Ken Strutin
Ken Strutin ()

Thanks to Ptolemy’s mismeasurement of the oceans, Columbus embarked on a trip to India that unexpectedly resulted in the discovery of America.1 So as long as there have been numbers, there have been miscalculations. Today, mathematical figuring, whether as evidence or analytics, plays a prominent role in cases relying on circumstantial proof and inferential reasoning. With progress in the revision of forensic science, it might be time also to renew acquaintance with the language of science.2

In criminal court, math can multiply mistakes and lead to injustice in several key ways: (1) the misuse of mathematics by prosecutors; (2) the failure of defense attorneys to recognize those errors; and (3) the courts’ inability or unwillingness to correct them.3 Indeed, there is a body of case law and scholarship that has been addressing these issues for more than a generation.4

Math can supplement or establish proof of identification or likelihood of an occurrence. And it has raised concerns over the inflation of evidence, juror confusion, credibility assessment, shifting and lessening burdens of proof, and the fundamental quandary of distilling human nature to statistical probabilities.

Sliding Rules

Ever since Leonardo Fibonacci introduced Western society to Hindu-Arabic numerals, mathematics has become more accessible and widespread. And in the courtroom it is finding an important place in criminal prosecutions.5

Much of forensic identity matching science relies on statistics and probabilities. Thus, the improbability that two particular kinds of evidence would match has been introduced to create unique linkage between the accused and the crime scene or victim. But forensic conclusions are only as good as the data behind them.

There have been noteworthy cases where math of this kind had been introduced to bolster seemingly scientific proof of a match without any reliable data or foundation, e.g., hair follicles in United States v. Massey, 594 F. 2d 676 (8th Cir. 1979); eyewitness identification in People v. Collins, 68 Cal. 2d 319 (Sup. Ct. 1968) and Commonwealth v. Ferreira, 460 Mass. 781 (Mass. Sup. Jud. Ct. 2011); gun purchase in State v. Sneed, 414 P.2d 858 (N.M. Sup. Ct. 1966); soil samples in Miller v. State, 399 S.W. 2d 268 (Ark. Sup. Ct. 1966); and a typewritten note in People v. Risley, 214 N.Y. 75 (1915).

Even the suggestion that the nature of mathematical conclusions might inflate the credibility of evidence has led to reversal or at least criticism, e.g., conviction rates in Dorsey v. State, 350 A. 2d 665 (Md. Ct. App. 1976); likelihood of children fabricating testimony in State v. Hernandez, 531 N.W. 2d 348, 350 n.1 (Wis. Ct. App. 1995); overstating claims in closing argument in Meredith v. Com., 959 S.W. 2d 87 (Ky. Sup. Ct. 1997); and quantifying reasonable doubt in State v. Carlson, 267 N.W. 2d 170, 176 (Minn. Sup. Ct. 1978).

On the other hand, when there is some support in scientific studies or the evidence of guilt is otherwise overwhelming or the mathematics were not the linchpin of the case, the conviction has stood.6

Lastly, a new twist to forensic evidence is the potentiality of the CSI effect.7 Where the presence of the CSI influence is supportable, it can impact probability or relevance and might serve as a secondary explanation for the mis-assessment of mathematical proof.

The Human Equation

Before Harvard law professor and mathematician Laurence Tribe became a nationally known constitutional scholar, he clerked at the California Supreme Court when it was asked to decide People v. Collins, 68 Cal. 2d 319 (Sup. Ct. 1968).8

Collins and his wife had been convicted of robbery, stealing a woman’s purse. The victim and other witnesses provided varying and unclear pictures of the culprits, certainly not enough to support a conviction in the state’s view. So the prosecution called an expert.

A local college math professor testified about probabilities based on six factors including race, physical appearance, and the color of the getaway car—all of which were shards of evidence from eyewitnesses that did not add up. The prosecutor elicited fantastical odds all but eliminating the possibility that anyone other than the defendant and his wife had been responsible.

The gravamen of Collins was the introduction of probability as proof without any foundation. The odds assigned to each factor and their independence were unfounded. And the Supreme Court of California did not hesitate to tamp down this criminal prosecution based on “inadequate evidentiary foundation” and “inadequate proof of statistical independence.”

Despite the impressive logic and allurement of statistics and probabilities, they fell short in accounting for human error and human nature. In the words of Justice Raymond L. Sullivan:

[N]o mathematical formula could ever establish beyond a reasonable doubt that the prosecution’s witnesses correctly observed and accurately described the distinctive features which were employed to link defendants to the crime.9

Collins was among the historical and contemporary cases of math injustice examined by mathematicians Leila Schneps and Coralie Colmez in their insightful book, “Math on Trial: How Numbers Get Used and Abused in the Courtroom.”10

In the introduction to another vignette in their book, the authors made this important observation about the inherent limits of forensic math:

Applying a mathematical model to a real-life situation is never likely to be completely accurate; the simpler the model and the more individual the behavior, the worse it will turn out. It should go without saying that this kind of reasoning cannot be used in a court of law without incurring a serious danger of being wrong.11

Misinterpretations, false assumptions, and misguided theories cannot transform synthetic proof into legal truth. However, they can inflate weak evidence and mislead juries and judges. The prism of the courtroom is narrow enough without encumbering it with uncertainty and unfairness.

