Police found the naked body of Diana Sylvester near her Christmas tree.
The 22-year-old San Francisco nurse had been sexually assaulted and stabbed in the heart. She lay on her back, her neck laced with scratches and her mouth open as if frozen in a scream.
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 dozens of interviews with leading scientific and legal authorities, a comprehensive review of scientific and academic papers in the field and court documents in cold hit cases.
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.
This potential for distortion is compounded in cold hit cases.
For years, police used DNA only to compare a crime-scene sample to a single person they had other reasons to suspect. In court, prosecutors could legitimately cite the remote odds that someone selected at random off the street would share the same genetic profile.
But in cold hit cases, the investigation starts with a DNA match found by searching thousands, or even millions, of genetic profiles in an offender database. Each individual comparison increases the chance of a match to an innocent person.
Nevertheless, police labs and prosecutors almost always calculate the odds as if the suspect had been selected randomly from the general population in a single try.
The problem will only grow as the nation's criminal DNA databases expand. They already contain 6 million profiles.
The danger of implicating an innocent person through a cold hit becomes particularly acute with crimes that are decades old, like Sylvester's killing. Witnesses have died, evidence has been lost and memories have faded. All of this puts greater weight on the DNA evidence, which also may have deteriorated.
Prosecutors and crime-lab analysts say they don't mention the database problem to juries because it could unfairly reveal that a defendant has a criminal record.
They also say that using more conservative statistics would not make a difference in many cases, because the odds would still overwhelmingly favor the prosecution. Some don't seem to understand the problem or rely on experts who disagree with the scientific mainstream.
Now the California Supreme Court is weighing the statistical and other concerns raised by cold hit cases -- the highest court yet to consider them. People vs. Nelson, which involves the 1976 murder of a college student in Sacramento, is scheduled for oral arguments Thursday.
It could influence how such cases are tried across the country and undermine an unknown number of convictions in California.
The stakes are high: There have been 50,000 cold hit cases across the nation, many only now headed to court. And next year, California will begin collecting DNA not only from convicted felons like Puckett but from anybody arrested on felony charges, regardless of whether they are found guilty.
"As these databases grow," said Jennifer Friedman, a Los Angeles public defender who co-wrote a brief in the Supreme Court case, "any of us could find ourselves in the situation Mr. Puckett is in."
'We're making love!'
It was three days before Christmas 1972, in an apartment building near San Francisco's Golden Gate Park. Helen Nigodoff, the building's landlady, heard thumping and other noises from the apartment above hers.
Nigodoff went upstairs to check on Sylvester. The door to the apartment was open. She saw a bearded man attempting to cover his face with his hand. "Go away!" he screamed, Nigodoff later told investigators. "We're making love!"
Nigodoff returned to her apartment and called police, who found Sylvester's body. There were no signs of forced entry or a struggle.
Initially, police focused on a street artist named Robert Baker, then 32, who had recently escaped from a mental institution. He had been identified as a suspect in a rape that occurred two weeks before Sylvester's killing and four blocks from her apartment.
The victim in that earlier case and a friend identified Baker as the rapist, but for reasons that are now unclear, authorities decided they did not have enough evidence to prosecute him.
Baker also was identified as the man who, four days after Sylvester was killed, harassed a woman and a young girl and followed them to their home a few doors from Sylvester's apartment, police records show.
He was not charged in that incident -- but he was booked for the rape four blocks from Sylvester's apartment.
Police thought he might also be Sylvester's killer.
In Baker's van, police found a parking ticket with drops of blood on it. The blood type was O, the most common, the same as Sylvester's. DNA testing was not available then.
The crime-scene fingerprints did not match Baker's, and he was never charged with Sylvester's killing. He died in 1978.
The investigation into Sylvester's death went cold.
Getting a cold hit
In 2004, San Francisco police received state funding to test DNA evidence from unsolved homicides.
A crime-lab analyst retrieved from storage a swab that had been taken from Sylvester's mouth back in 1972. It contained sperm presumably left behind by her assailant. Though the sample was severely degraded, the analyst was able to develop a partial DNA profile.
Most profiles examine 13 genetic markers, usually enough to distinguish between two people. The sperm sample produced only 5 1/2 and was mixed with traces of DNA from another person, probably Sylvester, the analyst determined.
It was too little information to search California's DNA database; for that, at least seven markers were needed. To bridge the gap, the analyst used evidence from additional markers that were too faint to be considered conclusive. When this profile, now expanded to the necessary seven, was compared with the 338,000 profiles of convicted offenders in the state's database, investigators got a cold hit.
The profile matched Puckett's.
His genetic information was in the database because he had pleaded guilty to two rapes and a sexual assault in the Bay Area in 1977, five years after Sylvester's killing. After his release in 1985, he had committed misdemeanor battery, but since 1988 his record had been clean.
