BUTZNER, Circuit Judge:
In this antitrust case, Wilder Enterprises, Inc., a movie exhibitor, appeals from an order of the district court directing a verdict for three competing exhibitors and ten national film distributors at the close of Wilder’s evidence. Wilder charges that the appellees deprived it of first-run films and caused the closure of its theaters by entering into an agreement to allocate first-run films in violation of the Sherman Act. 15 U.S.C. §§ 1 and 1px solid var(--green-border)">2. Viewing the evidence and all reasonable inferences that can be drawn from it in the light most favorable to Wilder, we conclude that the judgment in favor of the three exhibitors and six of the distributors must be vacated. There is sufficient proof against them to warrant submission of the case to a jury.1 We affirm the judgment in favor of the other appellees.
I
The exhibitor appellees are General Cinema Corporation of Virginia, Inc. (General), American Multi-Cinema, Inc. (AMC), and ABC Southeastern (ABC). They are chain or circuit exhibitors who operate in many markets, including Norfolk-Virginia Beach.
The distributor appellees, whose judgments we affirm, are Allied Artists Pictures Corporation, American International Pictures, Inc., Avco Embassy Pictures Corporation, and Buena Vista Distribution Company, Inc. We vacate the judgments in favor of Columbia Pictures Industries, Inc., Paramount Pictures Corporation, Twentieth Century Fox Film Corporation, United Artists Corporation, Universal Film Exchange, Inc., and Warner Brothers Distributing Corporation. These companies are national distributors, who license first-run films by soliciting bids or offers to negotiate from exhibitors in specific geographic markets. Frequently, the distributors’ solicitation letters contain suggested minimum terms.
Wilder is an independent film exhibitor, who operated two theaters in the Norfolk-Virginia Beach market. Before 1971 it had no trouble acquiring first-run pictures from the distributors. Starting in 1971, however, Wilder’s efforts to obtain films met with less success although it continued to bid or negotiate as it had in the past. During 1971 and 1972 Wilder realized that its efforts to rent first-run films were futile. As a result, it responded to the distributors’ solicitations less frequently and began showing x-rated movies. From 1973 until its theaters closed in 1975, only one film distributed by an appellee was licensed to its Norfolk-Virginia Beach theaters.
Wilder attributes the failure of its theaters to an agreement by the circuit exhibitors, ABC, AMC, and General to allocate among themselves the right to bid or negotiate for films offered by the distributors and to the participation of the distributors in this division of the market. This type of agreement is commonly known as a split or split of product. After initial denials, the exhibitors stipulated to the existence of the split and the method of its operation. The stipulation disclosed that periodically the exhibitors met and decided on the basis of rotation which of the three would bid or negotiate for a specific picture; the other two would refrain from competing.
[1140]*1140Both the exhibitors and the distributors contend that the evidence is insufficient to establish either that the distributors participated in the split or that the split infringed on Wilder’s opportunity to compete. These contentions, which were sustained by the district court, are critical, and the following brief summary of the law pertaining to splits will place them in perspective.
Film distributors are free to refuse to license films to any exhibitor when their decisions are based on independent business judgment. United States v. Colgate, 250 U.S. 300, 307, 39 S.Ct. 465, 468, 63 L.Ed. 992 (1919); Lamb’s Patio Theatre v. Universal Film Exchanges, 582 F.2d 1068 (7th Cir. 1978). Moreover, an exhibitor does not have a claim against other film exhibitors who, without distributor involvement, “split” the films they will bid on. Seago v. North Carolina Theatres, Inc., 42 F.R.D. 627 (E.D.N.C.1966), aff’d per curiam, 388 F.2d 987 (4th Cir. 1967). Accord, Admiral Theatre Corp. v. Douglas Theatre Co., 585 F.2d 877 (8th Cir. 1978); Dahl, Inc. v. Roy Cooper Co., 448 F.2d 17 (9th Cir. 1971); Viking Theatre Corp. v. Paramount Film Distributing Corp., 320 F.2d 285 (3d Cir. 1963), aff’d per curiam by an equally divided court, 378 U.S. 123, 84 S.Ct. 1657, 12 L.Ed.2d 743 (1964); Brown v. Western Massachusetts Theatres, Inc., 288 F.2d 302 (1st Cir. 1961); Royster Drive-In Theatres v. American Broadcasting-Paramount Theatres, Inc., 268 F.2d 246 (2d Cir. 1959).