In Hull v. United States, 404 U.S. 893 (1971), the petitioner had been convicted of smuggling marijuana. There was no direct evidence that he, and his companion, had crossed the border from Mexico into California, that their footprints matched those found in a sand trap near that location, or that they possessed the knapsacks with the contraband found 100 yards away.

The gap between mere suspicion and proof beyond a reasonable doubt had to be closed. So a government agent testified about prior similar smuggling investigations and that the particular border location near where the defendants had been arrested was a popular point of entry. In effect, he was profiling based on “criminal tendencies” of a sub-class of suspects, smugglers, found near the border on a few prior occasions.

The Supreme Court denied certiorari from the decision upholding the conviction. Even so, Justice William O. Douglas dissented and questioned the onus placed on the defense:

It is no answer that the defendant was free to challenge the Government’s general view of statistical probabilities by presenting other explanations of the circumstances or by impeaching the Government’s expert witness. We should not impose upon an accused the burden of independently generating probabilistic evidence and employing experts to study the criminal tendencies of a subgroup of the population. The Government should live up to higher standards and not be allowed to convict people of crimes on suspicion alone.12

Math Competence

Early on Professor Tribe sounded the alarm that math as proof or methodology might be the wrong lens for conning legal issues.13 This approach cautioned limits on mathematical descriptions of human events and values to forestall the risks of misusing math as proof of identity, occurrence or intention (frame of mind).14 To be sure, math has the same potential for a CSI effect as any forensic science.15

Still, while trial by math could be inherently misleading and unfair as in Collins, it was too important a tool to ignore or categorically exclude. Professor Tribe, among others, pointed out the availability of due process safeguards: (1) notice; (2) prejudice versus probity; (3) cross-examination; (4) defense expert; and (5) jury instructions.16 To which now must be added the increasingly important role of Frye/Daubert analyses. But the question remains whether these safeguards are enough for something as impartial and convincing as numbers?

Mathematical evidence or analytics need to be scrutinized with the same suspicion as any forensic proof, especially in terms of the credibility of the underlying data and the correct use of statistical principles. And while lawyer-mathematicians are uncommon, every attorney should know when mathematical applications, like any forensics, raise a red flag.17

In her recent article on the legal profession’s math competence, Lisa Milot, professor of law at the University of Georgia Law School, concluded that math errors fall principally into three categories to which counsel must be attuned: (1) miscalculation, (2) oversimplification, (3) and miscomprehension.18

And the ability to spot these issues hinges on legal education as much as on legal acumen.

Not all lawyers are bad at math. And not all instances of “bad math” involve innumeracy. Often, however, the difficulty lawyers have with selecting, presenting, calculating, analyzing, and critiquing numbers is a product of innumeracy and bears consequences for our ability to fully represent our clients.19

It appears that except for citation analysis and perhaps taxation or business law, math has not been fundamentally embedded in the legal curriculum.20 And this educational deficit might translate into ineffectiveness of counsel or even malpractice in some instances.

[I]nnumeracy prevents us from thinking critically about the information and assumptions underlying numbers and compromises transparency and comprehensibility in the law, undermining legal authority.21

Every attorney develops an ear for making objections, but numbers are more abstract and often times overawing. Thus, emendations to the law school curriculum as well as continuing legal education can encourage lawyers to develop an instinct about math as evidence.22

Polymath Approach

The addition of a 50-hour pro bono requirement for New York bar applicants, along with the impetus to enlarge the experiential law school curriculum, will increase the roster of law students and post-graduates seeking appropriate programs.23 To this landscape, a new type of clinical learning experience ought to be added, one that focuses on injustice created by or solved with mathematics.

Not every law student will have graduated from college with a math degree like Professor Tribe, but drawing on more than one field of experiential learning will create a new opportunity for interdisciplinary work.24 Teams of students from law, mathematics or criminal justice could review post-conviction cases where math played, or might play, a significant role.

The academies of law, math, criminal justice and even related disciplines such as business or accounting can foster these unique learning alliances. While law students investigate the legal merits, math students can scrutinize the data and formulae.25 Together they might open post-conviction doors through law and science otherwise impassable for the unrepresented and the incarcerated.26


Probabilities, statistical inferences and mathematical proofs are too powerful to be glossed over, underestimated or misunderstood. They deserve the same heightened scrutiny that forensic evidence is receiving.

