
574 F.Supp. 400 (1983)
DELTAK, INC., a corporation, Plaintiff,
v.
ADVANCED SYSTEMS, INC., a corporation, Defendant.
Civ. A. No. 80 C 6678.
United States District Court, N.D. Illinois, E.D.
October 20, 1983.
As Corrected October 21, 1983.
*401 David Hilliard, Pattishall McAuliffe & Hofstetter, Chicago, Ill., for plaintiff.
Gareth G. Morris, Arlington Heights, Ill., for defendant.


*402 DECISION AND OPINION
POSNER, Circuit Judge.[*]
This civil suit under the Copyright Act of 1976, 17 U.S.C. §§ 101 et seq., raises significant issues involving the computation of damages in a copyright case where the infringing item is not sold separately, and the use of expert witnesses. The case was tried before me in a two-day bench trial (August 16-17, 1983) limited to the issue of damages. At the conclusion of the trial I delivered a tentative oral opinion and asked the parties to submit post-trial briefs commenting on it. They have done so and I now make the following findings of fact and conclusions of law as required by Rule 52(a) of the Federal Rules of Civil Procedure. This opinion supersedes my oral opinion.
Deltak, Inc. brought this suit in December 1980 against Advanced Systems, Inc. (ASI), alleging copyright infringement. (A pendent claim under state law has been abandoned.) In May 1981 Judge Prentice Marshall, to whom the case was originally assigned, granted the plaintiff a preliminary injunction. He later granted summary judgment for the plaintiff on the issue of liability, leaving only the issue of damages for trial.
Deltak and ASI are two of the three largest firms in the business of selling video and audio tapes and textbooks used to teach data processing. ASI used to be the largest, but in the late 1970s Deltak passed ASI and this caused ASI to redouble its competitive efforts. In 1980 Deltak's sales revenues were about $30 million, ASI's about $24 million. Each firm's educational materials are highly substitutable for the other's.
The Deltak marketing effort included in the relevant period (1980-1981) a set of materials called the Career Development System (CDS). One component of the CDS is a large glossy pamphlet called the "Task List." On the left-hand side of each page of the Task List is a list of data-processing tasks that a company might want to teach its programmers, and on the right-hand side a list of the specific teaching materials that Deltak sells for each task. ASI paid $3,000 to two consultants to create a document that would combine the CDS task designations with a listing of ASI teaching materials. The consultants duplicated the left-hand side of the CDS Task List, using the identical language in which Deltak had described the tasks and arranging the task descriptions in the same order as Deltak; but on the right-hand side of each page, instead of listing the Deltak materials suitable to perform each task the authors of the infringing document listed ASI teaching materials. It was intended that ASI's salesmen and marketing representatives would show this document to Deltak customers to help them pick ASI materials to perform instructional tasks listed by Deltak. The initial impetus for the preparation of the document apparently had come from ASI customers who wanted to key ASI's library to the Deltak Task List.
ASI produced 42 copies of the document under conditions of secrecy and excitement. Fifteen were distributed to customers of Deltak who were actual or potential customers of ASI as well. Distribution began in August 1980, the lawsuit was brought as I have said in December 1980, and beginning shortly thereafter counsel for ASI began retrieving the copies that had been left with the customers. Some of these copies had disappeared and some had been destroyed but by the end of February 1981 none, so far as the evidence shows, was still in a customer's possession.
When Judge Marshall issued the preliminary injunction, and later when he granted summary judgment to Deltak, he held (and I agree) that there indeed was copyright infringement. He rejected ASI's argument that the copying of Deltak's Task List was within the fair-use exception to copyright liability, 17 U.S.C. § 107. Although it was certainly ASI's privilege to tell its customers which item in the ASI library could do a particular task in the CDS Task List, ASI did not stop there. It copied the exact language in which the *403 CDS Task List described each task and the exact sequence in which the tasks were listed, which was not a random sequence. The copying was deliberate, it was done by a substantial corporation that should have known better, and the documents submitted into evidence in connection with the deposition of ASI's Miss Sorn show consciousness of probable violation of the copyright laws. If Deltak had registered its copyright within the time provided by the Copyright Act, I would have no hesitation in awarding not only the maximum statutory damages under section 504(c)(2) of $50,000, but also attorney's fees, which are authorized by section 505 and are frequently awarded in cases of willful infringement even if no actual damages are proved. See, e.g., Taylor v. Meirick, 712 F.2d 1112, 1122 (7th Cir.1983); Twentieth Century Music Corp. v. Frith, 645 F.2d 6 (5th Cir.1981) (per curiam). However, the parties have agreed that Deltak may not get either statutory damages or attorney's fees, because it did not register its copyright in time. 17 U.S.C. § 412.
