opinion: POSNER, Circuit Judge.
  This is a personal injury suit under the diversity jurisdiction; the substantive issues are governed by the tort law of Illinois. The suit arises from an accident that occurred in 1983. The plaintiff, Davis, was 33 years old at the time, an experienced railroad worker who for the past six years had been employed as an inspector of cars by the Trailer Train Company, a lessor of piggyback cars to railroads. He made the inspections in railroad yards, among them Conrail’s marshaling yard in East St. Louis. On the day of the accident, Davis, driving an unmarked van that was the same color as the Conrail vans used in the yard but that lacked the identifying “C” painted on each Conrail van, arrived at the yard and saw a train coming in from east to west. He noticed that several of the cars in the train were Trailer Train cars that he was required to inspect. The train halted, and was decoupled near the front; the locomotive, followed by several cars, pulled away to the west. The remainder of the train was stretched out for three-quarters of a mile to the east; and because it lay on a curved section of the track, its rear end was not visible from the point of decoupling. An employee of Conrail named Lundy saw Davis sitting in his van, didn’t know who he was, thought it was queer he was there, but did nothing.
  Shortly afterward Davis began to conduct the inspections. This required him to crawl underneath the cars to look for cracks. One of the cars was the third from the end (that is, from the point where the train had been decoupled). Unbeknownst to Davis, a locomotive had just coupled with the other (eastern) end of the train. It had a crew of four. Two were in the cab of the locomotive. The other two, one of whom was designated as the rear brakeman, were somewhere alongside the train; the record does not show just where, but neither was at the western end of the train, where Davis was. The crew was ordered to move the train several car lengths to the east because it was blocking a switch. The crew made the movement, but without blowing the train's horn or ringing its bell. The only warning Davis had of the impending movement was the sudden rush of air as the air brakes were activated. He tried to scramble to safety before the train started up but his legs were caught beneath the wheels of the car as he crawled out from under it. One leg was severed just below the knee; most of the foot on the other leg was also sliced off. The train had not been “blue flagged.” It is law (49 C.F.R. § 218) as well as custom in the railroad industry that whenever work is being done on a train a blue metal flag be placed at either end to warn employees not to move the train. Though well aware of the custom, Davis had neither blue flagged the train before crawling under it nor asked an employee of Conrail to blue flag it.
  Davis brought this suit against Conrail, charging negligence. Conrail impleaded Trailer Train, seeking contribution in the event it had to pay damages to Davis, on the ground that Trailer Train had been negligent in failing to instruct Davis in proper safety procedures. A jury found for Davis, assessed damages at $3 million, but found that Davis’s own negligence had been one-third responsible for the accident, and therefore awarded damages of $2 million. In Conrail’s third-party suit against Trailer Train, which had been tried with the main claim, the jury held that Trailer Train had been one-third responsible for the accident; it therefore ordered Trailer Train to reimburse Conrail for one-third of the $2 million in damages. Conrail and Trailer Train appeal. Conrail argues that it was not negligent at all (which if correct would mean that Davis was entitled to zero damages) but that if it was, still the reduction in its liability of only one-third shows that the jury was carried away by “passion and prejudice,” so that there should be a new trial, or at the least a reduction in Conrail’s share of the damages vis-a-vis Davis. Trailer Train argues that it was not negligent even if Conrail was, and therefore it should not have to pay any part of the damage award.
