#### UNITED STATES FIDELITY & GUARANTY COMPANY, Plaintiff-Appellant, v. JADRANSKA SLOBODNA PLOVIDBA, Defendant-Appellee.

No. 81-2197.

United States Court of Appeals, Seventh Circuit.

Argued May 4, 1982.

Decided May 28, 1982.

*1023Harney B. Stover, Jr., Ross F. Plaetzer, Davis, Kuelthau, Vergeront, Stover, Werner & Goodland, S. C., Milwaukee, Wis., for plaintiff-appellant.

Steven B. Belgrade, Joseph V. McGovern & Assoc. Ltd., Chicago, 111., for defendantappellee.

Before BAUER and POSNER, Circuit Judges, and LARSON, Senior District Judge.*

*

 Of the District of Minnesota.

POSNER, Circuit Judge.

This is an appeal from a judgment exonerating the defendant, a Yugoslavian enterprise that owns the M/V *Makarska,*from negligence in connection with the death of a longshoreman, Patrick Huck, who fell into a hold.

The *Makarska*has five holds, numbered 1 through 5 from bow to stern, as shown in the following diagram:

Schematic Cross-Section of M/V *Makarska*

Holds 2 through 5 are identical, so far as we can glean from the record. (Oddly, no precise dimensions are given for the vessel.) Each has three decks. From top to bottom they are the weather deck, the upper ’tween deck, and the lower ’tween deck. Below *1024the lower ’tween deck is the main cargo area of the hold. Each deck contains a hatch roughly 30 feet across. When all three hatches in a hold are open, cargo can be loaded into (or unloaded from) the main cargo area. Hatchways of the typical maritime type (smaller than regular doorways, and with high thresholds) connect the holds laterally at each deck.

Hold number 1 is different from the others: its top is raised to form a forecastle. As a result the weather deck of hold number 1 is at a higher level than the weather deck of the other four holds, its upper ’tween deck is flush with the weather decks of the other holds, and its lower ’tween deck is flush with the upper ’tween decks of the other holds.

On the morning of the day he was killed, Huck was working with a party of longshoremen on the upper ’tween deck of hold number 1. The hatch above them (in the weather deck) was open to give them light, and the hatch beneath their feet (in the upper ’tween deck) was closed. The longshoremen completed their work in hold number 1 at noon and took their lunch break. When work resumed it was in hold number 4, but by the end of the afternoon the longshoremen were working on the weather deck of hold number 2, which is to say on the same level as, and adjacent to, the upper ’tween deck of hold number 1.

After the longshoremen had completed their work in hold number 1 and broken for lunch, the ship’s crew had come in and closed the hatch in the weather deck but opened the two hatches below it (the hatches in the upper ’tween and lower ’tween decks). This is a customary practice to facilitate a prompt start on loading and unloading cargo at the next port of call, for it can take as long as 30 minutes to open each hatch.

The closing of the hatch in the weather deck of hold number 1 plunged the entire hold into pitch darkness. Sometime during the late afternoon Huck, unobserved, entered hold number 1. He did so by stepping through the hatchway between the weather deck of hold number 2, where the longshoremen were then working, and the upper ’tween deck of hold number 1, now in darkness. It is unclear whether he opened the door in the hatchway or whether it was open already. It would not have been locked, but only latched, so if it was not already open he could easily have opened it. The hatch in the upper ’tween deck of hold number 1 — now open, but in darkness — begins about 6 to 10 feet in from the hatchway where Huck entered. But Huck’s body was found at the bottom of the forward part of hold number 1, some 40 feet in from the hatchway. This suggests that he had not walked directly into the open hatch, but rather had fallen in from the forward part of the upper ’tween deck after having successfully skirted the open hatch when he first entered.

The other longshoremen left the ship without noticing that Huck was not among them. His body was not found till the next morning. No one knows why Huck was in hold number 1. But it was stipulated that crates of liquor were stored in the forward part of the hold on the upper ’tween deck, the part from which Huck apparently fell, and it is conjectured that he was planning to steal some of the liquor on his way off the ship.

The jury returned a special verdict. It found that the shipowner had not been negligent but that Huck and his employer, the stevedore company (which was no longer a party to the suit), had been¡ and it assigned 25 percent of the responsibility for the accident to the stevedore company and 75 percent to Huck. The jury also found that Huck’s survivors had sustained no damages. This appeal questions the jury instructions, the jury’s obedience to them, and an evidentiary ruling by the trial court, and also argues that the undisputed facts show that the shipowner was negligent as a matter of law.