The only issue, therefore, is Deltak's right to actual damages or infringer's profits under sections 504(a) and (b) of the Copyright Act. The issue is somewhat novel because the item that was infringed, the CDS Task List, although nominally sold by the plaintiff was in fact a component of a larger product (the whole CDS packet) itself intended as a tool for selling something else (the teaching materials); and the infringer did not sell the infringing document either, but also used it as a sales tool. ASI argues that if the infringing item is not sold there cannot be any award of actual damages (the additional profits the copyright owner would have made but for the infringement) but only an award of statutory damages (provided the copyright was registered in time). That is an untenable position. Although I have found no reported decisions discussing the award of actual damages or of infringer's profits in such a case, the propriety of such an award is clearly implied by the many cases that hold that there is actionable infringement even if the infringing item is sold or priced separately. See, e.g., Herbert v. Shanley Co., 242 U.S. 591, 37 S.Ct. 232, 61 L.Ed. 511 (1917); Sailor Music v. GAP Stores, Inc., 668 F.2d 84 (2d Cir.1981). Suppose I composed a tune and copyrighted it, and Mr. Morris (ASI's counsel) came along and stole my tune in violation of the copyright laws and used it to advertise a cat food that he sells. He would not be selling the tune  ordinarily a seller does not charge his customers to listen to his commercials. He would in effect be giving away the tune to anybody who cared to listen to it, hoping it would induce the listener to buy his cat food. If I could prove that the theft had increased Morris's cat-food profits by a million dollars, these would be infringer's profits recoverable by me under section 504(b). Furthermore, if I just proved the gross revenues that Morris obtained from the infringement, and rested there, the statutory presumption in the second sentence of section 504(b) would come into play and the burden would shift to Morris to prove what fraction of those gross revenues were costs that he would have avoided had he not infringed and that therefore should be subtracted to calculate his profits from the infringement. Cf. Taylor v. Meirick, supra, 712 F.2d at 1121.
Against all this it can be argued that given the availability of statutory damages, there is no need to have a comprehensive concept of actual damages or of infringer's profits; the infringed plaintiff has a safety net. But since the maximum statutory damages are only $50,000 and an infringing work used as a marketing device could generate much greater profits for the infringer than $50,000 and cause much greater losses to the copyright owner, it would be unsound to infer from the provision for statutory damages a congressional intent to overthrow normal tort damage principles.
When the infringement consists of the unauthorized use of the plaintiff's sales tool, the plaintiff must establish either the extra profits that he would have had if the infringer had not used the sales tool, or *404 (aided by the statutory presumption I just mentioned) the extra profits that the infringer gained from using it. (Double counting is not allowed. Taylor v. Meirick, supra, 712 F.2d at 1120.) Although most of Deltak's effort at trial was an attempt to prove ASI's extra revenue from the infringement, it did make some effort to prove its own lost profits, based on the profit that it would have made on each additional copy of the CDS kit that it contends it would have sold but for the infringement; and I shall discuss this theory of damages first.
Deltak presented evidence that the price of the kit (for this is the unusual type of advertising that the seller actually sells to his customers), consisting of the Task List and certain other items, is $5,000 and that Deltak's cost of producing one more such kit is $75. I accept $4,925 as a reasonable estimate of the profit per kit for a small increase in production. Deltak wants me to multiply that number by 50, the number of copies of the infringing document that ASI made. But the only possible factual premise for such a measure of damages would be that Deltak would have sold 50 more copies of the CDS at $5,000 apiece had it not been for the infringement. That premise was not proved at trial and is almost certainly false. I will not quarrel with the figure of $5,000 for the sale price, though there was much evidence that Deltak's average realized revenue from the sale of CDS kits was far less. But there was no evidence that Deltak would have sold one more CDS, let alone 50 more, but for the infringement. Cf. Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152, 1158-60 (6th Cir.1978). ASI produced the 50 copies of the CDS Task List to give customers of Deltak who had the CDS kit, in an effort to wean them away from Deltak. And each page of the CDS Task List recites that the customer may photocopy the Task List for use at his business location. If any customer of Deltak who had a copy of the CDS Task List wanted another one for the convenience of its employees, it would make another copy itself, for the cost of duplication; it would not pay Deltak $5,000.