  Neither appellant challenges the $3 million price tag that the jury put on Davis’s injury, although Davis is able to walk with the aid of prosthetic devices, to drive, to work, and in short to lead almost a normal life. Of course the loss of a leg is a terrible disfigurement, especially for a young man, and a substantial award of damages would therefore be entirely justified even without any evidence of pain (and there was evidence of severe though transitory pain) or reduced longevity. But $3 million — only $170,000 of which represents lost earnings and past and future medical expenses — may well be excessive; and although appellate review of the amount of damages awarded by a jury or trial judge is highly deferential, we and the other courts of appeals have not hesitated to cut down grossly excessive damage awards. See, e.g., Joan W v. City of Chicago, 771 F.2d 1020, 1025 (7th Cir.1985); Douglass v. Hustler Magazine, Inc., 769 F.2d 1128, 1144 (7th Cir.1985); Abernathy v. Superior Hardwoods, Inc., 704 F.2d 963, 972-74 (7th Cir.1983); Dixon v. International Harvester Co., 754 F.2d 573, 590 (5th Cir. 1985); Harper v. Zapata Off-Shore Co., 741 F.2d 87, 91-93 (5th Cir.1984); Shaw v. United States, 741 F.2d 1202, 1210 (9th Cir.1984); Stratis v. Eastern Air Lines, Inc., 682 F.2d 406, 415 (2d Cir.1982). But as we have said, the defendants have not asked us to do that here.
  The defendants do complain, however, that the jury allocated too small a share of responsibility for the accident to Davis. They ask us to order either a remittitur or a new trial limited to damages, but alternatively they argue that the jury’s allocation shows that the jury was carried away by passion and prejudice, so that a new trial on liability as well as on damages should be ordered. See Douglass v. Hustler Magazine, Inc., supra, 769 F.2d at 1143. This argument has no merit. Although (as will become clear when we discuss the evidence of Conrail’s and Trailer Train’s negligence) the jury probably allotted too little of the blame for the accident to Davis, the error is not of such magnitude as to call into question the rationality of its verdict on whether the defendant was liable. Only in an unusual case will a court order a new trial on liability because of an error in assessing damages or in apportioning them among multiple defendants. This is not an unusual case. The jury may well have underestimated Davis’s relative fault, but it did not so take leave of its senses in dealing with tfiis issue that we are entitled to conclude that it did not use its reason in deciding whether Conrail was negligent at all.
  On the question of Conrail’s negligence, Davis presented three theories to the jury. The first was that Conrail’s employee Lun-dy, whose auto was equipped with a two-way radio, should have notified the crew of the train that an unknown person was sitting in a van parked near the tracks. We consider this a rather absurd suggestion. Lundy had no reason to think that the man in the van would climb out and crawl under a railroad car. If he had called the crew and told them there was a man in a van by the tracks, they undoubtedly would have replied, so what? Maybe, since the van resembled the vans used by Conrail employees, it should have occurred to Lundy that the person in the van had business on the tracks. But it is a big jump from recognizing that possibility to thinking that the man was in danger because he might crawl under a car without taking the usual precautions. And any Conrail employee would know better than to crawl under a car on a live track (a track that had not been blue-flagged). In sum, the probability that Davis would crawl under a car without first asking that it be blue flagged was too low, as it reasonably appeared to Lundy, to obligate Lundy to warn Davis or alert the train’s crew.
  In the famous negligence formula of Judge Learned Hand, which is recognized to encapsulate the more conventional verbal formulations of the negligence standard, see Prosser and Keeton on the Law of Torts 173 and n. 46 (5th ed. 1984), a defendant is negligent only if B < PL, meaning, only if the burden of precautions is less than the magnitude of the loss if an accident that the precautions would have prevented occurs discounted (multiplied) by the probability of the accident. See United States v. Carroll Towing Co., 159 F.2d 169, 173 (2d Cir.1947). If P is very low, elaborate precautions are unlikely to be required even if L is large, see United States Fidelity & Guaranty Co. v. Ja-dranska Slobodna Plovidba, 683 F.2d 1022, 1027-28 (7th Cir.1982); and here the necessary precautions would have been elaborate.