An exhibitor has a cause of action when distributors participate in the split and deny the exhibitor access to films. Such an arrangement creates an impermissible horizontal conspiracy among the exhibitors operating the split and a vertical conspiracy between them and the participating distributors. It is a type of group boycott that violates the antitrust laws. Klor’s v. Broadway-Hale Stores, 359 U.S. 207, 79 S.Ct. 705, 3 L.Ed.2d 741 (1959). See Dahl, Inc. v. Roy Cooper Co., 448 F.2d 17,19 (9th Cir. 1971); II E. Kintner, Federal Antitrust Law §§ 10.27-31 (1980). In short, Wilder must show that it was denied the opportunity to obtain films enjoyed by ABC, AMC, and General because the distributors participated in the split.
Only one independent exhibitor, K. W. Andrews, participated in the split. His complaint about his inability to get first-run pictures induced an officer of AMC to invite him to a meeting of the exhibitors engaged in the split. Although Andrews attended a number of meetings, he was not allowed to bid for exclusive licenses. Rather, he was permitted to bid on a day and date basis for any picture AMC got in the split.2 ABC and General declined to allow Andrews to play day and date any pictures they received in the split.
Andrews testified at length about the distributors’ involvement in the split. At one of the meetings, an AMC employee called a Universal official to check on the license terms Universal was requesting for High Plains Drifter. Universal had not yet sent bid solicitation letters to exhibitors in the market. The AMC employee stated that he had received the film in the split and asked if Andrews could play the picture day and date with AMC.
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BUTZNER, Circuit Judge:
In this antitrust case, Wilder Enterprises, Inc., a movie exhibitor, appeals from an order of the district court directing a verdict for three competing exhibitors and ten national film distributors at the close of Wilder’s evidence. Wilder charges that the appellees deprived it of first-run films and caused the closure of its theaters by entering into an agreement to allocate first-run films in violation of the Sherman Act. 15 U.S.C. §§ 1 and 1px solid var(--green-border)">2. Viewing the evidence and all reasonable inferences that can be drawn from it in the light most favorable to Wilder, we conclude that the judgment in favor of the three exhibitors and six of the distributors must be vacated. There is sufficient proof against them to warrant submission of the case to a jury.1 We affirm the judgment in favor of the other appellees.
I
The exhibitor appellees are General Cinema Corporation of Virginia, Inc. (General), American Multi-Cinema, Inc. (AMC), and ABC Southeastern (ABC). They are chain or circuit exhibitors who operate in many markets, including Norfolk-Virginia Beach.
The distributor appellees, whose judgments we affirm, are Allied Artists Pictures Corporation, American International Pictures, Inc., Avco Embassy Pictures Corporation, and Buena Vista Distribution Company, Inc. We vacate the judgments in favor of Columbia Pictures Industries, Inc., Paramount Pictures Corporation, Twentieth Century Fox Film Corporation, United Artists Corporation, Universal Film Exchange, Inc., and Warner Brothers Distributing Corporation. These companies are national distributors, who license first-run films by soliciting bids or offers to negotiate from exhibitors in specific geographic markets. Frequently, the distributors’ solicitation letters contain suggested minimum terms.
Wilder is an independent film exhibitor, who operated two theaters in the Norfolk-Virginia Beach market. Before 1971 it had no trouble acquiring first-run pictures from the distributors. Starting in 1971, however, Wilder’s efforts to obtain films met with less success although it continued to bid or negotiate as it had in the past. During 1971 and 1972 Wilder realized that its efforts to rent first-run films were futile. As a result, it responded to the distributors’ solicitations less frequently and began showing x-rated movies. From 1973 until its theaters closed in 1975, only one film distributed by an appellee was licensed to its Norfolk-Virginia Beach theaters.
