CLEVENGER, Circuit Judge.
This is a patent infringement suit in which Michael L. McGinley charges Franklin Sports, Inc. (“FSI”) with willful infringement of claims 1, 2, 6, and 7 of U.S. Patent No. 5,407,193 (“the '193 patent”). On summary judgment, the United States District Court for the District of Kansas ruled in favor of McGinley on the issue of infringement, and the case proceeded to [1343]*1343trial on the issues of validity and willfulness. The jury found that the asserted claims were not invalid and were willfully infringed. On a subsequent motion filed by FSI for judgment as a matter of law (“JMOL”), the trial court set aside the jury verdict on validity, holding that the asserted claims of the '193 patent are invalid as obvious pursuant to 35 U.S.C. § 103(a).
McGinley appeals the district court’s grant of JMOL of invalidity and the earlier denial of McGinley’s motion for leave to amend the complaint to join his business, S.C. Products, Inc. (“SCP”), as an additional plaintiff. On cross-appeal, FSI challenges the district court’s grant of summary judgment in favor of McGinley on infringement and the denial of its motion for a new trial on willfulness.
Because we conclude that the district court erred in finding that no reasonable jury could have reached a verdict of non-obviousness, we reverse the JMOL of invalidity. We affirm the district court’s rulings in all other respects.
I
Background
The application for the '193 patent was filed on July 3, 1991, and the patent issued on April 18, 1995. In general terms, the '193 patent discloses and claims an instructional pitching device in the form of a regulation baseball with specific “finger placement indicia” for teaching students how to grasp a baseball for throwing different types of pitches. With the endorsement of a famous professional baseball pitcher, McGinley’s invention was marketed and distributed as the Roger Clemens Instructional Baseball (“RCIB”). FSI also manufactured and sold a baseball designed to teach students to throw different types of pitches. The accused device in this case, the Franklin Pitch Ball Trainer 2705 (“FSI’s 2705 baseball”), was sold in the United States from at least as early as April 1995 to March 1999.
In the preferred embodiment of the claimed invention, an aspect of which is illustrated in the following figure, three sets of finger placement indicia 11 are positioned on the cover 17 of a regulation baseball 10. Each set of indicia 11 is intended to illustrate the placement of a student pitcher’s index and middle fingers so as to throw a particular type of pitch (e.g., two-seam fast ball, slider, curve ball, etc.).
[1344]*1344[[Image here]]
Indicia 11 are presented in two sizes, to allow the indicia intended for a left-handed student to be easily distinguished from the indicia intended for a right-handed student. The smaller indicia, exemplified by indicia 24 and 26, are intended for use by left-handed pitchers, while the larger indi-cia, as represented by indicia 20 and 22, are intended for use by right-handed pitchers. Moreover, indicia 11 are coded by coloring all indicia which are representative of a certain type of pitch in one color and indicia representative of another type of pitch in a different color. To further assist a student in learning how to throw a particular pitch, the indicia are shaped so as to indicate the relationship of the palm of the hand in grasping the ball. Specifically, the portion of each “egg-shaped” in-dicium to be situated closest to the palm is slightly tapered so as to indicate the correct orientation of the baseball in the palm. Although the preferred embodiment of the '193 patent makes no provisions for “thumb placement indicia,” the written description of the '193 patent repeatedly states that the thumb is generally to be positioned on the baseball at a location opposite the corresponding set of finger placement indicia.
As originally filed in 1991, the claims of the '193 patent required that eight sets of finger placement indicia be provided on a single baseball pitching training device. Specifically, the four original claims all required the presence of indicia demarcating the placement of fingers for four specific types of pitches (ie., curve ball,- two-seam fast ball, slider, and four-seam fast ball), for both left-handed and right-handed students. These claims were rejected on obviousness grounds in view of U.S. Patent No. 2,925,273 (“Pratt”), which had issued on February 16, 1960, more than thirty years before McGinley’s filing date. Pratt was brought to the attention of the Patent and Trademark Office (“PTO”) via an Information Disclosure Statement (“IDS”) filed concurrently with McGinley’s priority patent application by McGinley’s counsel.