  Davis’s second theory of Conrail’s negligence is even more fantastic. It is that before the train was moved, a member of the crew should have walked its length, looking under the cars. The probability that someone was under a car was too slight, as it reasonably would have appeared to the crew, to warrant the considerable delay in moving the train that would have been caused by having a crew member walk its entire length and then walk back, a total distance of a mile and a half. It might have taken an hour, since the crew member would have had to look under each one of the train’s 50 cars, and since the cars were only 12 inches off the ground, so that he would have had to get down on all fours to see under them.
  Davis’s third theory is more plausible. He argues that it was negligent for the crew to move the train without first blowing its horn (also referred to as the whistle) or ringing its bell. Since no member of the crew was in a position where he could see the train’s western end, which was now its rear end, a reasonable jury could find — we do not say we would have found if we had been the triers of fact— that it was imprudent to move the train without a signal in advance. Although the crew had no reason to think that Davis was under a car, someone — whether an employee of Conrail or some other business invitee to the yard (such as Davis) — might have been standing in or on a car or between cars, for purposes of making repairs or conducting an inspection; and any such person could be severely, even fatally, injured if the train pulled away without any warning or even just moved a few feet. Regarding the application of the Hand formula to such a theory of negligence, not only was B vanishingly small — for what would it cost to blow the train’s horn? — but P was significant, though not large, once all the possible accidents that blowing the horn would have averted are added together. For in determining the benefits of a precaution — and PL, the expected accident costs that the precaution would avert, is a measure of the benefits of the precaution— the trier of fact must consider not only the expected cost of this accident but also the expected cost of any other, similar accidents that the precaution would have prevented. Cf. Conway v. O’Brien, 111 F.2d 611, 612 (2d Cir.1940), rev’d on other grounds, 312 U.S. 492, 61 S.Ct. 634, 85 L.Ed.2d 969 (1941). Blowing the horn would have saved not only an inspector who had crawled under the car (low P), but also an inspector leaning on a car, a railroad employee doing repairs on the top of a car, a brakeman straddling two cars, and anyone else who might have business in or on (as well as under) a car. The train was three-quarters of a mile long. It was not so unlikely that somewhere in that stretch a person was in a position of potential peril to excuse the crew from taking the inexpensive precaution of blowing the train’s horn. Or so at least the jury could conclude without taking leave of its senses.
  Against this conclusion Conrail and Trailer Train hurl a number of arguments. One is that precautions would not have been effective; Davis himself testified that he would not have heard the train’s bell. But we do not consider this so damaging a concession as the defendants do. Davis would not have heard the bell, no, but it does not mean that he would not have heard the horn. The horn is deafening, and Conrail’s assertion (for which no evidence was offered) that the horn would have been inaudible at three-quarters of a mile is as implausible as it is unsubstantiated.
  A better point is that there is so much traffic in a marshaling yard that sounding the horn every time a train is moved would cause a cacophony that would deprive the horn of its efficacy as a warning. If horns were blowing all the time, Davis would not know, when the horn sounded, whether it was the horn for this train or some other train. Either he would ignore it or he would be spending all his time scrambling out from under and then back under the cars he was inspecting. The problem with this argument is that Conrail put in no evidence on how busy the marshaling yard was either at the time of the accident or at any other time. We know it is a large (four square miles) and busy yard, but we do not know how frequently trains are actually moved in a large and busy yard. Every 15 minutes? Every hour? Conrail could easily have put in evidence on this point, but did not. Moreover, Davis is not contending that due care requires that the horn be blown before every move. Maybe this move was special, because of the length of the train in combination with the curvature of the track and the fact that all of the crew members were at or near the front of the train. Even if the yard is very busy, if the horn were sounded only in the unusual case where there was more than average danger from a sudden movement the danger of cacophony would be diminished.