Wilder attributes the failure of its theaters to an agreement by the circuit exhibitors, ABC, AMC, and General to allocate among themselves the right to bid or negotiate for films offered by the distributors and to the participation of the distributors in this division of the market. This type of agreement is commonly known as a split or split of product. After initial denials, the exhibitors stipulated to the existence of the split and the method of its operation. The stipulation disclosed that periodically the exhibitors met and decided on the basis of rotation which of the three would bid or negotiate for a specific picture; the other two would refrain from competing.
[1140]*1140Both the exhibitors and the distributors contend that the evidence is insufficient to establish either that the distributors participated in the split or that the split infringed on Wilder’s opportunity to compete. These contentions, which were sustained by the district court, are critical, and the following brief summary of the law pertaining to splits will place them in perspective.
Film distributors are free to refuse to license films to any exhibitor when their decisions are based on independent business judgment. United States v. Colgate, 250 U.S. 300, 307, 39 S.Ct. 465, 468, 63 L.Ed. 992 (1919); Lamb’s Patio Theatre v. Universal Film Exchanges, 582 F.2d 1068 (7th Cir. 1978). Moreover, an exhibitor does not have a claim against other film exhibitors who, without distributor involvement, “split” the films they will bid on. Seago v. North Carolina Theatres, Inc., 42 F.R.D. 627 (E.D.N.C.1966), aff’d per curiam, 388 F.2d 987 (4th Cir. 1967). Accord, Admiral Theatre Corp. v. Douglas Theatre Co., 585 F.2d 877 (8th Cir. 1978); Dahl, Inc. v. Roy Cooper Co., 448 F.2d 17 (9th Cir. 1971); Viking Theatre Corp. v. Paramount Film Distributing Corp., 320 F.2d 285 (3d Cir. 1963), aff’d per curiam by an equally divided court, 378 U.S. 123, 84 S.Ct. 1657, 12 L.Ed.2d 743 (1964); Brown v. Western Massachusetts Theatres, Inc., 288 F.2d 302 (1st Cir. 1961); Royster Drive-In Theatres v. American Broadcasting-Paramount Theatres, Inc., 268 F.2d 246 (2d Cir. 1959).
An exhibitor has a cause of action when distributors participate in the split and deny the exhibitor access to films. Such an arrangement creates an impermissible horizontal conspiracy among the exhibitors operating the split and a vertical conspiracy between them and the participating distributors. It is a type of group boycott that violates the antitrust laws. Klor’s v. Broadway-Hale Stores, 359 U.S. 207, 79 S.Ct. 705, 3 L.Ed.2d 741 (1959). See Dahl, Inc. v. Roy Cooper Co., 448 F.2d 17,19 (9th Cir. 1971); II E. Kintner, Federal Antitrust Law §§ 10.27-31 (1980). In short, Wilder must show that it was denied the opportunity to obtain films enjoyed by ABC, AMC, and General because the distributors participated in the split.
Only one independent exhibitor, K. W. Andrews, participated in the split. His complaint about his inability to get first-run pictures induced an officer of AMC to invite him to a meeting of the exhibitors engaged in the split. Although Andrews attended a number of meetings, he was not allowed to bid for exclusive licenses. Rather, he was permitted to bid on a day and date basis for any picture AMC got in the split.2 ABC and General declined to allow Andrews to play day and date any pictures they received in the split.
Andrews testified at length about the distributors’ involvement in the split. At one of the meetings, an AMC employee called a Universal official to check on the license terms Universal was requesting for High Plains Drifter. Universal had not yet sent bid solicitation letters to exhibitors in the market. The AMC employee stated that he had received the film in the split and asked if Andrews could play the picture day and date with AMC. Andrews talked with the Universal official who asked him if he had “been allowed in.” When Andrews gave an affirmative response, the official said Andrews would be allowed to play the film day and date with AMC if he could satisfy the $5,000 requested guarantee. Subsequently, when Universal sent its bid solicitation letter to all exhibitors in the market, it offered to license the film on a day and date basis. Eventually, it was licensed on those terms to AMC and Andrews. When Andrews participated in the split, bid solicitation letters for films split to AMC allowed offers to exhibit the film on a day and date basis.