Like the claims originally filed by McGinley, Pratt disclosed, inter alia, a conventional baseball having multiple sets of finger placement indicia for teaching baseball players to throw different types of pitches. Specifically, in the embodiment illustrated in Figure 4 (shown below), [1345]*1345Pratt’s written description disclosed the placement of finger and thumb placement indicia for three types of pitches (ie., fast ball, curve ball, and screw ball). Equatorial band 17 was an important feature of Pratt’s claimed invention. When a student threw Pratt’s baseball correctly, bands of complementary colors in the equatorial band would blend into a single color to provide a visual indication to the student that the ball had been thrown with proper rotation.
[[Image here]]
Although the similarities between Pratt’s disclosure and McGinley’s then-existing claims are striking, there are also a few differences between Pratt’s teachings and McGinley’s initially claimed invention. First, Pratt did not provide for different sets of indicia on a single ball for distinguishing between left-handed and right-handed students. Also, Pratt’s finger placement indicia were described and illustrated as being circular, but “phantom lines” illustrating the placement of fingers 21, 22 and thumb 23 were included in the patent figures. These phantom lines, however, are not described in Pratt as actual markings on the baseball. In contrast, the finger placement indicia in the preferred embodiment of McGinley’s invention are actually marked on the ball, and are “egg-shaped” and slightly tapered at one end to indicate the proper orientation of the ball with respect to the student’s palm.
Another prior art reference which was brought to the attention of the PTO via McGinley’s IDS was U.S. Patent No. 3,110,494 (“Morgan”), which issued on November 12, 1963. In contrast to Pratt and the '193 patent, which are based on using a conventional regulation baseball, Morgan describes a baseball training device using a lightweight and inexpensive baseball “replica” fabricated in the form of plastic or metallic hemispherical shells which occupy a minimum of space before use, but which can be easily assembled by gluing the two hemispherical halves together. In Figure 6 of Morgan (shown below) and the accompanying written description, a single set of finger-shaped marks D", E", and L" (for teaching proper placement of the forefinger, middle finger, and thumb, respectively) are provided on the baseball training device to teach a student how to throw a baseball with a particular curve or break.
Throughout the prosecution history of the '193 patent, McGinley’s claims at issue in this case were rejected in view of Pratt on anticipation grounds. With respect to [1346]*1346Morgan, although this reference was before the PTO during the entire pendency of McGinley’s patent application, it was never explicitly relied upon as a basis for a rejection based on a prima facie case of anticipation or obviousness.
Ultimately, in 1995, after a series of rejections, amendments, and responses (including a partially successful appeal to the Board of Patent Appeals and Interferences and the filing of a continuation application), the '193 patent issued with 14 claims. Ten of the issued claims {i.e., claims 3-5 and 8-14) explicitly retain the original limitation requiring the inclusion of finger placement indicia on a single baseball pitching training device for both left-handed and right-handed students. These claims were not asserted in this case. Instead, McGinley asserted the remaining four claims {ie., independent claim 1 and dependent claims 2, 6, and 7) against FSI, alleging willful infringement by making and selling the 2705 baseball. The asserted claims read as follows in their entirety:
1. A baseball pitching training device for duplicating finger placement on a baseball by a student comprising:
a baseball cover;
a plurality of sets of finger placement indicia on said cover, said sets of indi-cia comprising:
a first set of indicia demarcating the placement of finger [sic] for throwing a first pitch;
a second set of indicia demarcating the placement of fingers for throwing, [sic] a second pitch;
a third set of indicia demarcating the placement of fingers for throwing a third pitch;
means for indicating the orientation of the baseball relative to the palm of the hand; and means for coding said finger placement indicia sets for identification of each of said indicia associated with any one of said sets.
2. The device as claimed in claim 1 wherein said means for coding comprises a color for association with each indi-cia of a particular set.
6. The device as claimed in claim 1, wherein said means for indicating orientation comprises shaping said indicia to distinguish that portion of the baseball to be located proximate to the palm of the hand.