Deltak argues, however, that a law-abiding ASI would have come to Deltak and said, "Sell us 50 copies of your CDS Task List for use by us as a marketing tool." Although I do not deny that the Task List had some potential value to ASI as a marketing tool or that the value of the infringer's use is a permissible basis for estimating damages, see, e.g., Sid & Marty Krofft Television Productions, Inc. v. McDonald's Corp., 562 F.2d 1157, 1174 (9th Cir.1977), the particular scenario in which ASI goes hat in hand to Deltak to buy 50 copies  or one copy  of the Task List is quite fantastic even on the counterfactual hypothesis (fundamental to this approach to estimating damages) that ASI had a pure heart. Not only is it very unlikely that even a pure-hearted ASI would have been willing to tip its competitive hand to Deltak in this fashion, but if all ASI wanted was the content of the Task List in order to track the tasks in its own library it had only to ask a customer to show it (perhaps lend it) his copy of the CDS. It had only to say to the customer, "Tell us what you're getting from Deltak and we'll tell you whether we can do the same thing better or cheaper," and the customer would break out his copy of CDS and reply, "We do this task, this task, and that task," and ASI would respond, "We can give you this tape, this tape, and that tape to do those tasks better or cheaper."
Deltak's only other damage theory is that the infringement increased ASI's profits. I want to begin my discussion of this theory with a comment on the witnesses' credibility. There were only four live witnesses: for the plaintiff, Mr. King, chairman of the board of Deltak, and Dr. Alfred Kuehn, an expert witness; for the defendant, Dr. Robert Blattberg, an expert witness, and Mr. Wallack, a financial officer of ASI.
The burden of Mr. King's testimony was that CDS was a vitally important marketing tool in the sale of Deltak's educational materials and that the theft of that tool, as *405 one might describe the infringement, was bound to boost ASI's sales. Mr. King was a very smooth, well-rehearsed witness  an effective advocate for the plaintiff, steeped in the plaintiff's legal contentions. But when it came to actual evidence, I was not impressed. In particular, I disbelieve his estimate that it cost $1 million to create the CDS Task List. Mr. King testified that there are no documents which support this estimate, and none was presented at the trial. He testified that a follow-on to CDS, a computerized system called Delta I, cost ASI $800,000 to develop. He added that there was documentary back-up for this estimate, though no back-up was placed in evidence. Delta I is not only computerized but lists many more tasks than the CDS Task List, which was put together by a task force of seven or eight people, working part time. I am skeptical that a company whose annual revenues (gross, not net) are only $30 million would spend $1 million to compile a simple list of a few hundred tasks  and keep no record of the expenditure. Cf. Stevens Linen Assocs. v. Mastercrafts Corp., 656 F.2d 11, 15 (2d Cir.1981). Mr. King's testimony did not dispel my skepticism.
Dr. Alfred Kuehn is an expert in marketing with a most impressive curriculum vitae, but his testimony illustrated two recurrent problems in the use of expert testimony and makes this litigation a case study in the misuse of the expert witness  a very old problem in the law. "Experts are nowadays often the mere paid advocates or partisans of those who employ and pay them, as much so as the attorneys who conduct the suit. There is hardly anything, not palpably absurd on its face, that cannot now be proved by some so-called `experts.'" Keegan v. Minneapolis & St. L.R.R., 76 Minn. 90, 95, 78 N.W. 965, 966 (1899), quoted in Albers v. Church of the Nazarene, 698 F.2d 852, 858 (7th Cir.1983). "Enough has been said elsewhere as to the natural bias of one called in such matters to represent a single side and liberally paid to defend it. Human nature is too weak for that; I can only appeal to my learned brethren of the long robes to answer candidly how often they look impartially at the law of a case they have become thoroughly interested in, and what kind of experts they think they would make, as to foreign law, in their own cases." Hand, Historical and Practical Considerations Regarding Expert Testimony, 15 Harv.L.Rev. 40, 53 (1901). Dr. Kuehn's testimony did not draw to any significant degree on his professional expertise; he was little more than a mouthpiece or amplifier through which Deltak's counsel addressed argument to the trier of fact. And the adversary setting caused Dr. Kuehn to lose scientific detachment and adopt an advocate's posture. These problems are related.
The evidence presented by Dr. Kuehn consisted, on the one hand, of statistical computations embodied in charts that could have been prepared by a child or by a lawyer  which so far as anything partaking of mathematics or statistics is concerned are virtual synonyms. None of Dr. Kuehn's professional expertise is reflected in these charts, which are simple comparisons of ASI and Deltak contract revenues from different groups of customers before and after the distribution of the infringing document. No tests of statistical significance were presented and no effort was made, using multiple-regression analysis or any other statistical or empirical technique, to correct for other factors besides the infringing document that might have accounted for the increase in ASI's sales during the infringement period to the customers who received the document, though there were indeed other factors at work as we shall see.