The exhibitors also called distributors during split meetings to verify the release dates of pictures under consideration. If Andrews missed a split meeting, he would sometimes call the distributors to find out [1141]*1141what films he had received in the split. Occasionally, the distributors would call him with the information. These conversations took place before bid solicitations were sent to all of the exhibitors in the market. On one such occasion an employee of Fox called Andrews to tell him that he and AMC had received Towering Inferno in the split and that the guarantee would be $50,000. Andrews said that he wasn’t positive he could pay the guarantee. Fox then sent out a solicitation letter offering to license the picture on a day and date basis. Andrews was told by a Fox employee that if he couldn’t pay the suggested guarantee, the picture would be licensed to AMC. When Andrews couldn’t furnish the guarantee, the bid solicitation was withdrawn and reissued on an exclusive basis. Fox licensed the picture to AMC alone. On another occasion, a Columbia employee informed Andrews, prior to the solicitation letter on The Last Detail, that Andrews and AMC had received that picture in the split. Andrews said that he could play the picture, and it was licensed to Andrews and AMC.
Another example of distributor participation in the split involved The Man With a Golden Gun. Prior to the time the bid solicitation was circulated, Andrews called an employee of United to inquire whether AMC got the picture and to inform him that Andrews was to play day and date. The employee said AMC had the picture and told Andrews the specifics as to play date, percentages, and hold over. United subsequently licensed the film to AMC and Andrews.
Andrews brought another independent exhibitor, Schoenfeld, to a split meeting, but the exhibitors objected to his participation. Schoenfeld also gave evidence of distributor participation in the split. He testified that he had called a Fox employee to ask about the availability of a picture, and the employee responded that he wasn’t sure when the picture would be available, but he would know after the next meeting of the “Norfolk Surgical Society.”
Schoenfeld testified that after he had been excluded from the split, “I received no first-run product. There was no way I could receive a product the way the system was operated.”
We conclude that this evidence was sufficient to submit to the jury the issue of the existence of a conspiracy among ABC, AMC, General, Columbia, Fox, Paramount, United Artists, Universal, and Warner to violate the Act. Factual differences distinguish this case from Seago v. North Carolina Theatres, Inc., 42 F.R.D. 627 (E.D.N.C. 1966), aff’d per curiam, 388 F.2d 987 (4th Cir. 1967), and Admiral Theatre Corp. v. Douglas Theatre Co., 585 F.2d 877 (8th Cir. 1978). In Seago there was no evidence of the distributors’ knowledge of the split. In Admiral, although the distributors knew of the split, they did not participate in it. Here, in contrast, there is direct and circumstantial evidence that these distributors participated in the split by subsequently circulating letters soliciting bids in conformity with the arrangements derived from the split. Most of the films were then licensed as split. This case also differs from Viking Theatre Corp. v. Paramount Film Distributing Corp., 320 F.2d 285 (3d Cir. 1963), where the court emphasized: “There is no evidence that any exhibitor requesting participation in the split of product would have been excluded.” 320 F.2d at 293. Here, to the contrary, there is evidence that ABC, AMC, and General split the product among themselves and excluded others.
On cross examination Andrews testified that he had no knowledge of any agreement among the distributors to: (1) discriminate against any exhibitor; (2) maintain or raise minimum license fees; (3) select theaters for licensing; or (4) conduct sham bidding.