On Oct. 12, 2005, San Francisco Police Inspector Joseph Toomey knocked on the door of the Stockton mobile home where Puckett lived with his wife.
Puckett hobbled to the door clutching a bag of urine, explaining that he had just had triple-bypass heart surgery, Toomey later testified. During a 2 1/2 -hour interview, Toomey showed Puckett photos of Sylvester and the crime scene.
"You never had sex with that girl?" Toomey asked.
"No," Puckett said.
"You've never been in the house we showed you?"
Puckett volunteered to give Toomey a fresh sample of his DNA.
When it matched the same markers as the earlier test, Puckett was arrested and charged with murder.
The case was assigned to the San Francisco public defender's office, which had recently hired a DNA specialist named Bicka Barlow.
Barlow had earned a master's degree in genetics from Cornell University before going to law school. A veteran of dozens of DNA cases, she considered Puckett's the weakest match she had ever seen.
Typically, prosecutors rely on FBI statistics to estimate the rarity of a particular DNA profile in the general population. This calculation is known as the Random Match Probability.
The chance that two unrelated people will share the same 13 markers can be as remote as 1 in a quadrillion -- a number with 15 zeros. Because the match in Puckett's case involved only 5 1/2 genetic locations, the chance it was coincidental was higher but still remote: 1 in 1.1 million.
But Barlow thought this figure vastly exaggerated the strength of the evidence. It did not take into account how Puckett had been identified: through a search of a large database.
The general-population figures used by prosecutors portray the odds of matching crime-scene DNA to a single, randomly selected person.
But because database searches involve hundreds of thousands or millions of comparisons, experts say using the general-population statistic can be misleading.
Think of a lottery. If you buy a single ticket, your chances of hitting the jackpot are remote. If you buy many tickets, your odds improve with each purchase. In Barlow's view, the prosecution in effect bought hundreds of thousands of lottery tickets to find the match with Puckett. She contended that this greatly increased the odds of a match to an innocent person.
Barlow argued during pretrial hearings that the jury should be told about the recommendation of two leading panels of scientific experts, one convened by the National Research Council and the other by the FBI. Both committees settled upon a statistical remedy to adjust for the many individual comparisons made during a database search. It has been widely but not universally embraced by scientists.
In every cold hit case, the panels advised, police and prosecutors should multiply the Random Match Probability (1 in 1.1 million in Puckett's case) by the number of profiles in the database (338,000). That's the same as dividing 1.1 million by 338,000.
For Puckett, the result was dramatic: a 1-in-3 chance that the search would link an innocent person to the crime.
Barlow knew the concern was not just hypothetical. A database search had implicated an innocent man in Britain in 2001. A DNA profile of six markers from a crime scene had matched Raymond Easton, who was arrested and charged with robbery.
Easton, however, suffered from advanced Parkinson's, had a solid alibi and lived 170 miles from the crime scene. Six months after his arrest, police agreed to test four additional DNA markers. Easton was cleared.
When an FBI official learned of the British case, he called the coincidental match "mind-blowing." The chance of such a match was 1 in 37 million in the general population. But the odds of finding a match in Britain's extensive DNA database were 1 in 57.
In Puckett's case, David Merin, a deputy San Francisco district attorney, argued that the statistical adjustment recommended by the scientific panels would be "confusing and misleading." Like prosecutors around the country, he relied on the FBI's guidance. He cited a paper by an FBI expert, Bruce Budowle, that said the database adjustment was "not intended to replace" the general-population statistic.
The author of the National Research Council recommendation that Budowle cited told The Times that Budowle was wrong: "The intent was to replace Random Match Probability," said David O. Siegmund, a professor of statistics at Stanford University.
Superior Court Judge Jerome Benson ruled in favor of Merin. In doing so, he followed a California appellate court ruling on the same issue. The jury would never hear the 1-in-3 statistic.
'Our day in court'
When the case went to trial in January, the passage of three decades since the killing presented problems for both the prosecution and the defense.
Merin had warned Sylvester's four younger siblings, who flew in from Maine and Arizona, that because the crime-scene DNA was so degraded, a conviction was not a certainty.
"We just felt we needed our day in court," said Donna Sylvester Gaylord, 56, who went to nursing school with Diana. "And my sister deserved to have the way she died acknowledged by the state of California."
The other physical evidence at the crime scene couldn't be linked to Puckett. None of the 26 sets of fingerprints in Sylvester's apartment matched his. So Merin, who was 36 and trying his first murder case, relied heavily on circumstantial evidence.
Puckett "happened to be in San Francisco in 1972," Merin told jurors in his opening argument. Merin could not place Puckett in Sylvester's neighborhood on the day of the slaying. But Puckett had applied for a job near the medical center where Sylvester worked.
With the court lights dimmed and a photo of Sylvester's naked body displayed on a screen, Merin argued that Puckett's 1977 sexual assaults showed an "MO" consistent with Sylvester's killing.
