POSNER, Chief Judge.
We have before us a charming miniature of a case. In 1993 Dolores Howard, age 65, slipped and fell in a puddle of liquid soap that someone — no one knows who — had
spilled on the floor of the aisle in a Wal-Mart store in Cahokia, Illinois. She was injured, and brought suit against Wal-Mart in an Illinois state court; the defendant removed the case to federal district court. At the time the suit was brought and removed, there was enough possibility that Howard’s injury was severe (the injured leg had become infected) to lift the case just over the then $50,000 threshold for a diversity suit. But later she recovered and at trial asked for only $25,000 in damages. The jury awarded her $18,750. Wal-Mart has appealed out of fear (its lawyer explained to us at argument) of the precedential effect in future slip-and-fall cases of the judge’s refusal to grant judgment for Wal-Mart as a matter of law. We don’t tell people whether to exercise their rights of appeal, but we feel impelled to remind Wal-Mart and its lawyer that a district court’s decision does not have prece-dential authority, e.g.,
Old Republic Ins. Co. v. Chuhak & Tecson, P.C.,
84 F.3d 998, 1003-04 (7th Cir.1996);
Anderson v. Romero,
72 F.3d 518, 525 (7th Cir.1995)—let alone a jury verdict or an unreported order by a magistrate judge (by any judicial officer, for that matter) refusing on unstated grounds to throw out a jury’s verdict.
The issue on appeal is whether there was enough evidence of liability to allow the case to go to a jury, and, specifically, whether there was enough evidence that an employee rather than a customer spilled the soap. See
Donoho v. O’Connell’s, Inc.,
13 Ill.2d 113, 148 N.E.2d 434 (1958);
Wind v. Hy-Vee Food Stores, Inc.,
272 Ill.App.3d 149, 208 Ill.Dec. 801, 650 N.E.2d 258, 262 (1995). Even if a customer spilled it, Wal-Mart could be liable if it failed to notice the spill and clean it up within a reasonable time.
Donoho v. O’Connell’s, Inc., supra,
148 N.E.2d at 437-38;
Swartz v. Sears, Roebuck & Co.,
264 Ill.App.3d 254, 201 Ill.Dec. 210, 636 N.E.2d 642, 654 (1993). It has a legal duty to make its premises reasonably safe for its customers. But there is no evidence with regard to how much time elapsed between the spill and the fall; it may have been minutes. Wal-Mart is not required to patrol the aisles continuously, but only at reasonable intervals. See
Culli v. Marathon Petroleum Co.,
862 F.2d 119 (7th Cir.1988) (collecting Illinois cases). So Howard could prevail only if there was enough evidence that an employee spilled the soap to satisfy the requirement of proving causation by a preponderance of the evidence.
The accident occurred in the morning, and morning is also when the employees stock the shelves. The defendant presented evidence that the puddle of liquid soap on which Howard slipped was about the diameter of a softball and was in the middle of the aisle. Howard testified that it was a large puddle on the right side of the aisle and “when I got up, I had it all over me, my coat, my pants, my shoes, my socks.” An employee could have dropped one of the plastic containers of liquid soap on the floor while trying to shelve it and the container could have broken and leaked. Or the cap on one of the containers might have come loose. Or the containers might have been packed improperly in the box from which they were loaded onto the shelves and one of them might have sprung a leak. Alternatively, as Wal-Mart points out, a customer, or a customer’s child, might have knocked a container off the shelf. A curious feature of the case, however, is that the container that leaked and caused the spill was never found. Howard argues, not implausibly, that a customer who had come across a damaged container or had damaged it would be unlikely to purchase it, having lost part of its contents — a large part, if Howard’s testimony was believed; and the jury was entitled to believe it — or indeed to put it in her shopping cart and risk smearing her other purchases with liquid soap. In light of this consideration, we cannot say that the jury was irrational in finding that the balance of probabilities tipped in favor of the plaintiff, though surely only by a hair’s breadth.
Is a hair’s breadth enough, though? Judges, and commentators on the law of evidence, have been troubled by cases in which the plaintiff has established a probability that only minutely exceeds 50 percent that his version of what happened is correct. The concern is illuminated by the much-discussed bus hypothetical. Suppose that the plaintiff is hit by a bus, and it is known that 51 percent of the buses on the road
where the plaintiff was hit are owned by Bus Company A and 49 percent by Company B. The plaintiff sues A and asks for judgment on the basis of this statistic alone (we can ignore the other elements of liability besides causation by assuming they have all been satisfied, as in this case); he tenders no other evidence. If the defendant also puts in no evidence, should a jury be allowed to award judgment to the plaintiff? The law’s answer is “no.” See Richard W. Wright, “Causation, Responsibility, Risk, Probability, Naked Statistics, and Proof: Pruning the Bramble Bush by Clarifying the Concepts,” 73
la. L. Rev.