The other part of Dr. Kuehn's testimony consisted of his opinion of the credibility of particular deposition witnesses. No suggestion was made and it is not my impression that among the recognized skills of a marketing expert is the ability to evaluate credibility in the transcript of a deposition. Cf. Stigler, What Does an Economist Know?, 33 J. Legal Educ. 311 (1983). Although I do not exclude the possibility that such an expert reading a deposition in the light of his specialized knowledge might *406 have useful insights, they were very scarce in Dr. Kuehn's testimony. He did point out that to ask a businessman whether he has used a particular document in making a purchasing decision is to ask an ambiguous question to which the answer is potentially misleading. That was a valid observation that Dr. Kuehn backed up by pointing out, plausibly (and Dr. Blattberg said much the same thing), that a customer may not be able to quantify the influence of particular factors in a purchasing decision. But for the most part Dr. Kuehn in testifying about the depositions was arguing credibility just like a lawyer.
Dr. Kuehn displayed a characteristic that may be to some extent inherent in the psychology of the adversary process  exaggeration. I do not suggest that he testified in a deliberately false way. On the contrary, he impressed me as passionately sincere. But what frequently happens, and what I believe must have happened here, is that in the course of working with the lawyer who has hired him the expert witness comes to identify the interests of the lawyer's client with his own interests. He becomes an advocate; and when he is subjected to protracted cross-examination, as happened here, his identification increases and he throws all caution to the winds.
Dr. Kuehn testified for example that the probability that the infringing document had no effect on ASI's sales was less than one in a trillion. In the mouth of a layman I would regard that as absurd hyperbole. In the mouth of an expert with a considerable background in mathematics I regard it as a reckless statement having disturbing implications for a legal system that admits certain testimony only because it is given by experts. He also testified that the sales increase that ASI experienced in the infringement period (roughly the last quarter of 1980) was so great as to be an unusual phenomenon in the business world. But it was only trivially greater than an increase that ASI had experienced in one quarter in 1978. When one considers that there are thousands of companies in the United States that are larger than ASI and perhaps a million companies that are smaller, and when one considers the sales fluctuations to which even very large businesses are subject, the suggestion that this sales increase was so unusual as to demonstrate a causal relationship between the infringing document and the fortunes of ASI becomes completely unbelievable.
The importance of safeguarding the integrity of the trial process requires the trial judge, when he believes that an expert's testimony has fallen below professional standards, to say so, as many judges have done. For some recent examples see Berkey Photo, Inc. v. Eastman Kodak Co., 603 F.2d 263, 305-08 (2d Cir.1979); Buffalo Broadcasting Co. v. American Soc'y of Composers, Authors & Publishers, 546 F.Supp. 274, 293 n. 42 (S.D.N.Y. 1982); American Bearing Co. v. Litton Indus., 540 F.Supp. 1163, 1171-75 (E.D.Pa. 1982); Bonjorno v. Kaiser Aluminum & Chem. Corp., 518 F.Supp. 102, 113 n. 23, 117-18 (E.D.Pa.1981); Zenith Radio Corp. v. Matsushita Elec. Indus., 505 F.Supp. 1313, 1338 (E.D.Pa.1980); United States v. Tracinda Investment Corp., 477 F.Supp. 1093, 1110 (C.D.Cal.1979). It is difficult to imagine what other deterrent there is to the misuse of expert testimony. And incidentally I am not the first judge to criticize Dr. Kuehn's testimony. See Bonjorno v. Kaiser Aluminum & Chem. Corp., supra, 518 F.Supp. at 118 ("The total effect [of Dr. Kuehn's testimony] was that of a witness who did not know what he was talking about").
The defendant's expert witness, Dr. Blattberg, was not subjected to such extensive cross-examination as Dr. Kuehn and his method of testimony was somewhat different. The charts that he produced and submitted were more sophisticated statistically than Dr. Kuehn's. Beyond that, however, I did not have the impression that Dr. Blattberg's testimony drew heavily on the knowledge that he must have obtained over the years as a professor of marketing and as a marketing consultant. Besides his statistical evidence his principal evidence consisted of his impressions of the deposition *407 testimony and of a handful of ASI documents which suggest that in the last quarter of 1980 ASI was using other marketing devices that may explain a substantial part of the new contracts signed by ASI in that quarter.
Dr. Blattberg strained my credence when he compared depositions to surveys; I cannot believe that a company trying to estimate the effect of a marketing tool would emulate the methods that lawyers use in taking depositions. I also do not think that Dr. Blattberg was the best possible witness to sponsor the documents that described ASI's marketing strategy, although Deltak did not object to the admission of these documents. An ASI executive who was knowledgeable about that strategy was listed as a witness but for some reason was not called.
