Cover Story
March-April 2020

Likelihood ratios for lawyers

By Raymond Valerio
Chief of the Forensic Science Unit, Bronx County (New York) District Attorney’s Office

As a New York State prosecutor for more than 15 years, it has been my experience that many prosecutors are uncomfortable with scientific evidence.

Knowing this, I wrote an article for the WIRE Interdisciplinary Journal, where members of the Texas Forensic Science Commission read (and apparently liked!) it. It was then recommended that Texas prosecutors consider the following discussion to ensure fairness when using statistics applied to forensic evidence. This article highlights the issues prosecutors have faced in New York State, but the general principles cross jurisdictional borders.[1]

‘I didn’t go to law school for statistics!’

With the proliferation of probabilistic genotyping software in forensic DNA analysis, prosecutors are faced with the challenge of understanding complex statistical conclusions and their corresponding meanings. Unlike many scientists, lawyers rarely learn statistics in college or law school; statistics are neither a subject on state bar examinations nor a topic in any core continuing legal education course. Therefore, when faced with complicated DNA comparison statistics, prosecutors may unknowingly present misleading—or even incorrect—arguments to the fact-finder. In this primer, I explain how to fairly argue probabilistic genotyping statistics in forensic DNA analysis.

            At the conclusion of a trial, before a jury evaluates the evidence, the prosecutor presents a closing argument. In the closing argument, the prosecutor persuasively marshals the evidence and is permitted to make reasonable inferences based on facts adduced during the trial.

            To illustrate the significance of appropriate prosecutorial argument, an example helps. On December 11, 2012, Jennifer Ramsaran went missing in Chenango County, New York. After her body was discovered in February 2013, her husband, Ganesh Ramsaran, was charged with murder. During the trial, the prosecution elicited testimony that the defendant filed a missing person report on December 11, the day of his wife’s disappearance. Trial testimony highlighted the defendant’s whereabouts before and after the missing person report.

            Forensic testimony at trial established there was a mixture of DNA on a bloodstain found on Mr. Ramsaran’s sweatshirt. The forensic scientist testified that the defendant was the major contributor and that the victim “could not be excluded” as the minor contributor to the bloodstain. Statistical analysis revealed that it was 1.661 quadrillion times more likely that the blood sample from the sweatshirt contained a mixture of the defendant and victim’s blood than two randomly selected individuals. The defendant was convicted of murder and sentenced to 25 years to life in prison.

            On appeal in 2016, the intermediate appellate court reversed the defendant’s conviction and ordered a new trial. The court’s analysis centered on the prosecutor’s statements in summation: “On that sweatshirt is [the defendant’s] wife’s DNA,” and the DNA report “shows that [the victim’s] DNA was on that area where the bloody spot is.” Then, in summarizing the forensic expert’s testimony, the prosecutor said, “We have the forensic people who say … [the victim’s] DNA is on that sweatshirt, to some degree.” Ultimately, the court concluded that the prosecutor’s misstatements alone were enough to reverse the conviction—the inaccurate and misleading description of the DNA evidence deprived the defendant of a fair trial.[2] In 2017, though, the highest appellate court in New York State reviewed this case, disagreed with the intermediate appellate court, and the conviction was restored.[3]

            Lawyers and forensic scientists alike must learn lessons from cases like this. One court found the prosecutor’s statements fundamentally unfair while another found them permissible. How can a prosecutor be confident that a conviction will not be reversed based on an improper comment regarding statistical conclusions during summation?

            Prosecutors must consider two questions to ensure fair argument of DNA statistics to a fact- finder. First, do I understand the conclusion? Second, do I understand the value of the conclusion? American inventor Charles Kettering once said, “Knowing is not understanding. There is a great difference between knowing and understanding: You can know a lot about something and not really understand it.”[4] Let’s explore these two questions.

Do I understand the conclusion?

During the pendency of a case, the prosecutor gathers evidence from various sources. Witnesses are located, interviewed, and prepared for trial testimony. Prosecutors scrutinize police officers’ observations and paperwork. Now, more than ever before, forensic evidence is tested and, if possible, compared with DNA from a defendant. For that reason in particular, prosecutors must remember Kettering’s wisdom. Simply knowing the results of forensic analysis does not mean one understands the conclusions. This is even truer when complicated algorithms are the foundation for DNA mixture analysis.

            Many laboratories are using probabilistic genotyping software to aid in interpreting DNA mixtures. When a defendant’s DNA profile is compared to DNA recovered on evidence from the crime scene, most probabilistic genotyping software platforms generate a statistic called a “likelihood ratio,” which gives weight to the conclusion reached by analysts. Simply put, a likelihood ratio (LR) is a statistic that compares two scenarios and presents which scenario is more likely. In the context of forensic DNA analysis, the LR assesses the evidentiary support that a person of interest (e.g., the defendant) is a possible contributor to the crime scene evidence.