1001, 1050-1051 (1988), and cases cited there. Our hypothetical ease is a variant of
Smith v. Rapid Transit,
317 Mass. 469, 58 N.E.2d 754 (1945), where the court held that it “was not enough” “that perhaps the mathematical -chances somewhat favor the proposition that a bus of the defendant caused the accident.”
Id.
at 755.
Kaminsky v. Hertz Corp.,
94 Mich.App. 356, 288 N.W.2d 426 (1979), is sometimes cited as being contrary to
Smith,
but this is not an accurate reading. Besides the fact that the corresponding percentages were 90 percent and 10 percent, there was nonstatistical evidence pointing to the defendant’s ownership of the truck that had caused the accident.
Smith
and
Kaminsky
involve explicitly probabilistic evidence. But as all evidence is probabilistic in the sense of lacking absolute certainty, all evidence can be expressed in probabilistic terms, and so the problem or dilemma presented by those cases is general. The eyewitness might say that he was “99 percent sure” that he had seen the defendant, and jurors appraising his testimony might reckon some different probability that he was correct. What powers the intuition that the plaintiff should lose the bus case is not the explicitly probabilistic nature of the evidence, but the evidentiary significance of missing evidence.
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POSNER, Chief Judge.
We have before us a charming miniature of a case. In 1993 Dolores Howard, age 65, slipped and fell in a puddle of liquid soap that someone — no one knows who — had
spilled on the floor of the aisle in a Wal-Mart store in Cahokia, Illinois. She was injured, and brought suit against Wal-Mart in an Illinois state court; the defendant removed the case to federal district court. At the time the suit was brought and removed, there was enough possibility that Howard’s injury was severe (the injured leg had become infected) to lift the case just over the then $50,000 threshold for a diversity suit. But later she recovered and at trial asked for only $25,000 in damages. The jury awarded her $18,750. Wal-Mart has appealed out of fear (its lawyer explained to us at argument) of the precedential effect in future slip-and-fall cases of the judge’s refusal to grant judgment for Wal-Mart as a matter of law. We don’t tell people whether to exercise their rights of appeal, but we feel impelled to remind Wal-Mart and its lawyer that a district court’s decision does not have prece-dential authority, e.g.,
Old Republic Ins. Co. v. Chuhak & Tecson, P.C.,
84 F.3d 998, 1003-04 (7th Cir.1996);
Anderson v. Romero,
72 F.3d 518, 525 (7th Cir.1995)—let alone a jury verdict or an unreported order by a magistrate judge (by any judicial officer, for that matter) refusing on unstated grounds to throw out a jury’s verdict.
The issue on appeal is whether there was enough evidence of liability to allow the case to go to a jury, and, specifically, whether there was enough evidence that an employee rather than a customer spilled the soap. See
Donoho v. O’Connell’s, Inc.,
13 Ill.2d 113, 148 N.E.2d 434 (1958);
Wind v. Hy-Vee Food Stores, Inc.,
272 Ill.App.3d 149, 208 Ill.Dec. 801, 650 N.E.2d 258, 262 (1995). Even if a customer spilled it, Wal-Mart could be liable if it failed to notice the spill and clean it up within a reasonable time.
Donoho v. O’Connell’s, Inc., supra,
148 N.E.2d at 437-38;
Swartz v. Sears, Roebuck & Co.,
264 Ill.App.3d 254, 201 Ill.Dec. 210, 636 N.E.2d 642, 654 (1993). It has a legal duty to make its premises reasonably safe for its customers. But there is no evidence with regard to how much time elapsed between the spill and the fall; it may have been minutes. Wal-Mart is not required to patrol the aisles continuously, but only at reasonable intervals. See
Culli v. Marathon Petroleum Co.,
862 F.2d 119 (7th Cir.1988) (collecting Illinois cases). So Howard could prevail only if there was enough evidence that an employee spilled the soap to satisfy the requirement of proving causation by a preponderance of the evidence.
The accident occurred in the morning, and morning is also when the employees stock the shelves. The defendant presented evidence that the puddle of liquid soap on which Howard slipped was about the diameter of a softball and was in the middle of the aisle. Howard testified that it was a large puddle on the right side of the aisle and “when I got up, I had it all over me, my coat, my pants, my shoes, my socks.” An employee could have dropped one of the plastic containers of liquid soap on the floor while trying to shelve it and the container could have broken and leaked. Or the cap on one of the containers might have come loose. Or the containers might have been packed improperly in the box from which they were loaded onto the shelves and one of them might have sprung a leak. Alternatively, as Wal-Mart points out, a customer, or a customer’s child, might have knocked a container off the shelf. A curious feature of the case, however, is that the container that leaked and caused the spill was never found. Howard argues, not implausibly, that a customer who had come across a damaged container or had damaged it would be unlikely to purchase it, having lost part of its contents — a large part, if Howard’s testimony was believed; and the jury was entitled to believe it — or indeed to put it in her shopping cart and risk smearing her other purchases with liquid soap. In light of this consideration, we cannot say that the jury was irrational in finding that the balance of probabilities tipped in favor of the plaintiff, though surely only by a hair’s breadth.