I turn to the evidence that was introduced on the key factual question in this case, which is whether and to what extent the infringing document generated business for ASI that it would otherwise not have had. The principal evidence was deposition testimony admitted by stipulation and statistical computations. The former consisted for the most part of testimony of witnesses deposed by the defendant, but the depositions contain some evidence that is helpful to the plaintiff. In particular, Miss Sorn of ASI persuades me (involuntarily on her part) that she believed that the infringing document would be a valuable marketing tool; and the exhibits to her deposition  documents written by her explaining this  are very effective in conveying that message. However, I realize that people engaged in sales promotion are inveterate chest-thumpers, given to hyperbole and military metaphors that are not to be taken literally. Although Miss Sorn appears to have persuaded herself that the infringing document would be a valuable marketing tool, that was no more than a prediction colored by a hope.
Deltak places a good deal of weight on the deposition of Miss Donnelly, who worked for Chemical Bank during the infringement period, when the bank signed a contract with ASI. She testified not only that she received the infringing document but that it was very important in Chemical Bank's decision to sign the contract. I give her deposition no weight, however, though not primarily because shortly after the events of October 1980 she went to work for Deltak. After first being deposed by the defendant and giving very weak evidence of any causal relationship between the infringing document and Chemical Bank's action, she was later redeposed by the plaintiff and strengthened her testimony. The defendant deposed her superior at Chemical Bank, Miss Miley, who gave credible and disinterested testimony completely contradicting Miss Donnelly's.
The rest of the deposition testimony, given by customers who received the infringing document, is that the document was not useful, they would have paid nothing for it, it did not influence their purchasing decisions. Deltak argues that the customers were afraid of being sued for copyright infringement if they admitted the full extent to which they had used the infringing document. It is true that to the extent they did use it they were themselves infringers, because copyright embraces the exclusive right to use as well as to sell the copyrighted material. But to be intimidated they would have had to fear that Deltak might actually sue them for copyright infringement. The idea that Deltak would sue some of its best customers in circumstances where it would be very difficult to prove damages from a particular customer's use of the infringing document strikes me as very remote, and I am sure would have struck Deltak's customers the same way. Nothing in any of the testimony suggests intimidation, and certainly not all of the deponents were intimidated. The one who was at once the most persuasive and the most helpful to the defendant, Mr. Boice, had at the time he gave his deposition left Hennepin County, Deltak's customer, to become a business school professor. He could not have feared that he or his employer would be sued for copyright infringement.
*408 Deltak's attack on the deponents' credibility is not entirely without foundation. Mr. Boice had some ill will towards Deltak. I nevertheless found his evidence credible. Carol Miller, while working for a customer of both Deltak and ASI, was a paid ASI consultant on the side. Whether she had a conflict of interest in a legal sense, her relationship with ASI undermined her credibility. But except for Donnelly and Miller I found the deponents credible.
Deltak also points out that Mr. Morris did not depose the actual contract signatories at the customer companies. Much of Deltak's cross-examination in the depositions consisted of asking the deponents, "Who else might have seen the infringing document in your company? Who else had signatory responsibility? Who were your superiors and peers?" But the people whom Mr. Morris deposed were prima facie reasonable people to question in reference to this litigation, because they had had custody of the infringing document and had returned it to Deltak. Maybe Mr. Morris pulled a fast one in picking Miss Miller, the ASI consultant, to depose, but I do not consider his choice of deponents to be so biased that I should disregard what they said. Deltak was free to depose other employees of these companies. In the course of the depositions Deltak's counsel collected a long list of names of other such employees who had potential access to the infringing document or a role in the contracting process. He could have deposed any of them; but if he did, the depositions were not placed in the record.
I was particularly impressed by one theme that ran throughout the deposition testimony. Clearly articulated by Messrs. Boice, Hoffman, Wankmuller, and Tufano, it is that the infringing document had little value because the thing copied, the CDS Task List, itself had little value. The evidence on this score is detailed and plausible and suggests the following hypothesis: Miss Sorn and others in ASI, having discovered from their customers that ASI's principal competitor, Deltak, had a task list as part of its marketing kit, and having received a suggestion from a customer (maybe more than one) that it would be useful to be able to key ASI's capabilities to the CDS Task List, conceived a scheme of doubtful lawfulness for getting a competitive edge on Deltak. Believing that the CDS was a valuable marketing tool they decided to purloin it and integrate it with their own library and use this marketing tool to clobber Deltak. But the deposition testimony suggests that Miss Sorn and the others misconceived the value of Deltak's CDS. The customers had made up their own task lists as they got more experience with he libraries of the various suppliers, and as a result they did not use the CDS Task List very much and therefore were not much interested in ASI's version of it.
