FOR THE RECORD:
DNA evidence: A May 4 article in Section A about the statistical calculations involved in describing DNA evidence in a murder case contained an arithmetic error. It said that multiplying the probability of 1 in 1.1 million by 338,000 was the same as dividing 1.1 million by 338,000. Actually, it's the same as dividing 338,000 by 1.1 million. The answer, a 1 in 3 probability of a coincidental match between crime scene DNA and genetic profiles in a state database, was correct. —

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For more than three decades, Sylvester's slaying went unsolved. Then, in 2004, a search of California's DNA database of criminal offenders yielded an apparent breakthrough: Badly deteriorated DNA from the assailant's sperm was linked to John Puckett, an obese, wheelchair-bound 70-year-old with a history of rape.

The DNA "match" was based on fewer than half of the genetic markers typically used to connect someone to a crime, and there was no other physical evidence.

Puckett insisted he was innocent, saying that although DNA at the crime scene happened to match his, it belonged to someone else.

At Puckett's trial earlier this year, the prosecutor told the jury that the chance of such a coincidence was 1 in 1.1 million.

Jurors were not told, however, the statistic that leading scientists consider the most significant: the probability that the database search had hit upon an innocent person.

In Puckett's case, it was 1 in 3.

The case is emblematic of a national problem, The Times has found.

Prosecutors and crime labs across the country routinely use numbers that exaggerate the significance of DNA matches in "cold hit" cases, in which a suspect is identified through a database search.

Jurors are often told that the odds of a coincidental match are hundreds of thousands of times more remote than they actually are, according to a review of scientific literature and interviews with leading authorities in the field.

Two national scientific committees, including the FBI's DNA advisory board, have recommended portraying the odds more conservatively. But interviews with expert witnesses and DNA analysts from crime labs across the country show that few if any have adopted that approach.

The FBI lab, which oversees the nation's offender databases, has disregarded the recommendation of its own advisory board, bureau officials acknowledged. So far, the courts have ruled in law enforcement's favor on this issue.

As a result, some experts fear, a technology best known for freeing the innocent could be causing its own miscarriages of justice.

"It is only a matter of time until someone is wrongfully convicted because of this," said Keith Devlin, a Stanford mathematician who has studied the problem.

DNA profiles are widely perceived as a unique genetic fingerprint. In fact, they are slivers of the human genome -- up to 13 markers that contain about a millionth of the information on all the chromosomes. Relatives often share many markers, and even unrelated people on average share two or three.

So DNA "matches" by themselves can never definitively link someone to a crime.

The best science can do is to estimate the likelihood that a match has occurred by sheer chance. These statistics are easily distorted or misunderstood by lawyers, judges, juries and even expert witnesses.