7. The device as claimed in claim 1 wherein said indicia are shaped to indicate a correct orientation of the baseball with respect to the palm of the hand.
'193 patent, col. 5, ll. 29-48; col. 5, ll. 61-64; col. 6, ll.1-3.
The district court held a Markman hearing on January 21, 1999, and issued an order construing the disputed claims of the '193 patent shortly thereafter. McGinley v. Franklin Sports, Inc., 45 F.Supp.2d 1141 (D.Kan.1999) (McGinley I). On cross-appeal, FSI challenges only the district court’s interpretation of the claimed “means for indicating the orientation of the baseball relative to the palm of the hand.” The district court construed the term as a means-plus-function limitation pursuant to 35 U.S.C. § 112, ¶ 6, and concluded that the corresponding structure included “a slight taper at the portion of each indicia situated closest to the palm of the hand, and any equivalents of such structure.” Id. at 1146. FSI’s position on appeal is that the claim limitation is not entitled to any range of equivalents whatsoever.
Based on its claim interpretation, the district court granted McGinley’s motion for partial summary judgment on the issue of infringement on October 28, 1999. McGinley v. Franklin Sports, Inc., 75 F.Supp.2d 1218, 1224-25 (D.Kan.1999) [1347]*1347(McGinley II). At the same time, however, the district court denied FSI’s motion for partial summary judgment on validity, id. at 1225-32, finding disputed issues of material fact with respect to the obviousness issue. The case proceeded to trial, and on January 19, 2000, the jury returned a verdict in favor of McGinley, finding the '193 patent not invalid and willfully infringed.
FSI then filed a post-trial motion, seeking JMOL on the issues of validity and willfulness. In the alternative, FSI also moved for a new trial. On April 5, 2000, the district court set aside the jury’s verdict and granted FSI’s motion for JMOL on invalidity, concluding that “as a matter of law, plaintiffs patent is invalid as obvious in light of Pratt or the combination of Pratt and Morgan.” Judgment was entered in favor of FSI, and this appeal followed, vesting us with jurisdiction pursuant to 28 U.S.C. § 1295(a)(1).
II
Claim Interpretation
As the first step of the infringement and validity analyses in this case, we resolve any claim interpretation disputes on appeal, without deference to the district court. Amazon.com, Inc. v. Barnesandnoble.com, Inc., 239 F.3d 1343, 1351, 57 USPQ2d 1747, 1751-52 (Fed.Cir.2001); Cybor Corp. v. FAS Techs., Inc., 138 F.3d 1448, 1456, 46 USPQ2d 1169, 1174-75 (Fed.Cir.1998) (en banc); Markman v. Westview Instruments, Inc., 52 F.3d 967, 979, 34 USPQ2d 1321, 1329 (Fed.Cir.1995) (en banc), aff'd, 517 U.S. 370, 116 S.Ct. 1384, 134 L.Ed.2d 577, 38 USPQ2d 1461 (1996).
The only claim interpretation dispute remaining on appeal concerns the limitation in all of the asserted claims requiring “means for indicating the orientation of the baseball relative to the palm of the hand.” There is no dispute that this term should be construed as a means-plus-function limitation pursuant to 35 U.S.C. § 112, ¶ 6, and that the claimed function is “indicating the orientation of the baseball relative to the palm of the hand.” The only dispute on appeal concerns identification of the corresponding structure.
The district court ruled that the corresponding structure included egg-shaped indicia having “a slight taper at the portion of each indicia situated closest to the palm of the hand, and any equivalents of such structure.” McGinley I at 1146. In contrast, FSI’s position is that the claim limitation is not entitled to any range of equivalents whatsoever, on the basis that the written description of the '193 patent discloses only egg-shaped indicia with tapered ends, and that undisclosed equivalents cannot be construed to be within the scope of a patent claim. In support for its position, FSI points out that the only orientation means explicitly described in the '193 patent is a slight taper to the finger placement indicia, which are to be understood as being shaped in the form of egg-shaped ovals by inspecting the figures of the '193 patent:
To further assist the student the indicia are shaped so as to indicate the relationship of the palm of the hand in grasping the ball. The portion of each indicia intended to be situated closest to the palm is slightly tapered thereby to assist the student in achieving correct orientation of the ball in the palm.