The statistical portions of Dr. Kuehn's testimony were built around two exhibits, Plaintiff's Exhibits 11 and 17 (both reprinted at the end of this opinion). Exhibit 11 is a simple comparison of ASI's dollar revenues, by quarter, beginning with the first quarter of 1979 and ending with the second quarter of 1982, from the 15 companies (incorrectly described as 14 companies in Exhibits 11 and 17) that received the infringing document and from ASI's other customers. Dr. Kuehn directed my attention to the peak that occurs in the fourth quarter of 1980. This is the infringing period; although not all of the copies of the infringing document were retrieved until February 1981, no contracts with these customers were signed in January 1981. In the fourth quarter of 1980 ASI signed 7 contracts with 6 of the 15 companies that received the infringing document. (Actually one of the contracts was signed in the third quarter but Dr. Kuehn treated it as a fourth-quarter sale, as shall I though again wondering why Deltak could not have been more precise in its presentation of evidence.) The total dollar value of the contracts was $442,580. However, one of them, a $50,000 contract with Hennepin County, was signed before Hennepin County received the document. Dr. Kuehn conjectured, though without basis in the evidence, that the county signed in anticipation of receiving the document. I do not *409 believe that. Why would anyone spend good money in reliance on a promise to give him a document which, since it was already in existence, could have been handed over to him on the spot?
With Hennepin County excluded ASI's revenues from the group of 15 during the infringing period are $392,580. Dr. Kuehn did not and could not testify that all of these sales were due to the infringing document; even without it ASI would obviously have had some sales in the fourth quarter, especially since, as shown in Defendant's Exhibit 15-1 and (less clearly) in Plaintiff's Exhibit 11, ASI's sales tend to be bunched toward the end of the year. Dr. Kuehn made an effort to estimate what ASI's revenues from these customers would have been if the infringing document had not been distributed, but unfortunately he did not confine his estimate to the infringing period. (Deltak's post-trial brief contains such an estimate, but it comes too late; the trial is over.) Instead he projected ASI's revenues (ex-infringement) from the fourth quarter of 1980 through the second quarter of 1982, where the parties agreed to cut off ASI's damage liability. ASI's total revenues from the group of 15 customers (including Hennepin County) during this period was $1,074,000; and based on ASI's sales to these customers before the infringement Dr. Kuehn estimated that ASI would have sold them $444,694 worth of educational materials if it had not infringed. Dr. Kuehn thus ascribed to the infringement about 55 percent of ASI's sales to the 15 customers in the damage period.
His rationale for extending the damage period well after the recovery of all copies of the infringing document, a recall completed in February 1981, was various. He speculated that the document may have been shown to customers that we do not know about; that is possible, of course, but I cannot base my decision on assumptions that are neither self-evidently true nor have any evidentiary basis. He speculates more plausibly that once ASI signed up a customer with the help of the infringing document it had a better shot at contract renewals and upgradings thereafter. But he presented no evidence that would enable me to put a number on these lost revenues. Pulling a figure out of the air he said that ASI would continue to get $250,000 a year in residual revenues from the infringement even after the second quarter of 1982  indeed, forever. He acknowledged that such revenues might decay through time but he also said the effect of the infringement might be amplified through time, which I find incredible. He could have attempted to compute a decay rate for this marketing tool; there is a literature on the depreciation of advertising, see, e.g., Ayanian, Advertising and Rate of Return, 18 J. Law & Econ. 479 (1975), which could be extended to other methods of promotion. If he had done so, and discounted the estimated future profits of the infringement to present value, I would have given serious consideration to his testimony.
Somewhat more persuasively, Plaintiff's Exhibit 17 purports to show that beginning on October 1, 1980, and continuing until June 30, 1982, there was a quantum leap in the sales of ASI to the 15 customers who received the infringing document, compared to ASI's sales to its other customers. However, the same exhibit indicates that there was no decline in Deltak's sales to these 15 customers (or any of its other customers) during this period. This is extremely puzzling. Here is a marketing tool that we are told is focused on customers of Deltak. Its purpose was to take business away from Deltak, business Deltak had won through CDS, and shift it to ASI; but if you look at Exhibit 17 you will see that Deltak lost none of the business of these 15 customers, but instead sold more to them. ASI did do better after October 1, 1980, than before but how this could have been the result of a marketing tool whose raison d'etre was to take business away from a competitor that was unaffected by it is unexplained.