In 1946 the Supreme Court held that a longshoreman injured while working on a ship could recover damages from the shipowner under the admiralty doctrine of unseaworthiness. *Seas Shipping Co. v. Sieracki,*328 U.S. 85, 66 S.Ct. 872, 90 L.Ed. 1099 (1946). To establish unseaworthiness the longshoreman did not have to prove that the owner had been negligent, but only that the accident had been caused by the defective or unreasonably dangerous condition of the ship; the analogy to strict products liability is apparent. In *Sieracki*the defect was in the original construction of a part of the ship’s gear and the shipowner neither knew nor had reason to know of the defect.

*1025Under the regime of *Sieracki*the shipowner was liable even if the defect or unreasonably dangerous condition had been created by the stevedore, that is, by the longshoreman’s employer. But in such a case the shipowner could get indemnity from the stevedore, so that liability ultimately came to rest on the party that could have avoided the accident at least cost. See *Ryan Stevedoring Co. v. Pan-Atlantic S.S. Corp.,*350 U.S. 124, 76 S.Ct. 232, 100 L.Ed. 133 (1956); *Italia Societa per Azioni di Navigazione v. Oregon Stevedoring Co.,*376 U.S. 315, 324, 84 S.Ct. 748, 754, 11 L.Ed.2d 732 (1964).

All this was changed in 1972, when Congress amended the Longshoremen’s and Harbor Workers’ Compensation Act. The amendments, so far as they are relevant to this case, substituted negligence for unseaworthiness as the standard of liability in actions by longshoremen against shipowners and abolished the shipowner’s right of indemnity against the stevedore. See 33 U.S.C. § 905(b). Congress did not attempt to define negligence; after 200 years of judicial experience with the negligence standard it would have been redundant and confusing to do so. Any necessary fine tuning was left to the courts. See S.Rep. No.1125, 92d Cong., 2d Sess. 11 (1972). Yet the courts have had trouble articulating and applying the negligence standard of the amended act — see, e.g., the long discussion of standard of liability in *Johnson v. A/S Ivarans Rederi,*613 F.2d 334, 337-49 (1st Cir. 1980) — especially with regard to whether the shipowner should be required to backstop, as it were, the safety measures taken by the stevedore, or whether he can rely on the stevedore to keep the longshoremen out of harm’s way.

The Supreme Court addressed that issue last year, in *Scindia Steam Nav. Co. v. De Los Santos,*451 U.S. 156, 101 S.Ct. 1614, 68 L.Ed.2d 1 (1981), and held that “the shipowner has no general duty by way of supervision or inspection to exercise reasonable care to discover dangerous conditions that develop within the confines of the cargo operations that are assigned to the stevedore.” *Id.*at 172, 101 S.Ct. at 1624. In *Scindia,*a winch that was part of the ship’s gear had been malfunctioning for two days before the accident, but the stevedore continued to use it. In the Court’s view, the fact that the shipowner knew of the malfunction would not in itself make him negligent; it might be reasonable for him to rely on the stevedore’s judgment that the winch, though defective, was safe enough. See *id.*at 175, 101 S.Ct. at 1626. But if the stevedore’s judgment was “so obviously improvident that [the shipowner], if it knew of the defect and that [the stevedore] was continuing to use it, should have realized the winch presented an unreasonable risk of harm to the longshoremen,” then the shipowner would have a duty to intervene and repair the winch. *Id.*at 175-76,101 S.Ct. at 1626. This is analogous to the common law duty of a principal to the employees or other potential accident victims of an independent contractor. See, e.g., *Hixon v. Sherwin-Williams Co.,*671 F.2d 1005, 1009-10 (7th Cir. 1982).

The longshoreman in *Scindia*was injured by something which though part of the ship’s gear was being operated at the time of the accident by another longshoreman rather than by a member of the ship’s crew. The liability of the shipowner for accidents resulting from conditions under the exclusive control of the ship’s crew was thus not in issue. But the Court noted that if the shipowner “fails to exercise due care to avoid exposing longshoremen to harm from hazards they may encounter in areas, or from equipment, under the active control of the vessel during the stevedoring operation,” he is liable under the negligence standard of section 905(b). 451 U.S. at 167, 101 S.Ct. at 1622. This is dictum, but so obviously right that we accept it unhesitatingly as an authoritative statement of the shipowner’s duty in such circumstances.