%'193 patent, col. 5, ll.16-22.
FSI’s argument on this point is wholly without merit, for it misunderstands the statute. Drafters of means-plus-function claim limitations are statutorily guaranteed a range of equivalents extending beyond that which is explicitly disclosed in the patent document itself:
[1348]*1348An element in a claim for a combination may be expressed as a means or step for performing a specified function without the recital of structure, material, or acts in support thereof, and such claim shall be construed to cover the corresponding structure, 'material, or acts described in the specification and equivalents thereof
35 U.S.C. § 112, ¶6 (1994) (emphasis;added). We therefore affirm the .district court’s claim construction.
Ill
Infringement
This brings us to FSI’s cross-appeal from the district court’s grant of McGinley’s motion for summary judgment of infringement. At the summary judgment stage, the district court compared the asserted claims of the '193 patent as they had been construed in McGinley I to undisputed evidence concerning FSI’s 2705 baseball. In the accused FSI 2705 baseball, the finger placement indicia are in the shape of finger-like outlines that are blunted at the end furthest from the fingertips.
Summary judgment is appropriate “if the pleadings, depositions, answers to interrogatories, and admissions on file, together with the affidavits, if any, show that there is no genuine issue as to any material fact and that the moving party is entitled to a judgment as a matter of law.” Fed.R.Civ.P. 56(c). For purposes of the motion, “[t]he evidence of the nonmovant is to be believed, and all justifiable inferences are to be drawn in his favor.” Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 255, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986).
Upon reviewing the record before it at that stage of the litigation, the district court concluded that FSI had not demonstrated the existence of any genuine issue as to any material fact concerning infringement. Specifically, the finger-shaped markings on the accused FSI 2705 baseball were found by the district court to be functionally identical and structurally equivalent to the tapered egg-shaped indicia disclosed in the '193 patent:
Although the markings on defendant’s ball are shaped somewhat differently than those found on plaintiffs product,1 the court concludes that the difference is insubstantial: an elongation of the finger indicia, coupled with “blunting” the ends of each mark, as opposed to tapering them, adds nothing of significance to the structure disclosed in plaintiffs patent specification. Both types of indicia show the student precisely how to grip the baseball, and the difference between the structure used to accomplish this function is, at best, an insignificant alteration.
McGinley II at 1224 (footnote not in original). We review de novo the district court’s legal conclusion that summary judgment of infringement was warranted in this case. Ethicon Endo-Surgery, Inc. v. United States Surgical Corp., 149 F.3d 1309, 1315, 47 USPQ2d 1272, 1275 (Fed.Cir.1998).
On appeal, FSI does not quibble with the district court’s conclusion that the finger-shaped markings on the accused FSI [1349]*13492705 baseball are structural equivalents of the tapered egg-shaped indicia described in the '193 patent. Instead, FSI simply argues that the “means for orienting” limitation in the asserted claims is not entitled to a range of equivalents at all. Since we have already rejected that argument, FSI’s cross-appeal on infringement fails as well. Moreover, our review of the record reveals that FSI did not present any non-conclusory evidence in opposition to McGinley’s summary judgment of infringement which would tend to indicate that an artisan of ordinary skill would not consider the finger-shaped indicia on the accused FSI 2705 baseball to be structural equivalents of the tapered egg-shaped indicia explicitly described in the '193 patent. Therefore, we affirm the district court’s grant of summary judgment of infringement.
IV
Obviousness
A patent is invalid for obviousness if “differences between the subject matter sought to be patented and the prior art are such that the subject matter as a whole would have been obvious at the time the invention was made to a person having-ordinary skill in the art to which said subject matter pertains.” 35 U.S.C. § 103(a) (1994). “Throughout the obviousness determination, a patent retains its statutory presumption of validity, see 35 U.S.C. § 282, and the movant retains the burden to show the invalidity of the claims by clear and convincing evidence as to underlying facts.” Rockwell Int’l. Corp. v. United States, 147 F.3d 1358, 1364, 47 USPQ2d 1027, 1031-32 (Fed.Cir.1998).