  The defendants’ strongest argument is that Conrail had no duty to warn persons who might be in or on or under the train— given the blue flag rule. There is in general no duty to anticipate and take precautions against the negligence of another person. Such a requirement would tend to induce potential injufers to take excessive safety precautions relative to those taken by potential victims; the cost of safety would rise. Thus, “If the motorist on the through highway had to travel at such a speed that he could stop his car in time to avoid collisions with vehicles which ignore stop signs on intersecting roads, the purpose of having a through highway in the first place would be entirely thwarted.” Hession v. Liberty Asphalt Products, Inc., 93 Ill.App.2d 65, 74, 235 N.E.2d 17, 22 (1968). See Kofahl v. Delgado, 63 Ill. App.3d 622, 626, 20 Ill.Dec. 429, 433, 380 N.E.2d 407, 411 (1978); LeRoy Fibre Co. v. Chicago, Milwaukee & St. Paul Ry., 232 U.S. 340, 352, 34 S.Ct. 415, 417, 58 L.Ed. 631 (1914) (separate opinion of Holmes, J.); Phillips v. Croy, 173 Ind.App. 401, 405, 363 N.E.2d 1283, 1285 (1977); Kelsay v. Consolidated Rail Corp., 749 F.2d 437, 451 (7th Cir.1984) (dissenting opinion). It is true that if precautions necessary to prevent an undue risk of injury to persons who are exercising due care are omitted and a careless person is injured as a result, then in a jurisdiction such as Illinois where the complete defense of contributory negligence has given way to the partial defense of comparative negligence the careless victim can recover some damages. But he can do so, in general, only if there was a breach of duty to the careful.
  The defendants argue that the rule regarding blue flagging excuses the crew from any duty of care to persons who might be injured by a sudden starting of the train, because all such persons can protect themselves by blue flagging and are careless if they fail to do so. There is some evidence, however, that the rule was honored in the breach. Davis inspected cars at the yard three or four times a week, never posted or requested the posting of a blue flag, and was seen by many employees of Conrail without remonstrance from them. Maybe all these people were careless but maybe the rule of blue flagging is not so universal as the defendants claim. Common sense tells us that there must be times when there are no blue flags handy; and if the railroad thought it could prove that the rule of blue flagging was so steadily observed (though not in this instance) that the probability that someone, not careless, would be working on or in or under a train that had not been blue flagged was so small as to excuse the crew from a duty to sound any warning signal before moving the train, it should have put in evidence to this effect — evidence, for example, of where the flags are stacked.
  Of course there was much evidence that Davis was negligent in failing to blue flag the train (or request that it be blue flagged) before crawling under it. When he saw the western end of the train pull away he assumed the train would stay put. Yet as an experienced railroad worker he knew perfectly well that the train could be pulled from either end, and since he couldn’t see the other end from where he was working, he was taking a grave risk that a locomotive would hook on to that end and pull the train east, crushing him beneath it. He may well have been more negligent than the railroad. But we do not think the jury was irrational to find that the railroad was negligent as well. The burden of sounding the horn would have been trivial, and the expected benefits positive; for despite the blue flag rule there was some probability that an employee or invitee was working in or dangerously near the train, reasonably believing that he would receive some warning before the train pulled away. Of course, the horn might have done no good, because Davis might not have known (given his distance from the locomotive) that it was the horn of the train he was under; this possibility qualifies any possible estimate of the benefits. But this was a matter for the jury to consider; a rational jury could have concluded that the horn would have warned him.
  Moreover, we were careful to qualify our statement of the rule that a potential injurer is entitled to assume that potential victims will exercise due care, by saying that this was true “in general.” A certain amount of negligence is unavoidable, because the standard of care is set with reference to the average person and some people have below-average ability to take care and so can’t comply with the standard, and because in any event efforts at being careful produce only a probability, not a certainty, of avoiding careless conduct through momentary inattention. Potential injurers may therefore be required to take some care for the protection of the negligent, especially when the probability of negligence is high or the costs of care very low. See Prosser and Keeton on the Law of Torts, supra, § 33, at pp. 198-99. You cannot close your eyes while driving through an intersection, merely because you have a green light. If, as the jury could have found, Conrail could have avoided this accident by the essentially costless step of blowing the train’s horn, it may have been duty-bound to do so even if only a careless person would have been endangered by a sudden movement of the train.
