View source for Hand formula

{{Use American English|date = April 2019}}
{{Short description|United States legal term}}
{{Other uses|Negligence (disambiguation)}}
{{Redirect|Hand rule|the physics mnemonic devices|right hand rule|and|left hand rule}}

{{Tort law}}
In the [[United States]], the '''Hand formula''', also known as the '''Hand rule''', '''calculus of negligence''', or '''BPL formula''', is a conceptual formula created by Judge [[Learned Hand]] which describes a process for determining whether a legal [[duty of care]] has been breached (see [[negligence]]).  The original description of the calculus was in ''[[United States v. Carroll Towing Co.]]'',<ref>''[[U.S. v. Carroll Towing]]'', 159 F.2d 169 ([[2d Cir.]] 1947).</ref> in which an improperly secured [[barge]] had drifted away from a [[pier]] and caused damage to several other boats.

== Articulation of the rule ==
Hand stated:

{{quote|[T]he owner's duty, as in other similar situations, to provide against resulting injuries is a function of three variables: (1) The probability that she will break away; (2) the gravity of the resulting injury, if she does; (3) the burden of adequate precautions.}}

This relationship has been formalized by the [[law and economics]] school as such: an act is in breach of the [[duty of care]] if:

:<math>PL>B</math>

where ''B'' is the cost (burden) of taking precautions, and ''P'' is the probability of loss (''L'').  ''L'' is the gravity of loss.  The product of P x L must be a greater amount than B to create a duty of due care for the defendant.

== Rationale ==
The calculus of negligence is based on the [[Coase theorem]].  The tort system acts as if, before the injury or damage, a contract had been made between the parties under the assumption that a [[Rationality|rational]], cost-minimizing individual will not spend money on taking precautions if those precautions are more expensive than the costs of the harm that they prevent.  In other words, rather than spending money on safety, the individual will simply allow harm to occur and pay for the costs of that harm, because that will be more cost-efficient than taking precautions.  This represents cases where B is greater than PL.

If the harm could be avoided for ''less'' than the cost of the harm (B is less than PL), then the individual ''should'' take the precautions, rather than allowing the harm to occur.  If precautions were not taken, we find that a legal duty of care has been breached, and we impose liability on the individual to pay for the harm.

This approach, in theory, leads to an optimal allocation of resources; where harm can be cheaply avoided, the legal system requires precautions.  Where precautions are prohibitively expensive, it does not.  In marginal-cost terms, we require individuals to invest one unit of precautions up until the point that those precautions prevent exactly one unit of harm, and no less.

=== Mathematical rationale ===
The Hand formula attempts to formalize the intuitive notion that when the [[Expected value|expected]] loss <math>\mathbb{E}(L)</math> exceeds the cost of taking precautions, the duty of care has been breached:<math display="block">\mathbb{E}(L) > B</math>To assess the expected loss, [[Statistics|statistical methods]], such as [[regression analysis]], may be used. A common metric for quantifying losses in the case of [[Work accident|work accidents]] is the [[present value]] of lost future earnings and medical costs associated with the accident.<ref>{{Cite book|url=https://www.litigationeconomics.com/PDF/eguide-eco-damages.pdf|title=How Economists Compute Lost Earnings and Other Economic Damages in Personal Injury Cases|last=Stephenson|first=Stanley P.|publisher=James Publishing|year=2013|access-date=2019-12-16|archive-date=2023-08-12|archive-url=https://web.archive.org/web/20230812072545/https://www.litigationeconomics.com/PDF/eguide-eco-damages.pdf|url-status=dead}}</ref> In the case when the probability of loss is assumed to be a single number <math>P</math>, and <math>L</math> is the loss from the event occurring, the familiar form of the Hand formula is recovered. More generally, for continuous outcomes the Hand formula takes form:<math display="block">\int_{\Omega} Lf(L)dL > B</math>where <math>\Omega</math> is the domain for losses and <math>f(L)</math> is the [[probability density function]] of losses. Assuming that losses are positive, common choices for loss distributions include the [[Gamma distribution|gamma]], [[Log-normal distribution|lognormal]], and [[Weibull distribution|Weibull]] distributions.

== Criticism ==
Critics point out that term "gravity of loss (L)" is vague, and could entail a wide variety of damages, from a scratched fender to several dead victims.<ref name="Glannon">{{cite book|last=Glannon |first=Joseph W. |title=The Law of Torts |edition=3rd |year=2005 |publisher=[[Aspen Publishers]] |location=New York, NY |pages=73–74}}</ref>  Even then, on top of that, how exactly a juror should determine a value for such a loss is abstract in itself.  The speculative nature of the rule also seizes upon how a juror should determine the probability of loss (P).<ref name="Glannon"/>

Additionally, the rule fails to account for possible alternatives, whether it be the use of alternate methods to reach the same outcome, or abandoning the risky activity altogether.<ref name="Glannon"/>

Human teams estimating risk need to guard against judgment errors, cf. [[absolute probability judgement]].