Indeed, post-conviction DNA testing has implicitly introduced the idea that new math might lead to new outcomes.27 And due to the prevalence of numerically laden forensics and other mathematically enhanced circumstantial evidence, this type of proof ought to constitute an independent category of newly discovered evidence.28

Perhaps it is life in an age ruled by 1s and 0s that creates a false confidence in the infallibility of figures. But numbers are only proxies that must be based on facts and reason in order to pass the evidentiary bar. And it is the duty of counsel to defend the accused with mathematical confidence.

Ken Strutin is director of legal information services at the New York State Defenders Association.


1. See Joseph Jacobs, “The Story of Geographical Discovery: How the World Became Known” 32-34 (D. Appleton & Comp. 1898).

2. See David McCord, “Primer for the Nonmathematically Inclined on Mathematical Evidence in Criminal Cases: People v. Collins and Beyond,” 47 Wash. & Lee L. Rev. 741 (1990).

3. See generally Ken Strutin, “Calculating Justice: Mathematics and Criminal Law,” LLRX, Dec. 8, 2013.

4. See generally McCormick on Evidence (7th ed. 2013) (§208 Surveys and Opinions Polls; §209 Correlations and Causes: Statistical Evidence of Discrimination; §210 Identification Evidence, Generally; §211 Paternity Testing); Reference Manual on Scientific Evidence (Fed. Jud. Ctr. 3rd ed. 2011) (Chps: “Reference Guide on Statistics” (pp. 211-302); “Reference Guide on Multiple Regression” (pp. 303-57); “Reference Guide on Survey Research” (pp. 359-423); “Reference Guide on Estimation of Economic Damages” (pp. 425-502)).

5. See, e.g., Ken Strutin, “Changing Definitions of Computers,” NYLJ, May 17, 2011, at 5.

6. See generally “Admissibility, in Criminal Case, of Statistical or Mathematical Evidence Offered for Purpose of Showing Probabilities,” 36 A.L.R.3d 1194.

7. Cf. Robinson v. State, 2013 Md. LEXIS 900 (Ct. App. Md. Nov. 27, 2013) (predicate for anti-CSI effect jury instruction was proof that effect existed).

8. See Stephen Reinhardt, “Tribute to Professor Laurence Tribe,” 42 Tulsa L. Rev. 939, 940 (2006).

9. Collins, 68 Cal. 2d at 330.

10. Leila Schneps and Coralie Colmez, “Math on Trial,” at 24-37.

11. Id. at 167.

12. Hull, 404 U.S. at 897.

13. See Laurence H. Tribe, “Trial by Mathematics: Precision and Ritual in the Legal Process,” 84 Harv. L. Rev. 1329, 1330-32 (1971).

14. Id. at 1339.

15. Id. at 1334.

16. Id. at 1338.

17. See generally Ken Strutin, “Forensic Due Process: Lawyering With Science,” N.Y.L.J., March 22, 2012, at 5.

18. See Lisa Milot, “Illuminating Innumeracy,” 63 Case W. Res. 769, 773 (2013).

19. Id. at 788.

20. Id. at 811 (“Survey of Numerically Focused Law Classes”).

21. Id. at 772.

22. See generally Arden Rowell and Jessica L. Bregant, “Numeracy and Legal Decision Making,” SSRN (2013).

23. See generally Ed Finkel, “Free Clinic: Gaining Clinical Training Without a Formal Organization,” ABA Student Lawyer, December 2013; Cathryn Miller-Wilson, “Harmonizing Current Threats: Using the Outcry for Legal Education Reforms to Take Another Look at Civil Gideon and What it Means to Be an American Lawyer,” 13 U. Md. L.J. Race Relig. Gender & Class 49, 53 (2013) (advocating the “creation of a post-J.D. teaching law firm”).

24. See Ken Strutin, “Allied Learning Experiences: Multidisciplinary Internship Collaborations,” AALS Sect. on Teaching Methods Newsletter, Winter 2011-2012, at 21; Ken Strutin, “Clemency Clinics: A Blueprint for Justice,” LLRX, June 17, 2012.

25. See, e.g., “With an Eye Toward Justice, FIVS Interdisciplinary Faculty Member Takes Statistics to the Courtroom,” Texas A&M Forensic and Investigative Sciences Program News, Oct. 20, 2012; Lisa Bliss et al., “A Model for Interdisciplinary Clinical Education: Medical and Legal Professionals Learning and Working Together to Promote Public Health,” 18 Int’l J. Clinical Legal Educ. 149 (2012).

26. See Ken Strutin, “Post-Conviction Justice in the Information Age: The Trial Never Ends,” N.Y.L.J., Nov. 19, 2013, at 5.

27. See, e.g., William C. Thompson et al., “Forensic DNA Statistics: Still Controversial in Some Cases,” Champion, December 2012, at 12. See generally Ken Strutin, “DNA Evidence: Brave New World, Same Old Problems,” LLRX, Oct. 14, 2013.

28. See, e.g., Ken Strutin, “Arson, Fire Science and the War on Error: Part II,” N.Y.L.J., March 26, 2013, at 5.