  Conrail’s next argument is that the danger to Davis was open and obvious, and that this is a complete defense to liability. We agree with the premise but not the conclusion. The Illinois Supreme Court has held that, as a corollary to the replacement of contributory by comparative negligence, assumption of risk is no longer a complete defense to liability for negligence. Coney v. J.L.G. Industries, Inc., 97 Ill.2d 104, 119, 73 Ill.Dec. 337, 344, 454 N.E.2d 197, 204 (1983); Duffy v. Midlothian Country Club, 135 Ill.App.3d 429, 433-37, 90 Ill.Dec. 237, 241-43, 481 N.E.2d 1037, 1041-43 (1985). This proposition must not be taken too literally. If you agree to engage in a dangerous activity, such as hang gliding or technical rock climbing or riding a high-spirited horse, and one of the known dangers materializes with no negligence by the defendant, you cannot recover damages from him. Clark v. Rogers, 137 Ill.App.3d 591, 92 Ill.Dec. 136, 484 N.E.2d 867 (1985). There is by hypothesis no negligence in such a case and the term “assumption of risk” as used in it merely explains why there is not rather than providing a defense to a prima facie case of negligence. The defense of assumption of risk — the defense that ceased to be a complete defense when contributory negligence ceased to be a complete defense — comes into play if the defendant’s negligence created a danger that was apparent to the plaintiff, who nonetheless decided to risk it, as where a man dashes into a house that is on fire because of the defendant’s negligence, in an attempt to save his battered fedora, and is burned to death in the attempt. And that is conduct that can equally well be described as encountering an open and obvious danger — a defense assumed to be equivalent to assumption of risk in Nordhaus v. Vandalia R. Co., 242 Ill. 166, 173, 89 N.E. 974, 977 (1909). Davis knew there was a chance that the train would pull away without warning, but reckoned the chance small (perhaps counting on the railroad to be more careful than it was), and decided to take it. Such conduct in the face of an obvious danger of negligence is the type of assumption of risk that closely resembles contributory negligence (“secondary” assumption of risk, it is sometimes called) and that has been abolished along with contributory negligence as a complete defense to liability. It does not presuppose the defendant’s lack of negligence. It reduces the injurer’s liability, but not to zero, if the injurer is negligent.
  Both appellants argue that the jury should not have found Conrail twice as negligent as Davis. If this is what the jury did, the argument is sound and a remittitur should be ordered, subject to a technical question whether remittitur is proper in a case of malapportionment of damages, as distinct from excessive damages. Strictly speaking it is not, for we have just seen that the decision on apportionment is a decision on liability, and not on the amount of damages. But we think logic ought to give way to practical convenience and to the policy behind the device of remittitur, which is that if the plaintiff is willing to accept a lower amount of damages rather than incur the risks and expense of a new trial, and the defendant cannot complain because that lower amount would have been within the jury’s power to award, it is a just economy to terminate the suit without a retrial. The policy is fully applicable to a case such as this where the defendants are complaining that the jury placed too large a share of the blame on them, as we implicitly held in Davis v. United States, 716 F.2d 418, 430-31 (7th Cir.1983) (additur). See also Schwartz, Comparative Negligence § 18.4, at pp. 306-07 (1974).
  Although we thus have the power to cut down Conrail’s share of the damages, we decline to exercise it. Maybe the jury thought Conrail twice as negligent as Davis — an unreasonable allocation — but there is another interpretation of what the jury did which saves its verdict. Although there was only one defendant, Conrail, there were two tortfeasors, Conrail and Trailer Train. They inflicted an indivisible injury and thus were joint tortfeasors, meaning that each was fully liable to the plaintiff for the damages attributable to the other, though the one that was sued had a right to seek contribution from the other. The jury’s decision to shift one-third of the damages it had assessed against Conrail to Trailer Train implies that the jury divided up the $3 million damage assessment as follows: % to Davis, % to Conrail, and % to Trailer Train. Although as an original matter we would think Davis more rather than slightly less blameworthy than Conrail, we are not prepared to say that the allocation of fault is unreasonable.
