Strength of Evidence and Likelihood Ratio Scales

A forensic scientist who reports 'the likelihood ratio for this DNA profile is 4.7 x 10^12' has communicated accurately but not usefully to most triers of fact. The number is simultaneously too large to be intuitive and too abstract to carry emotional weight without a reference point. Courts in England and Wales, Australia, the Netherlands, and elsewhere have consistently found that raw LR figures, without contextualisation, are not well understood by jurors or even by some judges.

Verbal equivalence scales address this by providing a bridge between the statistical output and natural language. The scientist calculates or estimates the LR, locates it on the laboratory's agreed scale, and reports the corresponding phrase, such as 'very strong support for the proposition that the DNA originated from the suspect'. The phrase is more accessible than the number, and when accompanied by an explanation of what 'support' means in the LR framework, it allows a court to understand both the direction and the rough magnitude of the evidence.

The price of accessibility is potential misinterpretation. A phrase that says 'strong support for the prosecution hypothesis' can be misread as a statement about the defendant's guilt rather than about the relative probability of the evidence under two competing hypotheses. This risk is not hypothetical. Documented cases in the UK, Australia, and elsewhere include instances where evaluative language was misunderstood at trial, contributing to the broader reform of forensic reporting standards that has taken place since the 2000s.

Harold Jeffreys was a British mathematician and geophysicist whose 1961 book Theory of Probability set out a Bayesian framework for scientific inference. As part of that framework, he proposed a scale for interpreting Bayes factors: the ratio of the probability of the data under one hypothesis to the probability of the data under another. His scale used log10 of the Bayes factor as the primary axis, and assigned verbal labels to successive intervals.

Jeffreys did not design his scale for forensic use. He was concerned with hypothesis testing in scientific publication, not with courtroom communication. Forensic scientists adopted and adapted the scale because it was already well-known in Bayesian statistics and its logarithmic structure was convenient: LR values in forensic science commonly span from 1 to 10^15 or beyond, and a log scale compresses this range into a manageable set of intervals.

The adaptations introduced by forensic scientists have varied. Some laboratories apply the original Jeffreys boundaries without change. Others shift the boundaries upward on the basis that forensic decisions carry higher stakes than scientific publication and that a higher LR should be required before using a phrase like 'strong'. Still others add levels at the high end of the scale to distinguish between an LR of 10^6 and an LR of 10^12, which are both 'decisive' on the original Jeffreys scale but represent very different magnitudes of evidence.

The ENFSI Guideline for Evaluative Reporting in Forensic Science, first published in 2015, provides the most widely referenced European standard for LR-based reporting. Its verbal scale runs from 'limited support' at LR values just above 1 to 'overwhelmingly strong support' at the highest LR values. The guideline explicitly states that the verbal terms are directional, toward either the prosecution or defence proposition, and that they describe the strength of the evidence, not the probability of guilt.

The ENFSI guideline's critical contribution is not the specific words chosen but the framework requirements surrounding them. A laboratory using the ENFSI scale must: define the propositions at an appropriate level (offence-level or activity-level), state the conditioning assumptions, specify which scale is being applied and why, and ensure that the evaluative statement is accompanied by text explaining what the LR framework means. The scale without the framework is incomplete.

The Association of Forensic Science Providers in the UK published a scale in 2009 that has been influential in British laboratory practice. It uses seven levels with approximate boundaries at log10(LR) = 1, 2, 4, 5, and 6, meaning that an LR of 10^5 is 'strong support' and an LR of 10^6 is 'very strong support'. Other countries have developed their own variants. The Netherlands Forensic Institute has published its own scale; the Australian and New Zealand Forensic Science Society has produced guidelines that reflect the ENFSI framework but are adapted to Australian court requirements.

The most fundamental criticism of verbal scales is that the boundary values between levels are arbitrary. There is no mathematical reason why log10(LR) = 2 should mark the transition from one verbal category to the next. The boundaries are consensus choices made by expert committees, and different committees have made different choices. Critics argue that this arbitrariness is hidden when the verbal phrase is presented in a report without the underlying LR value, because the reader cannot know how close the actual LR was to the boundary.

