These numbers are a bracing reminder that admissions of guilt are unreliable far more often than is generally believed. Some defendants, especially the young or mentally impaired, can be pushed to admit guilt when they are innocent. Some with prior criminal records may not be able to afford bail but don’t want to spend months in pretrial detention or risk a much longer sentence if they choose to go to trial.

Official misconduct — including perjury, withholding of exculpatory evidence and coercive interrogation practices — occurred in three of every four exonerations involving homicide, and it was an important factor in many other cases as well.

As high as these exoneration numbers are, they still understate the scope of the problem, since not all cases involving misconduct come to light.

The good news is that Americans are starting to grasp the depth of the problem. The Innocence Project, now more than 20 years old, has shown again and again how many ways a conviction can be obtained wrongfully. And in-depth investigations of questionable murder convictions by popular shows like “Serial” and “Making a Murderer” have led to calls for greater prosecutorial accountability.

As technologies like DNA testing have become more widely used, some prosecutors’ offices have begun to take responsibility for correcting their own errors. In the last seven years, almost two dozen offices in 11 states and the District of Columbia have opened conviction-integrity units to re-examine old cases. But the units vary widely in effectiveness. Half have never exonerated anyone, while two, in Brooklyn and in Harris County, Tex., were responsible for one-third of last year’s exonerations.