  Trailer Train makes two further arguments. The first, which we shall not consider, is that one of the instructions invited the jury to attribute Davis’s negligence to his employer, Trailer Train, and thus, once the jury had found Davis one-third responsible for the accident, to hold Trailer Train one-third liable for the damages assessed against Conrail in Davis’s claim. The instruction did invite this weird mode of assessment, but Trailer Train did not object to the instruction when given. It first objected in its post-trial motions. That was too late. If plain error is ever a valid basis in a civil case for overlooking an appellant’s failure to have objected to the instruction that he claims was given erroneously before the jury was instructed, it is only so in an exceptional case. Parrett v. City of Connersville, 737 F.2d 690, 698 (7th Cir.1984); Exxon Cory. v. Exxene Cory., 696 F.2d 544, 549 (7th Cir.1982). A case is not exceptional when a substantial corporation, well able to afford effective legal representation, asks us to give it a new trial, merely because its lawyer made a mistake at the first trial. No excuse for the mistake is . offered, though we do not mean to suggest that any excuse would have been adequate. A litigant cannot allow the case to go to the jury on instructions that he knows or should know are incorrect, and if he loses get a new trial. Trailer Train cannot put Conrail to the expense of a new trial because of an error that Trailer Train should have caught when the error could still have been corrected.
  Since the jury merely acted in accordance with an instruction to which no objection was made, perhaps no more need be said to reject Trailer Train’s appeal. A jury verdict that is reasonable in light of the instructions given and not objected to cannot be upset by being shown to be unreasonable in light of instructions that were never given. “[I]n a civil case each party must live with the legal theory reflected in instructions to which it does not object.” Will v. Comprehensive Accounting Corp., 776 F.2d 665, 675 (7th Cir.1985). We also think, however, that there was some evidence of Trailer Train’s negligence. The nature of the inspections that Davis’s job for Trailer Train called for him to make required that he crawl under the cars, but Trailer Train never told him how he should protect himself when he did so. It relied on the fact that Davis was an experienced railroad worker who knew all about blue flags and the danger of being under a car when the train started to move. Trailer Train had no safety rules for its employees. This we think is some evidence of negligence. It is true that a firm of electricians is not liable for negligence because it fails to tell its employees that they shouldn’t stick their fingers into sockets without shutting off the power. Some dangers are too obvious to warrant work rules. But Trailer Train’s inspectors do not control their work environment in the same way that an electrician or plumber controls his. Davis could not switch off the power for the train. All he could do was either personally or by requesting a Conrail employee blue flag the train so that the crew would be warned not to move it.
  A reasonable jury could find (if barely) that Trailer Train should have made clear to Davis that he was not to inspect any car without insisting on blue flagging and should have prescribed a procedure for implementing this requirement. Since blue flagging takes some time, the absence of a work rule put Davis in a potential dilemma. If he was too meticulous about safety, this might slow down his inspections too much and jeopardize his job. Trailer Train should have dispelled any doubt that safety must come first. It strikes us (and more important must have struck the jury) as unusual that a worker in such a dangerous job should be allowed to go about his work without receiving any instructions with regard to safety. He should have been more careful and if so would have averted this terrible accident. But that just means he was contributorily negligent; it does not completely excuse Trailer Train for relying entirely on his prudence and caution.
  Although the evidence of the defendants’ negligence is thin, the instructions were defective, and the damages probably too large both before and after being reduced for Davis’s negligence, some, perhaps all, of these errors were within the power of the defendants’ counsel to prevent. Although not fully satisfied that justice was done, we can find no reversible error.
  Affirmed.