Although it is well settled that the ultimate determination of obviousness is a question of law, it is also well understood that there are factual issues underlying the ultimate obviousness decision. Richardson-Vicks Inc. v. Upjohn Co., 122 F.3d 1476, 1479, 44 USPQ2d 1181, 1183 (Fed.Cir.1997). Specifically, the obviousness analysis is based on four underlying factual inquiries, the well-known Graham factors: (1) the scope and content of the prior art; (2) the differences between the claims and the prior art; (3) the level of ordinary skill in the pertinent art; and (4) secondary considerations, if any, of nonob-viousness. Graham v. John Deere Co., 383 U.S. 1, 17-18, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966); Kegel Co., Inc. v. AMF Bowling, Inc., 127 F.3d 1420, 1430, 44 USPQ2d 1123, 1130 (Fed.Cir.1997).
At trial, FSI argued, inter alia, that the asserted claims of the '193 patent were obvious in view of either Pratt alone, or in view of Pratt in combination with Morgan. FSI’s obviousness theories are best summarized in its own words from its opening brief on appeal:
The only element of the asserted claims that is not clearly anticipated by the Pratt patent is the finger shaped marks that orient the ball with respect to the palm of the user’s hand. However, this feature is obvious in light of the lines indicating finger placement on the drawings of the Pratt patent. Moreover, the concept of a set of finger marks to orient the ball is clearly taught in the Morgan patent. It would have been obvious to one of ordinary skill in the art to substitute the finger marks of the Morgan patent for the marks of the Pratt patent. Or, stated another way, it would have been obvious to place three sets of marks on the Morgan ball in light of the teaching of Pratt.
In other words, FSI argued to the jury that the “missing element” in Pratt (i.e., the “means for orientation”) can be found either in the “phantom lines” of Pratt or in Figure 6 of Morgan. McGinley argued at [1350]*1350trial that there was no motivation to combine the prior art as suggested by FSI, and that even if such a motivation to combine had been demonstrated, that the commercial success of both McGinley’s RCIB and FSI’s accused 2705 baseball constituted sufficient evidence of secondary considerations that would negate any prima facie showing of obviousness.
The jury agreed with McGinley. Specifically,- in the special verdict form used in this case, the jury answered three questions that are relevant to this appeal in favor of McGinley. First, the jury found that FSI had not proven by clear and convincing evidence that each of the elements of the invention defined in claims 1, 2, 6 and 7 of the '193 patent is disclosed in Pratt. This was a factual finding. In re Beattie, 974 F.2d 1309, 1311, 24 USPQ2d 1040, 1041 (Fed.Cir.1992) (“What, a reference teaches is a question of fact.”).
Second, the jury found that FSI had not proven by clear and convincing evidence that any of the asserted claims were invalid as being obvious in view of Pratt alone. Finally, the jury found that FSI had not proven by clear and convincing evidence that any of the asserted claims were invalid as being obvious in view of a combination of Pratt and Morgan. These latter two findings by the jury are directed to the ultimate legal issue of obviousness, and provide no insight as to the jury’s findings with respect to the underlying factual underpinnings. The parties do not object to the phrasing of the questions that were posed to the jury in the verdict form, nor do they challenge the district court’s comprehensive jury instructions on obviousness.