Dr. Blattberg tried to show that the anomaly in ASI's sales which Dr. Kuehn *410 had found in the infringement period was less than appeared. He did this primarily through a model which assumes (plausibly enough) that the amount of business an ASI customer can be expected to do with ASI is a function of its previous dealings with ASI; in particular, if the customer had a small contract with ASI in the past and then signs a new contract he can be expected in that contract to increase his purchases by a larger percentage than if his previous contract had been a big one. For the companies that signed during the infringement period (and a few months later, because Dr. Blattberg extended the sample so that he would have some more data to work with), Dr. Blattberg attempted to estimate from the size of their earlier contracts how much business they probably would have given ASI in the ordinary course even if nothing special had happened in that period. As a result of this statistical procedure he was able to explain all but 24 percent of the jump in ASI's sales to the 15 companies in the fourth quarter of 1980 (Defendant's Exh. 15-4).
Dr. Blattberg also made a computation that showed that in the period preceding the infringement the actual usage by ASI's customers of its educational materials was rising; and he suggested that this rising trend of usage could be expected to lead in the following period to the signing of additional contracts by these customers  they were contented customers, using more of the stuff, so presumably were more likely than others to sign additional contracts. This is some evidence that any otherwise unexplained growth in the fourth quarter of 1980 was attributable to other factors than infringement.
Dr. Blattberg also sponsored some internal ASI documents that tended to indicate that other competitive marketing methods had become effective at the same time that the infringement was committed. First, discounts were offered to ASI's large customers. Since the 15 customers who received the infringing document are all large customers while many of ASI's other customers are not large, the discounts would tend to boost sales to those 15 in relation to the other customers as a group. It is true that, depending on the price elasticity of demand for a seller's product, a discount may reduce rather than increase the seller's gross revenues from the product; it would reduce them for example if a 2 percent discount produced only a 1 percent increase in the quantity demanded of the product. No evidence was presented on the price elasticity of demand for ASI's or Deltak's teaching materials. But it is unlikely that ASI would cut price if it thought the result would be to sell a larger quantity (necessarily at higher cost) yet get less revenues for its efforts, so probably the discounts resulted in greater revenues (at least gross revenues) to ASI.
Second, ASI announced a price increase to take effect on November 1, 1980, and it suggested to its marketing representatives that they urge customers to sign up by October 31 to beat the increase. And of the 7 contracts signed during the infringement period 5 were signed in October. Since this inducement was available to all customers of ASI, it may appear irrelevant in explaining why sales to 15 customers grew more rapidly in this period than sales to other customers. But the fact that these were disproportionately large customers may have made them more sensitive to an impending price rise, as it would cost them more.
Third, during the infringement period ASI was offering an extra 2 percent commission to sales representatives for taking business away from a competitor and giving it to ASI; and ASI's primary competitor was Deltak.
Although all of these promotional devices were in effect throughout 1980, and not just in the fourth quarter, ASI's sales tend to be concentrated in the fourth quarter of the year, so presumably any inducements available over the whole year would have a special effect in that quarter. Dr. Blattberg opined that these three lawful marketing devices accounted for the otherwise unexplained growth in sales to the 15 customers who received the infringing document. *411 But his testimony did not add much to the documents themselves, which to the extent they speak to the issues in the case speak for themselves. It was unfortunate that the only live evidence with regard to the other marketing efforts was presented by Dr. Blattberg, who is not in ASI's marketing department and whose acquaintance with these documents is distinctly secondhand. Mr. Morris should have called a witness who could have presented more detailed information about what ASI did in the fourth quarter and who would have been subject to cross-examination.
I have now to decide whether Deltak has proved any damages and if so in what amount. I begin with the assumption that the only credible evidence of damages relates to the fourth quarter of 1980 and consists of the infringer's profits during that period. The question is how much of those profits would have accrued to ASI had it not created and circulated the infringing document.
The answer to a question that involves such uncertainty could depend on what the proper standard of proving damages in a copyright case is. One might be tempted to infer from section 504(c), the provision for statutory damages, that Congress did not want the courts to speculate about actual damages in a copyright case. For the plaintiff who cannot prove actual damages section 504(c) provides a statutory minimum that is generous by the standards of liquidated damages in federal statutes. But sometimes, despite all possible liberality by the court, a victim of copyright infringement will not be able to prove damages by the methods of litigation; and if the infringement is willful, section 504(c) allows the court to award the plaintiff a significant amount of money by analogy to general damages in defamation cases. It is unlikely therefore that section 504(c) was intended to upset a very long tradition in copyright (as in antitrust) cases that where a plaintiff has proved a wrong and the only issue is quantifying the damages from that wrong, the plaintiff is to be treated with liberality when it comes to resolving questions of fact. See Stevens Linen Assocs., Inc. v. Mastercraft Corp., supra, 656 F.2d at 14; Baldwin Cooke Co. v. Keith Clark, Inc., 420 F.Supp. 404, 407 (N.D.Ill.1976); cf. Story Parchment Co. v. Paterson Parchment Paper Co., 282 U.S. 555, 562-66, 51 S.Ct. 248, 250-52, 75 L.Ed. 544 (1931). There has to be some evidentiary basis for any award of damages other than statutory damages, but it does not have to be as solid as one would require if the issue were liability.