            Here is an example. The DNA mixture found on the swab of a gun’s trigger is approximately 10.4 trillion (1.04 x 1013) times more probable if the sample originated from defendant John Doe and one unknown person than if it originated from two unknown persons. Therefore, the LR supports that John Doe is included as a contributor to this sample.[5]

            Just as important as understanding what a LR does say is what a LR does not say. Several common misconceptions may cause a prosecutor to incorrectly present LR statistics. First, the LR is not a measure of how much more likely it is that the person of interest (e.g., the defendant) is the DNA donor to crime scene evidence. For example, it is improper to argue, “It is [LR] times more likely that the victim and the defendant are the contributors of this evidence profile than it is that the victim and a random, unrelated person are the contributors.” Instead, the LR is a measure of how likely it is to obtain the evidence result if the person of interest is included rather than not.

            Additionally, it is incorrect to argue, for example, “The LR is 100,000. Therefore, there is only a 1-in-100,000 chance that someone other than this defendant contributed the DNA on the crime scene evidence.” Yet another misconception is assuming definite inclusion or definite exclusion: that if an LR is greater than 1, a defendant is definitely included in the evidence mixture, and likewise, that a LR less than 1 means a defendant is excluded from the evidence mixture. Instead, the LR gives support, or weight, to a particular conclusion that is in line with the analyst’s interpretation.

            Understanding flows from trial preparation. Regardless of the prosecutor’s experience level, thorough trial preparation is the foundation for understanding statistical conclusions. It is through trial preparation that the forensic scientist explains both what the statistical conclusion is and what it is not. During trial preparation, the forensic scientist explains the foundation for the conclusion, the methodology behind the conclusion, and most importantly, the limitations to the conclusion. To that end, the prosecutor must walk through all expected testimony with the forensic scientist. Every question that the prosecutor intends to ask at trial should be reviewed with the expert. By reviewing all questions, the prosecutor should understand the limits of the conclusions, and the expert can precisely answer each question.

Do I understand the value of the conclusion?

Not only must prosecutors understand the conclusion through trial preparation, but it is also incumbent that the prosecutor understands the value of the conclusions. The prosecutor must be guided by the forensic scientist—the true expert in this arena. If the forensic scientist takes a proactive role in explaining the meaning of complicated conclusions, then it is more likely that the prosecutor will fairly present the value of the expert’s conclusion.

            For example, an LR that hovers just above the laboratory’s inconclusive range (e.g., an LR of one to 1,000) has significantly different value from an LR that exceeds the number of humans on Earth (e.g., 8,000,000,000). While both may include the defendant as a possible contributor, the latter statistic is more indicative of the defendant’s inclusion. Many, but not all, laboratories include sliding scales that describe the qualitative weight of the LR statistic (e.g., an LR between one and 10 is “limited support,” or an LR greater than 10,000 is “very strong support”). Without a sliding scale, the prosecutor must be guided by the forensic scientist’s expert opinion.

            After sufficient trial preparation, the prosecutor should understand the value of the statistical conclusion. Sometimes, the statistical conclusion is dispositive of guilt, but often a likelihood ratio statistic is merely corroborative. Where the line is drawn between dispositive of guilt and corroborative of guilt must be discussed with the forensic expert.

            Let’s say the prosecution is attempting to prove that the firearm recovered in the defendant’s vehicle on October 15 is the murder weapon from a September 1 homicide. After analysis, the DNA expert concludes that there is a mixture of three persons on the trigger of the firearm with no major contributor. When comparing the defendant’s DNA exemplar to the mixture on the gun’s trigger, the defendant is “included as a possible contributor” to the mixture. Using probabilistic genotyping software, the DNA expert concludes that the “DNA mixture found on the swab of the trigger is approximately 2.8 million times more probable if the sample originated from John Doe and two unknown persons than if it originated from three unknown persons.” The laboratory considers all likelihood ratios over 1,000 to be inclusionary and, using a sliding scale, considers any likelihood ratio over 100,000 to be “very strong support” for inclusion.

            In this example, the prosecutor cannot argue that the defendant matches the DNA on the trigger. However, it is fair argument to say the following:
            •          the laboratory threshold for inclusionary results is 1,000,
            •          2.8 million is significantly greater than the 100,000-LR laboratory standard for “very strong support,”
            •          the lab weighed two different scenarios and found that it is 2.8 million times more likely to see this DNA on the evidence if the defendant is a part of the mixture than of other unknown people, and
            •          this likelihood ratio corroborates other evidence in the case.
            The prosecutor must remember that no argument is “one size fits all.” The facts of the case and the conclusions of the DNA expert determine what is a fair argument.


In the Ramsaran case discussed earlier in this article, the value of the statistical conclusion was strongly corroborative of guilt—not guilt beyond a reasonable doubt. Although attorneys are accustomed to arguing reasonable inferences from adduced evidence, in the arena of forensic statistics, the conclusion is the conclusion. With an inclusionary likelihood ratio of 1.661 quadrillion, the prosecutor should have argued that the magnitude of this conclusion, coupled with all the other evidence in the case, met the burden of proof.

            DNA evidence is a critical tool in both the prosecution of crime and the exoneration of the innocent. Therefore, attorneys must be mindful of correctly presenting forensic statistical evidence to ensure fair trials.


[1]  There are some slight modifications to the previously published article.
[2]  People v. Ramsaran, 141 A.d.3d 865 (3rd Dept. 2016).
[3]  People v. Ramsaran, 29 NY 3d 1070 (2017).
[4] Charles/KetteringCharles-Quotations.htm, last visited January 28, 2020.
[5], last visited November 25, 2019.