Andrews’s lack of knowledge about any agreement to violate the Act does not preclude submission of the issue to the jury. Rarely can a formal agreement among alleged conspirators be established, and proof of its existence is not essential. Frey & Son v. Cudahy Packing Co., 256 U.S. 208, 41 S.Ct. 451, 65 L.Ed. 892 (1921); Unit[1142]*1142ed States v. Paramount Pictures, Inc., 334 U.S. 131, 142, 68 S.Ct. 915, 922, 92 L.Ed. 1260 (1948). Andrews was cautioned by the district court not to testify about any conclusions he drew from the facts. A jury, however, is not similarly constrained. It is their function to draw reasonable inferences from the facts. Evidence of the course of dealing by the three exhibitors who operated the split and the distributors who participated with them is sufficient, if accepted by the jury, to establish the existence of a conspiracy to restrain and monopolize commerce in violation of the Act. Norfolk Monument Co., Inc. v. Woodlawn Memorial Gardens, Inc., 394 U.S. 700, 704, 89 S.Ct. 1391, 1393, 22 L.Ed.2d 658 (1969); American Tobacco Co. v. United States, 328 U.S. 781, 809-10, 66 S.Ct. 1125, 1138-39, 90 L.Ed. 1575 (1946).
There is neither direct nor circumstantial evidence that Allied, American, Avco, and Buena Vista participated in the split.
II
The second element Wilder must prove is that the split directly injured its business. Admiral Theatre Corp. v. Douglas Theatre Co., 585 F.2d 877, 893 (8th Cir. 1978). We conclude that the evidence was sufficient to submit this issue to the jury. Most first-run films were licensed as split. Independent exhibitors were excluded from the split and denied access to many of these films. After the split started in 1971, Wilder had difficulty obtaining these films, its profits decreased, and eventually its theaters closed.
The exhibitors and distributors attribute loss of Wilder’s theaters to Wilder’s mismanagement and its switch to x-rated films. Although this defense may justify a verdict against Wilder, it is insufficient to remove the case from the jury.
III
A fair measure of an exhibitor’s damages is the loss of its receipts attributable to an unlawful distribution system. Bigelow v. RKO Radio Pictures, 327 U.S. 251, 262-63, 66 S.Ct. 574, 578-79, 90 L.Ed. 652 (1946). Three theories have been recognized for calculating damages. Under the demand theory, the exhibitor may calculate its damages by showing the profit it would have made on pictures it sought, but which were denied by the split, less the profit it made on the pictures it actually ran. Secondly, the exhibitor may show that it would have been futile to seek pictures allocated by the split. Its damages can be measured by comparing the exhibitor’s receipts with the receipts of a comparable theater operated by a participant in the split. Finally, the exhibitor can establish its damage by showing the diminution in value of its business property. These theories are not mutually exclusive. The jury may not speculate, but, acting upon probabilities and inferences it may base its verdict on a just and reasonable estimate derived from relevant data. See Bigelow v. RKO Pictures, 327 U.S. 251, 257-66, 66 S.Ct. 574, 576-580, 90 L.Ed. 652 (1946); Admiral Theatre Corp. v. Douglas Theatre Co., 585 F.2d 877, 893-96 (8th Cir. 1978).
Wilder proceeded on all three theories, but it relied primarily on futility. The district court erred in its analysis of this theory of damages. It held: “[T]o rely on the futility theory, plaintiff must show it made superior bids or offered superior terms for films which were rejected and licensed pursuant to inferior bids.” This ruling is more appropriate for the demand theory than the futility theory. An exhibitor can show futility in the manner outlined by the court, but we have found no authority that establishes this as the sole proof of futility. Here, Wilder introduced direct evidence that independents were denied access to first-run films by the split. It was this predicament that impelled Andrews to beg to be allowed to participate in the split even if only on restricted terms. Schoenfeld’s testimony that he could not get first-run films the way the system was operated is additional proof of futility. From all of this evidence, a jury could infer that Wilder’s bidding also would have been futile. Furthermore, when Wilder confronted several distributors demanding to know wheth[1143]*1143er successful bidders were guaranteeing the large sums specified in solicitations to bid, he received no answers. The distributor’s silence does not, contrary to Wilder’s contention, prove the existence of sham bidding, but it is relevant in determining whether Wilder’s concern about the futility of bidding was 'justified, or whether it failed to bid, as the exhibitors and distributors contend, because of mismanagement.
Having presented sufficient evidence of futility, Wilder should be allowed to compute his damages under this theory, and on remand the issue should be submitted to the jury. It is hardly necessary for us to observe that Wilder can present evidence under other theories, but there can be only one recovery.