Is a hair’s breadth enough, though? Judges, and commentators on the law of evidence, have been troubled by cases in which the plaintiff has established a probability that only minutely exceeds 50 percent that his version of what happened is correct. The concern is illuminated by the much-discussed bus hypothetical. Suppose that the plaintiff is hit by a bus, and it is known that 51 percent of the buses on the road
where the plaintiff was hit are owned by Bus Company A and 49 percent by Company B. The plaintiff sues A and asks for judgment on the basis of this statistic alone (we can ignore the other elements of liability besides causation by assuming they have all been satisfied, as in this case); he tenders no other evidence. If the defendant also puts in no evidence, should a jury be allowed to award judgment to the plaintiff? The law’s answer is “no.” See Richard W. Wright, “Causation, Responsibility, Risk, Probability, Naked Statistics, and Proof: Pruning the Bramble Bush by Clarifying the Concepts,” 73
la. L. Rev.
1001, 1050-1051 (1988), and cases cited there. Our hypothetical ease is a variant of
Smith v. Rapid Transit,
317 Mass. 469, 58 N.E.2d 754 (1945), where the court held that it “was not enough” “that perhaps the mathematical -chances somewhat favor the proposition that a bus of the defendant caused the accident.”
Id.
at 755.
Kaminsky v. Hertz Corp.,
94 Mich.App. 356, 288 N.W.2d 426 (1979), is sometimes cited as being contrary to
Smith,
but this is not an accurate reading. Besides the fact that the corresponding percentages were 90 percent and 10 percent, there was nonstatistical evidence pointing to the defendant’s ownership of the truck that had caused the accident.
Smith
and
Kaminsky
involve explicitly probabilistic evidence. But as all evidence is probabilistic in the sense of lacking absolute certainty, all evidence can be expressed in probabilistic terms, and so the problem or dilemma presented by those cases is general. The eyewitness might say that he was “99 percent sure” that he had seen the defendant, and jurors appraising his testimony might reckon some different probability that he was correct. What powers the intuition that the plaintiff should lose the bus case is not the explicitly probabilistic nature of the evidence, but the evidentiary significance of missing evidence. If the 51/49 statistic is the plaintiffs only evidence, and he does not show that it was infeasible for him to obtain any additional evidence, the inference to be drawn is not that there is a 51 percent probability that it was a bus owned by A that hit the plaintiff. It is that the plaintiff either investigated and discovered that the bus was actually owned by B (and B might not have been negligent and so not liable even if a cause of the accident, or might be judgment-proof and so not worth suing), or that he simply has not bothered to conduct an investigation. If the first alternative is true, he should of course lose; and since it
may
be true, the probability that the plaintiff was hit by a bus owned by A is
less
than 51 percent and the plaintiff has failed to carry his burden of proof. If the second alternative is true — -the plaintiff just hasn’t conducted an investigation — he still should lose. A court shouldn’t be required to expend its scarce resources of time and effort on a case until the plaintiff has conducted a sufficient investigation to make reasonably clear that an expenditure of public resources is likely to yield a significant social benefit. This principle is implicit in the law’s decision to place the burden of producing evidence on the plaintiff rather than on the defendant. Suppose it would cost the court system $10,000 to try even a barebones case. This expenditure would be worthless from the standpoint of deterring accidents should it turn out that the bus was owned by B. It makes sense for the court to require some advance investigation by the plaintiff in order to increase the probability that a commitment of judicial resources would be worthwhile.
These objections to basing a decision on thin evidence do not apply to the present case. Not only is there no reason to suspect that the plaintiff is holding back unfavorable evidence; it would have been unreasonable, given the stakes, to expect her to conduct a more thorough investigation. This is a tiny case; not so tiny that it can be expelled from the federal court system without a decision, but so tiny that it would make no sense to try to coerce the parties to produce more evidence, when, as we have said, no inference can be drawn from the paucity of evidence that the plaintiff was afraid to look harder for fear that she would discover that a customer and not an employee of Wal-Mart had spilled the soap.
We conclude, therefore, that the jury verdict must stand. And, Wal-Mart, this decision, a reported appellate decision, unlike the
decision of the district court, will have prece-dential authority!
Affirmed.