A second criticism concerns the transposition fallacy risk. Experimental studies, including jury simulation experiments conducted in the UK and Australia, have found that verbal phrases such as 'strong support for the prosecution hypothesis' are frequently misread as statements about the probability of guilt. Even legally trained readers show this pattern. The risk is not eliminated by including an explanation of the LR framework in the report, because jurors under time pressure or cognitive load may attend to the verbal phrase and ignore the explanation.

A third criticism is that verbal scales can obscure large differences in evidential strength within a single category. Under most scales, an LR of 10^6 and an LR of 10^10 might both receive the label 'extremely strong support', but in a Bayesian sense they shift the prior odds by very different amounts. This compression at the high end is a structural property of any scale with finite levels covering a range that spans fifteen or more orders of magnitude.

Proponents of verbal scales respond that the alternative, reporting only the raw LR, creates its own problems. Courts have been shown to overweight large numbers when they appear in evidence, treating an LR of 10^15 as qualitatively different from an LR of 10^10 even when the difference is operationally irrelevant. A verbal scale, when properly explained, provides a controlled simplification that is more honest about the limits of the underlying model than a precise-looking raw figure derived from population databases with their own assumptions and uncertainties.

Verbal equivalence scales originated in DNA evidence and have since spread to other forensic disciplines including fingerprint comparison, handwriting analysis, toolmark examination, and voice comparison. The application raises specific problems in each discipline. For DNA, the LR can often be calculated from population databases with known statistical properties. For fingermarks or handwriting, the LR must frequently be estimated from examiner experience or from small reference databases, and the uncertainty around the estimate is larger. Using the same verbal scale across disciplines with different underlying uncertainty levels can be misleading.

Jurisdictional variation is substantial. Courts in England and Wales operate under the guidance of the Forensic Science Regulator, whose Codes of Practice require evaluative reporting to follow the LR framework and to use verbal scales consistent with the AFSP or equivalent standards. In India, evaluative reporting using the Bayesian LR framework is not yet standard in most laboratory practice, though academic and regulatory discussions are active following the Bharatiya Sakshya Adhiniyam 2023, which continues to treat expert opinion as a category of evidence without specifying a reporting framework. In the United States, the President's Council of Advisors on Science and Technology (PCAST) 2016 report on forensic science recommended that probabilistic reporting frameworks be adopted more widely, but implementation remains uneven across federal and state jurisdictions. In the European Union, the ENFSI guideline is the primary reference across member states, though national accreditation requirements vary.

The result is that a forensic scientist who works in international cases may need to adapt their reporting to multiple sets of requirements. A report produced for a Dutch court under the Netherlands Forensic Institute's scale may need to be reformatted for use in an Australian court under different guidance. The propositions framework, the LR logic, and the direction of the verbal phrase are transferable; the specific verbal labels and boundary values are not.

The current consensus among forensic standards bodies is that a verbal scale must always be accompanied by the following elements: a statement of the prosecution and defence propositions at the appropriate level, a statement of the conditioning assumptions, identification of the scale being used, and an explanation of what the verbal phrase means in terms of the LR framework. These requirements appear in the ENFSI guideline, the UK Forensic Science Regulator's Codes of Practice, and equivalent documents from forensic science bodies in Australia and North America.

In practice, many laboratories include a standard explanatory paragraph in all evaluative reports. The paragraph explains that the scientist has calculated or estimated an LR, that the LR measures the probability of the evidence under two competing hypotheses, that the verbal phrase is derived from an agreed scale, and that the verbal phrase does not represent a probability of guilt. This boilerplate approach has been criticised as a procedural gesture rather than genuine communication, but it does ensure that the explanatory text is present in the record even if it is not read carefully.

Some scientists and courts have moved toward reporting the numerical LR alongside the verbal phrase, on the grounds that this provides the trier of fact with more information and makes the mapping transparent. The ENFSI guideline does not prohibit reporting the numerical LR but does not require it either. The UK Forensic Science Regulator's guidance is that numerical values may be reported where they can be derived and explained, but that the verbal phrase should always accompany them. The emerging consensus is that transparency about the number, the scale, and the assumptions is better than concealing any of them.