The Court in *Scindia*did not attempt to define negligence under section 905(b). But we find nothing in its opinion that is inconsistent with the negligence formula proposed in *Johnson v. A/S Ivarans Rederi, supra,*613 F.2d at 348, which requires “bal*1026ancing the usefulness to the ship of the dangerous condition and the burden involved in curing it against the probability and severity of the harm it poses.” This formula echoes that of Judge Learned Hand in *United States v. Carroll Towing Co.,*159 F.2d 169, 173 (2d Cir. 1947), also a maritime negligence case, though *Johnson*does not cite *Carroll Towing.*Judge Hand, designating by “B” the burden of the precautions necessary to avert an accident, by “L” the magnitude of the loss if the accident occurred, and by “P” the probability that if the precautions were not taken the accident would occur, reasoned that a shipowner or other alleged tortfeasor was negligent if B < PL, that is, if the burden of precautions was less than the harm if the accident occurred discounted (i.e., multiplied) by the probability that it would occur. The higher P and L are, and the lower B is, the likelier is a finding of negligence.

Though mathematical in form, the Hand formula does not yield mathematically precise results in practice; that would require that B, P, and L all be quantified, which so far as we know has never been done in an actual lawsuit. Nevertheless, the formula is a valuable aid to clear thinking about the factors that are relevant to a judgment of negligence and about the relationship among those factors. It gives federal district courts in maritime eases, where the liability standard is a matter of federal rather than state law, a useful framework for evaluating proposed jury instructions, for deciding motions for directed verdict and for judgment notwithstanding the verdict, and, in nonjury cases, for preparing Rule 52(a) findings. (For a good example of the use of the Hand formula by a district judge in this circuit in preparing Rule 52(a) findings, see Chief Judge Robson’s opinion in *Ohio River Co. v. Continental Grain Co.,*352 F.Supp. 505, 509 (N.D.Ill.1972).) We do not want to force the district courts into a straitjacket, so we do not hold that they must use the Hand formula in all maritime negligence cases. We merely commend it to them as a useful tool — one we have found helpful in this case in evaluating the plaintiff’s challenge to the jury instructions and its contention that negligence was shown as a matter of law.

Three jury instructions are challenged. The first reads: “A shipowner’s duty to provide longshoremen with a reasonably safe place to work is confined to those areas of the vessel where longshoremen may reasonably be expected to go.” This instruction is consistent with the Hand formula. Of course it is possible that a longshoreman will stray into a part of the ship where he has no business, but the probability (P in the Hand formula) seems too low to warrant the shipowner’s taking precautions against an accident to him. If Huck had wandered into the captain’s stateroom and slipped on a throw rug there, it would be unreasonable to impose liability on the shipowner even if the cost of doing without the throw rug would have been slight. Hold number 1 was not so remote from Huck’s work area as the captain’s stateroom would be, but all the challenged instruction did was ask the jury to decide whether it was a place where the shipowner should have expected Huck to be when the accident occurred, and this was proper.

The next challenged instruction reads: “The responsibility for the safety of the longshoremen in areas where longshoring work is being conducted rests with the [stevedore], and if you find the [stevedore] to be negligent, the shipowner is not to be held liable for the [stevedore’s] negligence.” The first clause in the instruction can be criticized in the abstract as an overgeneralization of the Supreme Court’s holding in *Scindia*(decided after the trial in this case). The stevedore has the primary but not exclusive responsibility for the safety of the longshoremen. If Huck had been injured as a result of a defect that was due to the shipowner’s negligence and was neither known nor reasonably knowable to the stevedore, the shipowner would be liable even if the accident had occurred in an area where longshoring operations were being conducted. But since the accident occurred in an area where longshoring operations were not being conducted, we do not see *1027how the plaintiff could have been prejudiced by this instruction; if anything, the instruction implies, helpfully to the plaintiff, that responsibility for the safety of longshoremen in areas where longshoring operations are not being conducted, such as hold number 1 when the accident occurred, is the shipowner’s. If there was error, it was harmless. See Fed.R.Civ.P. 61.

The third challenged instruction is unexceptionable and, again, harmless. It reads: “After stevedoring operations begin, the shipowner has no duty to superintend the operations of the stevedore or its employees.” This could be a paraphrase of the Supreme Court’s discussion in *Seindia of*the shipowner’s duty to inspect. The Court made clear that the shipowner does not have a duty to look over the stevedore’s shoulder, as it were, to make sure that he is conducting the stevedoring operations with due regard for the safety of his employees. The 1972 amendments rejected this broad concept of the shipowner’s duty. In the terms of the Hand formula the probability of an accident, given that the stevedore rather than the shipowner is actually conducting the stevedoring operations, is too slight to warrant making the shipowner take his own backup precautions to prevent the accident. In any event Huck could not be hurt by this instruction, for his theory was not that the shipowner had failed adequately to superintend the stevedore’s operations but that the shipowner had created a hidden danger to any longshoreman who strayed from the area where those operations were in progress.

