly suggests that PD clients are relatively more expensive to prosecute, especially at general district court levels where things like (costly) expert testimony are less common. (3) also suggests a level effect; when indigent defendants and relatively wealthy defendants have identical case details, the indigent defendants will probably do somewhat better in terms of trial outcomes as a group. (2) implies that as PD caseloads increase, the probability of continuances across the PD portfolio increase. Sentence maximizing prosecutors will know this, and will be induced to offer more favorable pleas or drop charges as needed.