When the trial ended I was inclined to think that a substantial, though not overwhelming, fraction of the gross revenues of $392,580 obtained in the last quarter of 1980 by ASI from the 15 customers who received the infringing document was not in the ordinary course of business, but was due to a combination of the infringing document and the other special marketing methods that ASI was using then. I thought this fraction could not be more than 55 percent, the estimate implied by Dr. Kuehn's testimony, and that it might well be less than 24 percent, the estimate implicit in Dr. Blattberg's Exhibit 15-4. After translating gross into net revenues I ended up using a figure of close to 50 percent, and I assigned one quarter of that figure to the infringing document and the rest to the lawful marketing methods.
On reflection, I believe that in making this calculation I gave insufficient weight to the deposition testimony and to Deltak's sales during the infringement period as shown in Plaintiff's Exhibit 17. The overwhelming testimony that the infringing document was an ineffectual marketing tool, corroborated by the utter lack of impact on Deltak, its intended victim, makes it highly implausible that the infringement actually increased ASI's revenues. Its revenues from the 15 customers who received the document did rise in the infringement period to an extent not fully explained by any of the evidence presented at trial; but it would exceed the bounds of permissible speculation to base a damage award on the hypothesis that the infringing document boosted ASI's revenues, when *412 there is so little evidence to support the hypothesis and so much to refute it. Cf. Taylor v. Meirick, supra, 712 F.2d at 1122. Even if I thought that some benefit must have accrued to ASI from the infringement I would be unable to assign a dollar value to the benefit, because of Deltak's failure to apportion causal responsibility for ASI's expected sales increase between the infringement and the other factors at work during the period. Dr. Kuehn's 55 percent estimate relates to a period much longer than the infringement period. No evidence was presented that would enable me to determine how much of ASI's revenues during the infringement period could reasonably be attributed to the infringement.
Since my decision may be appealed and the court of appeals may disagree with my finding that Deltak has failed to prove that ASI's revenues rose because of the infringement, I shall go on and determine what percentage of the gross revenues attributable to the infringement (if there were any) are infringer's profits. The plaintiff is of course entitled only to the infringer's net revenues from infringement. However, as I noted earlier, once the plaintiff proves the defendant's gross revenues from infringement the burden shifts to the defendant to establish his own costs, which are then subtracted from gross revenues to yield profits.
On the basis of Mr. Wallack's testimony I conclude that the defendant proved that 52 percent of any contract revenues in the fourth quarter of 1980 were costs that should be subtracted from its gross revenues. As Mr. Wallack candidly admitted, the list of cost items that he testified to, which accounted in the aggregate for two-thirds of the revenues generated by the contracts, turned out to contain a good deal of cost data that for purposes of this case are fixed rather than variable costs. What is fixed and what is variable depends on the relevant time period. If, as I assume, all of ASI's infringement revenues were obtained over a three-month period, the only costs that would be relevant in deciding what profits ASI made on these contracts would be short-run variable costs, for those are the only costs it would have saved by not infringing. Taylor v. Meirick, supra, 712 F.2d at 1121. Most costs are variable in the long run, but in the short run, especially the very short run, most costs are not variable. So it is necessary to subtract from Mr. Wallack's estimates such things as depreciation and amortization of ASI's library, rent for warehousing tapes, interest, salaries of corporate marketing staff (who are not laid off and hired on the basis of what happens in a few months), and the accounting, legal, and other expenses that Mr. Wallack described as corporate overhead.
I asked Mr. Wallack to estimate the short-run variable-cost components in the revenue dollars allocable to these contracts, and he offered the following estimates, which I accept: 4.5 percent for variable cost of goods; 8.6 percent for royalties; 7 percent for distribution expense; 13 percent for sales commissions; and 19 percent for field sales expense. The total is 52.1 percent. This is a plausible figure; in a "knowledge" business such as Deltak and ASI are engaged in, a large part of a firm's costs are incurred in creating rather than reproducing its product, and those costs are fixed in the short run.
To summarize, I find that Deltak has failed to prove damages from the infringement. If I am wrong and some of ASI's revenues during the infringement period should be attributed to the infringement, I further find that 48 percent of those revenues represent profit to ASI. An appropriate judgment will be entered.
*413 
*414 
NOTES
[*]   Sitting by designation.