At the oral argument of this appeal the plaintiff’s counsel conceded that the instructions challenged in its brief were correct statements of the law, at least in the abstract, but argued that they were calculated to mislead the jury by focusing its attention on the stevedoring operations, and Huck was not injured while actually engaged in those operations. But the plaintiff’s theory of the case was stated clearly in an instruction proposed by the plaintiff and given by the court: “The defendant shipowner had a duty to exercise reasonable care under the circumstances to protect the longshoremen from conditions on the ship which presented an unreasonable risk of harm to the longshoremen, if the shipowner or the ship’s officers or employees knew or should have known about those conditions.” The plaintiff’s counsel argued to us that this instruction was not good enough, that the nature of the shipowner’s duty should have been spelled out more. But the plaintiff did not ask the trial judge to give any additional instructions on the shipowner’s duty and will not be heard to complain about this for the first time on appeal. See Fed.R.Civ.P. 51.

The plaintiff also contends that even if the instructions were satisfactory, the undisputed facts showed negligence by the shipowner as a matter of law. We again use the Hand formula to frame this issue. L, the loss if the accident occurred, was large. There was a 25 foot drop from the upper ’tween deck of hold number 1 to the bottom of the hold, and a fall from that height was very likely to cause serious injury or, as in this case, death. As to B, the burden of precautions, there were various ways the shipowner could have prevented the accident. He could have lit the hold, locked the hatchway leading to it from the weather deck of hold number 2, roped off the open hatch, or placed a sign at the hatchway (though the effectiveness of this last precaution may be doubted). Probably the cheapest way of avoiding the accident, however, would have been for the ship’s crew not to open the hatches until all the longshoremen had left the ship. This would have meant either the crew’s working after normal working hours, or, if the opening of the hatches was postponed till the following morning, delay in beginning stevedoring operations at the next port of call. We doubt that either alternative would be very costly so we judge B in this case to have been, at most, moderate, and possibly small.

If P, the probability of an accident if the precautions that would avert it were not taken, was high, then it would appear, in light of our discussion of L and B, that the shipowner was negligent in failing to take *1028one of the precautions that we have mentioned. But probably P was low. There was no reason for a longshoreman to reenter a hold after he had completed his work there and moved on to another part of the ship. The plaintiff speculates that Huck may have left a piece of clothing in hold number 1 and gone back to retrieve it. It does not seem very likely that anyone would enter a pitch-black hold to retrieve a glove or a sock or a jacket, when he could easily ask for light. It is far more likely that Huck entered for an illicit purpose. This would not defeat a recovery if the shipowner were negligent; neither assumption of risk nor contributory negligence is a defense to liability in a negligence action under section 905(b). See S.Rep.No.1125, *supra,*at 12; 1A Benedict on Admiralty §§ 116-17 (7th ed. 1981). But Huck’s motive in entering hold number 1 bears on the probability of the accident and hence on the cost-justified level of precautions by the shipowner. Cf. *Clemons v. Mitsui O.S.K. Lines, Ltd.,*596 F.2d 746, 750 n.17 (7th Cir. 1979). Unless it is common for longshoremen to try to pilfer from darkened holds— and it was the plaintiff’s burden to show that it is — the shipowner would have no reason to think it so likely that a longshoreman would be in a darkened hold as to require precautions against his falling through an open hatch.

Moreover, the relevant probability, so far as the Hand formula is concerned, is not the probability that a longshoreman would enter a darkened hold but the probability that he would fall into an open hatch in such a hold. The probability was small. The darkness was as effective a warning of danger as a sign would have been. Any longshoreman would know that there was a hatch on the floor and he could not rationally assume that it was closed. Only a reckless person would walk about in the hold in these circumstances, especially if he had no flashlight; Huck had none. There are reckless people as there are dishonest people; but the plaintiff did not try to prove that there are so many reckless dishonest longshoremen as to require the precautions that the defendant in this case would have had to take to avert injury to them.

We do not know whether Huck was aware of the custom of opening the hatches after the longshoremen left the hold, and for the reasons just suggested it is not critical whether he was or not. But probably he was. His body was found well forward of where he would have fallen had he walked straight into the hold. No doubt he was trying to skirt what he knew to be an open hatch. The shipowner was not required to anticipate that a longshoreman knowing of the open shaft would not be able to avoid it; this was possible — it happened — but the probability was too remote to warrant precautions beyond the implicit warning of darkness itself.

