Lawyers ‘get’ scales.  The scales of justice.  The scales that are tipped ever-so-slightly when the preponderance burden of proof is explained.  Indeed, that quantitative weighing is core to a civil case adjudication, and when mishandled may cause error and reversal:

the district court judge erred when he interrupted counsel’s argument and informed the jury that the reference to tipping the scales was “not a proper argument” and that the preponderance of the evidence was “not a matter of putting to see what weighs slightly more.” The district court judge then compounded this error when he charged the jury, reminding the jury that he had interrupted counsel’s argument and again informing the jury that tipping the scales was “not a correct measure of the burden of proof.” These statements at least implied that Blossom had to produce more evidence than would merely “tip the scales,” thereby imposing upon him an inappropriately stringent burden of proof.

Blossom v. CSX Transp., 13 F.3d 1477, 1480 (11th Cir. 1994).

At the same time, numbers have been rejected when used to explain the “beyond a reasonable doubt” standard.

This problem is exacerbated where the trial judge invokes a metaphorical scale that further suggests that applying the reasonabledoubt standard is a quantitative rather than qualitative exercise. Federal courts have consistently condemned efforts to define reasonable doubt by resort to scales and other analogies based on assessments of the quantity, rather than the quality, of the evidence presented. See, e.g., Reed v. Roe, 100 F.3d 964 (9th Cir. 1996) (government conceded error where the trial court described reasonable doubt by reference to a numerical scale); United States v. Pungitore, 910 F.2d 1084, 1145 (3d Cir. 1990) (use of scale analogy to illustrate proof beyond a reasonable doubt constituted an improper attempt to quantify reasonable doubt and citing cases disapproving of the practice). Cf. United States v. Hall, 854 F.2d 1036, 1044 (7th Cir. 1988) (Posner, J., concurring) (“It is one thing to tell jurors to set aside unreasonable doubts, another to tell them to determine whether the probability that the defendant is guilty is more than 75, or 95, or 99 percent.”).

Adorno v. Pierce, No. 14 C 00791, 2016 U.S. Dist. LEXIS 57093, at *29-30 (N.D. Ill. Apr. 29, 2016).

But these are instances of using numbers in argument to a jury.  What I write to suggest is that using numbers can be powerfully effective when making weighing arguments on evidentiary admissibility to a judge.  Two Evidence rules in particular come to mind.

First, is Rule 403.  In the seminal case of Old Chief v. United States, 519 U.S. 172, 182-83, 117 S. Ct. 644, 651 (1997) the Court described what is essentially a mathematical analysis for weighing alternative methods of proving a point in deciding whether 403 requires exclusion or ‘toning down’ of the challenged evidence:

On objection, the court would decide whether a particular item of evidence raised a danger of unfair prejudice. If it did, the judge would go on to evaluate the degrees of probative value and unfair prejudice not only for the item in question but for any actually available substitutes as well. If an alternative were found to have substantially the same or greater probative value but a lower danger of unfair prejudice, sound judicial discretion would discount the value of the item first offered and exclude it if its discounted probative value were substantially outweighed by unfairly prejudicial risk.

What does that look like?  Imagine two ways of proving the injuries sustained by a murder victim – a color photograph of the deceased or a medical examiner’s anatomical drawing.  The 403 analysis proposed here has two stages:


Item of evidence Probativeness (1 to 10) Unfair Prejudice (1 to 10)
Anatomical drawing 10 6.5
Color photograph 10 9


Under the Old Chief calculus, since the alternative [anatomical drawing] has the same probative value, “sound judicial discretion would discount the value of the item first offered and exclude it if its discounted probative value were substantially outweighed by unfairly prejudicial risk.”  That looks like this:


Item of evidence Probativeness (1 to 10) Unfair Prejudice (1 to 10)
Anatomical drawing 10 6.5
Color photograph 7 (discounted value) 9

The numbers inserted here are arbitrary ones, but they illustrate the point.  The Judge now decides whether the prejudice [9] substantially outweighs the discounted probativeness value [7].  Will a judge want to see numbers in a motion in limine?  Maybe not, but an attorney who walks through the process will have a better understanding of, and be better able to articulate, a 403 unfair prejudice analysis.

The same ‘numbers game’ works when a criminal defendant seeks to testify and has prior convictions that do not have deception and dishonesty as elements.  Under Federal Rule of Evidence 609, such crimes are admissible only when their probative value outweighs the prejudice to the accused.


Pick a crime.  DUI; drug selling; assault in a bar.  What is the probative value of each in terms of showing whether a person is untruthful?  Each has to be assigned some number, as Congress, by adopting 609, has determined it to have some link to truthful character.  But on a scale of 1-10, the numbers will be low – perhaps in the 1-3 range.  Now, what is the prejudice?  The jury knows that the accused is a criminal, and this has high risk of causing conviction by propensity.  Hence, the prejudiced will be in the 8-10 range.  The numbers call for exclusion.

This calculus might change if the current offense is relatively minor (e.g. theft) and the criminal conviction is also relatively minor (e.g. DUI).  But using numbers will help craft the argument and should inform the analysis.

So – will judges want to hear numeric arguments, or read them in pleadings?  Unlikely, but conceivable.  But when lawyers begin with numbers, rather than gut-check approaches, their analysis will be more cogent and lead to more persuasive argument.