IV
Because the case must be retried, we will address a number of other errors assigned by Wilder.
For reasons adequately explained by the district court, we find no error in its refusal to toll the statute of limitations. The court, however, should have allowed discovery about the split in 1971 and 1972 even though these years preceded the limitation period. This evidence is relevant to the issues of conspiracy and futility. For the same reason, the court should admit evidence about Jaws which was proffered to establish the split’s involvement in sham bidding.
The court excluded a stipulated list of films that were split because Wilder had not shown distributor participation in the split. Since we have concluded that evidence of this conduct was presented, the stipulation should be admitted. It is clearly relevant to the pervasiveness of the split and to provide underlying data for the application of the futility theory.
The court did not err in limiting, under the demand theory, Wilder’s proof to the 23 films he listed in an interrogatory. This limitation of proof is not, however, appropriate with respect to the futility theory, which, as we have pointed out, does not require proof of demand or. the denial of any specific film.
The court did not abuse its discretion by excluding Variety Magazine ratings of films Wilder played after the split unless it produced the ratings of films it played before the split.
The court should not have excluded the testimony of Wilder’s experts. The first, president of the National Independent Theaters’ Exhibitors’ Association, had operated his own theaters and studied splits in at least a dozen marketing areas. He was prepared to testify that ABC, AMC, and General were among the top five circuit exhibitors in the country and to offer the opinion that a split could not operate successfully without the participation of distributors. The district court excluded his testimony, primarily because the witness was not familiar with “trade highway traffic patterns, shopping habits, or anything else” in the Norfolk-Virginia Beach market.
There was no evidence that splits operated by large circuit exhibitors and national distributors would differ essentially because of geographic location. The witness qualified under Rule 702 of the Federal Rules of Evidence because his testimony would help the jury understand the intricacies of film distribution and the nature and effects of splits, subjects which are not common knowledge. As the advisory committee noted, “an intelligent evaluation of facts is often difficult or impossible without application of . . . specialized knowledge. The most common source of this knowledge is the expert witness ....” Rule 702, Advisory Committee’s Note. The witness’s testimony was relevant, Rule 402, and it satisfied the requirement of Rule 703.
The second expert whose testimony was excluded was an economist who was called on the issue of damages. This witness admitted he was not an expert in local real estate values. No local realtor was called to furnish underlying facts for the expert’s calculations, and no alternative showing, as required by Rule 703, was made [1144]*1144that the underlying data mentioned by the expert about local values was of a type reasonably relied on by other experts in the field. Accordingly, the district court did not err in excluding his testimony about diminution in the value of Wilder’s property. On the other hand, the expert’s testimony about the losses sustained by Wilder was admissible, especially in view of the evidence of futility. Contrary to the district court’s observations, proof of an exhibitor’s damages in an antitrust case is not so simple that a jury should be deprived of expert testimony. Calculation of damages is inherently difficult because it requires an estimation of gross receipts that were, in fact, never received. The asserted fallibility of the expert’s assumptions affected the weight of his testimony, not its admissibility. See Terrell v. Household Goods Carriers’ Bureau, 494 F.2d 16, 22-25 (5th Cir. 1974).
We find no abuse of discretion in the court’s exclusion of testimony that was simply cumulative to proof supplied by stipulation.
The court did not err in refusing to allow Wilder to contradict its answer to an interrogatory about house expenses on which the defendants had relied. Since the case must be retried, Wilder should be afforded an opportunity to clarify the difference between actual house expenses and “sliding scale” house expenses as used in the industry for bidding purposes and to supplement his answer by showing both figures. The element of unfair surprise to the defendants has been removed by the passage of time and events, and confusion over the house expenses should be dispelled.
The judgments in favor of Allied, American, Avco, and Buena Vista are affirmed, and they shall recover their costs against Wilder.
The judgments in favor of ABC, AMC, General, Columbia, Fox, Paramount, United Artists, Universal, and Warner are vacated, and the case is remanded for trial. Wilder, having substantially prevailed, shall recover his costs against these appellees.
AFFIRMED IN PART, VACATED IN PART, AND REMANDED.