In each of those crimes, Puckett had posed as a police officer to gain the woman's trust. The absence of forced entry to Sylvester's apartment indicated her killer had also used a ruse, Merin said.
Puckett had kidnapped his victims by holding a knife or ice pick to their necks, leaving scratches similar to those found on Sylvester's neck -- what Merin called "his signature."
On the stand, the three victims, who were in their early 20s when Puckett assaulted them, relived their terror.
"I recall his hand on my throat," testified one woman identified in court as Leslie B. "I recall trying to scream, which I wasn't able to. . . . He said he wanted to make love to me."
The prosecutor suggested that it was an unimaginable coincidence that police had stumbled across a suspect -- he didn't say how -- "who happened to be a serial rapist."
"What are the odds?" he asked jurors in closing.
The defense's first move in such cases normally would have been to question the investigators and everyone else who had contact with the DNA evidence to see if they'd followed proper procedures. But in Puckett's case, two of the three police inspectors had died, and the third was "severely mentally incapacitated" and in a rest home. The medical examiners who had conducted the autopsy on Sylvester also were dead.
The most important person missing, however, was Nigodoff, the landlady. She was the only one to get a good look at the assailant but had died in 2005, after Puckett was identified as a suspect. Both sides in the case debated whether Puckett fit the descriptions Nigodoff gave police in the 1970s.
At trial, Inspector Toomey testified that he had never shown Nigodoff a photo lineup that included Puckett, though he had 283 days to do so before she died.
Deputy Public Defender Kwixuan H. Maloof attacked the idea that Puckett's 1977 rapes followed a pattern similar to Sylvester's slaying. Puckett never threatened to kill his victims, put away his weapon shortly after commandeering the women's cars and tried to befriend them after the rapes, apologizing to one and offering another a job, Maloof said.
The judge didn't allow Ma- loof to tell jurors about Baker, saying the evidence against the street artist was too tenuous to raise a reasonable doubt. Because Baker had been buried nearly three decades earlier, exhuming his body was unlikely to yield usable DNA. The blood-spotted parking ticket found in Baker's van had been lost or destroyed.
Summing up the evidence for jurors, Maloof said that all the prosecution had was some "shoddy" DNA evidence.
An array of numbers
Through dueling experts, the prosecution and defense offered jurors a dizzying array of numbers to consider in weighing the DNA match.
A "likelihood ratio" presented by a prosecution expert placed the chance of a coincidental match at 1 in 1.7 million. A "combined probability of inclusion" put it at 1 in 152 billion.
The numbers all pointed to the virtual certainty that the DNA at the crime scene was Puckett's.
In an interview after the trial, Ranajit Chakraborty, the prosecution's DNA expert, told The Times that he generally favors giving jurors the database adjustment. He did not present an adjustment in this case because the judge, like most others, would not allow it.
In opening arguments, Merin sought to simplify things for jurors. "His DNA was found in her mouth," he said, drawing an inference allowed in court but not supported by science.
Merin focused the jury's attention on the 1-in-1.1-million general-population statistic, and did some quick arithmetic on a whiteboard.
There were about 18 million people in California in 1972, he said, half of them women. That left 8 million or 9 million men in the state. "You have eight or nine Caucasian men in the state that look like that crime-scene profile," Merin said.
"That man," he said, pointing at Puckett, "happens to be one of them."
His argument, a common one in DNA cases, was compelling. But it implied a certainty that DNA analysis cannot provide.
The defense team countered with its own experts, who made different calculations based on more conservative assumptions. Their numbers, 1 in 16,400 and 1 in 40,000, showed a greater, albeit still remote, chance of finding a coincidental match. Jurors would have to decide for themselves which numbers best fit the evidence.
Not long into their deliberations, jurors sent the judge a handwritten question: "How was [Puckett] identified as a person of interest?"
Consistent with his earlier ruling, Benson did not tell them about the database. He replied that they should not speculate about how Puckett was identified.
At 2:30 p.m. on March 6, after 48 hours of deliberation, the jurors filed into the courtroom with a verdict: guilty of murder in the first degree.
Puckett, now 74, sat motionless in his wheelchair. He later was sentenced to life in prison, with the possibility of parole after seven years. His attorneys said they would appeal.
Interviewed outside court after the verdict, jurors said they had struggled to weigh the different statistics. One said that the "likelihood ratio" was appealing because its name made sense in plain English.
In the end, however, jurors said they found the 1-in-1.1-million general-population statistic Merin had emphasized to have been the most "credible" and "conservative." It was what allowed them to reach a unanimous verdict.
"I don't think we'd be here if it wasn't for the DNA," said Joe Deluca, a 35-year-old martial arts instructor. Asked whether the jury might have reached a different verdict if it had been given the 1-in-3 number, Deluca didn't hesitate.
"Of course it would have changed things," he said. "It would have changed a lot of things."