Another factor bearing on the probability of an accident is that Huck was under the general supervision of the stevedore company that employed him. Even if the defendant should have regarded Huck as no better than a sheep wandering about the ship with no rational concern for his own safety, it was entitled to regard the stevedore as his principal shepherd. The stevedore had a work rule forbidding longshoremen to be anywhere on the ship except where stevedoring operations were actually in progress. The shipowner was entitled to rely on the stevedore to enforce this rule, if not 100 percent at least enough to make it highly improbable, in light of the other circumstances that we have discussed, that one of the longshoremen would stray away from the rest and fall into a darkened hold.

The fact that the practice of leaving the hatches open in darkened holds was customary (or so the jury could find) and not just an idiosyncrasy of this Yugoslavian ship or shipowner has additional relevance to this case. Although custom is not a defense to a charge of negligence, *The T. J. Hooper,*60 F.2d 737, 740 (2d Cir. 1932), it is a material consideration in evaluating the charge, especially where the victim and the alleged tortfeasor are linked, even if indirectly, in a voluntary relationship, as they were here. If a shipowner were to follow a practice that flunked the Hand formula — that in other words was not cost-justified, because *1029the expected accident costs associated with the practice exceeded the costs of abandoning the practice and so preventing any accident from happening — then he would have to pay his stevedores higher rates, to compensate them for the additional risk to their employees, the longshoremen, whom the stevedores must compensate under 33 U.S.C. § 904, regardless of fault, for any injury the longshoremen sustain in the course of their employment. And since by hypothesis the cost to the stevedores of the additional compensation — the expected accident cost, in other words — would exceed the cost of abandoning the practice (for otherwise the practice would be cost-justified), it would pay the shipowner to abandon it. Cf. Coase, *The Problem of Social Cost,*3 J.L. & Econ. 1 (1961). Hence if the shipowner persists in a dangerous practice — if the whole trade persists in the practice — that is some evidence, though not conclusive, that the practice is cost-justified, and not negligent.

But all this is not to say that the defendant’s conduct in this case was, in fact, nonnegligent. We are not the triers of fact. The jury found the defendant nonnegligent and our job is just to decide whether a reasonable jury could have so found. Obviously we think the jury’s finding was reasonable, just like the district court’s finding of nonnegligence in *Grayson*v. *Cordial Shipping Co.,*496 F.2d 710, 715 (7th Cir. 1974), a previous darkened-hold case in this circuit. The plaintiff has cited to us a number of darkened-hold cases where jury verdicts for plaintiffs were upheld, but none where a jury verdict for the defendant was set aside on the ground that the facts showed negligence as a matter of law. *Badalamenti v. United States,*160 F.2d 422 (2d Cir. 1947), heavily relied on by the plaintiff, is an example of a case where a finding of negligence was upheld. Like the other cases cited by the plaintiff it is factually distinguishable from the present case. There was no partition between the lighted and unlighted parts of the cargo area; and the longshoreman was injured while searching for rope that the shipowner had undertaken to provide for stevedoring operations and had left in an unlighted part of the deck. P was therefore higher than in this case. Also, there was no mention of any evidence of a custom of leaving the hatch open in darkened holds. But the more fundamental distinction is that the court in *Badalamenti*was upholding a judgment for the longshoreman, not, as we are being asked to do here, reversing a judgment against him.

The remaining issues can be discussed very briefly. The defendant was allowed to put in evidence a safety rule that the stevedore adopted (more precisely, formalized) after the accident. Evidence of repairs or of other safety measures adopted after an accident occurs is not admissible to “prove negligence .... ” Fed.R.Evid. 407. It was not admitted here to prove, but to disprove, negligence. The only one who could have complained about the admission of this evidence was the stevedore, who is not a party, and is not objecting.

Last, the plaintiff complains that the jury disobeyed the judge’s instructions by not determining the damages that Huck’s survivors would have been entitled to if the jury had found the defendant liable for his death. The special verdict asked the jury to assess damages, and did not add — only if you find liability; the intent (stated by the judge in his instruction, but not repeated in the special verdict) was that the jury assess damages even if it found no liability. But when asked, “What sum of money, if any, will fairly and reasonably compensate [Huck’s survivors] for [their] damages caused by” his death, the jury naturally answered zero: not because it thought the survivors had suffered no loss but because it thought that, given its finding of no liability, they were entitled to no compensation. This mistake does not imply that the jury’s finding of no liability was also based on a misunderstanding.

The judgment appealed from is

AFFIRMED.