== Use in practice ==
In the U.S., juries, with guidance from the court, decide what particular acts or omissions constitute negligence, so a reference to the standard of ordinary care removes the need to discuss this conceptual formula. Juries are not told this formula but essentially use their common sense to decide what an ordinarily careful person would have done under the circumstances. The Hand formula has less practical value for the lay researcher seeking to understand how the courts actually determine negligence cases in the United States than for the [[jury instructions]] used by the courts in the individual states.{{Citation needed|date=September 2020}}

Outside legal proceedings, this formula is the core premise of [[insurance]], [[risk management]], [[quality assurance]], [[information security]] and [[privacy]]{{clarify|date=July 2015}} practices.  It factors into [[due care]] and [[due diligence]] decisions in business risk.  Restrictions exist in the cases where the loss applies to human life or the probability of adverse finding in court cases. One famous case of abuse by industry in recent years related to the [[Ford Pinto]].

Quality assurance techniques extend the use of probability and loss to include uncertainty bounds in each quantity and possible interactions between uncertainty in probability and impact for two purposes.  First, to more accurately model customer acceptance and process reliability to produce wanted outcomes.  Second, to seek cost effective factors either up or down stream of the event that produce better results at sustainably reduced costs.  Example, simply providing a protective rail near a cliff also includes quality manufacture features of the rail as part of the solution.  Reasonable signs warning of the risk before persons reach the cliff may actually be more effective in reducing fatalities than the rail itself.

== Australia ==
In Australia, the calculus of negligence is a normative judgement with no formula or rule.<ref>{{cite AustLII|HCA|63|2005|litigants=Mulligan v Coffs Harbour City Council |parallelcite=(2005) 223 [[Commonwealth Law Reports|CLR]] 486 |date=21 October 2005 |courtname=auto}}.</ref>

In [[New South Wales]], the test is how a reasonable person (or other standard of care) would respond to the risk in the circumstances considering the 'probability that the harm would occur if care were not taken'<ref name="CLA2002">{{cite Legislation AU|NSW|act|cla2002161|Civil Liability Act 2002|5B}}(2)(a).</ref><ref>{{cite AustLII|HCA|5|1998|litigants=Romeo v Conservation Commission of the Northern Territory |parallelcite=(1998) 192 [[Commonwealth Law Reports|CLR]] 432 |date=2 February 1998 |courtname=auto}}.</ref> and, 'the likely seriousness of the harm',<ref name="CLA2002"/><ref>{{cite BAILII|court=UKHL |year=1950 |num=3 |litigants=[[Paris v Stepney Borough Council]] |parallelcite=[1951] {{abbr|AC|Appeal Cases}} 367 |courtname=auto}}.</ref> 'the burden of taking precautions to avoid the risk of harm',<ref name="CLA2002"/><ref>{{cite AustLII|HCA|9|2002|litigants=Woods v Multi-Sport Holdings Pty Ltd |parallelcite=(2002) [[Commonwealth Law Reports|CLR]] 460 |date= |courtname=auto}}.</ref> and the 'social utility of the activity that creates the risk of harm'.<ref name="CLA2002"/><ref>{{cite AustLII|FCA|20|1991|litigants=E v Australian Red Cross Society |parallelcite=(1991) 27 [[Federal Court Reports|FCR]] 310 |date= |courtname=auto}}.</ref> State and Territory legislatures require that the social utility of the activity that creates the risk of harm be taken into account in determining whether or not a reasonable person would have taken precautions against that risk of harm.<ref name="CLA2002"/> For example, in ''Haris v Bulldogs Rugby League Club Limited'' <ref name="Haris v Bulldogs">{{cite AustLII|NSWSC|53|2006|litigants=Haris v Bulldogs Rugby League Club Limited |date=17 March 2006 |courtname= auto}}.</ref> the court considered the social utility of holding football matches when determining whether a football club took sufficient precautions to protect spectators from the risk of being struck by fireworks set off as part of the entertainment during a game.<ref>{{Cite web |date=2006-03-15 |title="Spectator at football game injured by firework : application of s5B of CLA": Haris -v- Bulldogs Rugby League Club [2006] NSWCA 53 |url=https://mccabes.com.au/spectator-at-football-game-injured-by-firework-application-of-s5b-of-cla-haris-v-bulldogs-rugby-league-club-2006-nswca-53/ |access-date=2022-12-15 |website=McCabes |language=en-US |archive-date=2022-12-15 |archive-url=https://web.archive.org/web/20221215065003/https://mccabes.com.au/spectator-at-football-game-injured-by-firework-application-of-s5b-of-cla-haris-v-bulldogs-rugby-league-club-2006-nswca-53/ |url-status=dead }}</ref>

== References ==
{{reflist}}

[[Category:Tort law]]
[[Category:Law and economics]]
[[Category:Legal doctrines and principles]]