In its motion for JMOL, FSI argued that no reasonable jury could have concluded that the asserted claims were not obvious in view of either Pratt alone or in view of Pratt in combination with Morgan. The district court agreed, and granted FSI’s motion for JMOL. Specifically, the court found that “no reasonable jury could conclude that the motivation to combine Pratt and Morgan did not exist.” Moreover, the district court “simply [did] not believe that the evidence regarding secondary considerations [was] sufficient, to overcome its firm conclusion that, as a matter of law, plaintiffs patent is invalid as obvious in light of Pratt or the combination of Pratt and Morgan.” In sum, the district court concluded that “in light of Pratt alone, as well as in light of Pratt and Morgan in .combination, the claims set forth in the '193-patent are invalid as obvious.”2
We review a grant of JMOL without deference to the district court. Tex. Instruments Inc. v. Cypress Semiconductor Corp., 90 F.3d 1558, 1563, 39 USPQ2d 1492, 1496 (Fed.Cir.1996). Entry of JMOL is inappropriate unless the jury’s verdict is unsupported by substantial evidence or premised on incorrect legal standards. Applied Med. Res. Corp. v. United States Surgical Corp., 147 F.3d 1374, 1376, 47 USPQ2d 1289, 1290-91 (Fed.Cir.1998); accord Jackson v. City of Albuquerque, 890 F.2d 225, 230 (10th Cir.1989); J.I. Case Credit Corp. v. Crites, 851 F.2d 309, 311 (10th Cir.1988) (noting that JMOL is appropriate “only if the proof is all one way or so overwhelmingly preponderant in favor of the movant as to permit no other rational conclusion”).
In analyzing the correctness of a JMOL overturning a jury verdict of nonobviousness, we must consider the facts before the district court, and then determine whether the district court’s ultimate judgment on obviousness is correct as a matter [1351]*1351of law. Richardson-Vicks, 122 F.3d at 1479, 44 USPQ2d at 1183. In re-creating the facts as they may have been found by the jury, and in applying the Graham factors to the evidence of record in this case, we assess the evidence in the light most favorable to the verdict winner, in this case McGinley. Id.; accord Lucas v. Dover Corp., 857 F.2d 1397, 1400 (10th Cir.1988) (“In determining whether the grant of a motion for [JMOL] is appropriate, the court must view the evidence and indulge all inferences in favor of the party opposing the motion and cannot weigh the evidence, consider the credibility of witnesses or substitute its judgment for that of the jury.”) (internal quotations omitted).
Whether a patent claim is obvious under section 103 depends upon the answer to several factual questions and how the factual answers meld into the legal conclusion of obviousness vel non. In this case, we think that the central question is whether there is reason to combine the Pratt and Morgan references, because if the references are properly combined, it is certain that the claims are prima facie invalid for obviousness. If the jury was entitled to conclude that these two references should not be combined, then the asserted claims of the '193 patent cannot be invalid for obviousness in the light of the proposed combination. If those claims are not invalid under a combination of Pratt and Morgan, then, as a matter of logic, those claims cannot be invalid in the light of Pratt alone. We thus turn first to the issue of whether Pratt and Morgan must be combined.
The genius of invention is often a combination of known elements which in hindsight seems preordained. To prevent hindsight invalidation of patent claims, the law requires some “teaching, suggestion or reason” to combine cited references. Gambro Lundia AB v. Baxter Healthcare Corp., 110 F.3d 1573, 1579, 42 USPQ2d 1378, 1383 (Fed.Cir.1997). When the art in question is relatively simple, as is the case here, the opportunity to judge by hindsight is particularly tempting. Consequently, the tests of whether to combine references need to be applied rigorously. See In re Dembiczak, 175 F.3d 994, 999, 50 USPQ2d 1614, 1617 (Fed.Cir.1999), limited on other grounds by In re Gartside, 203 F.3d 1305, 53 USPQ2d 1769 (2000) (guarding against falling victim to the insidious effect of a hindsight syndrome wherein that which only the inventor taught is used against its teacher).
Whether a motivation to combine prior art references has been demonstrated is a question of fact. Winner Int’l Royalty Corp. v. Wang, 202 F.3d 1340, 1348, 53 USPQ2d 1580, 1586 (Fed.Cir.2000). The assessment of whether to combine references in a given case has sometimes been viewed conceptually as a subset of the first Graham factor, the scope and content of the prior art. See, e.g., id.; Monarch Knitting Mach. Corp.v. Sulzer Morat Gmbh, 139 F.3d 877, 881-83, 886, 45 USPQ2d 1977, 1981-82, 1985 (Fed.Cir.1998). Although that view is not incorrect, accurate assessment of whether to combine references may require attention to other Graham factors. For example, the level of skill in the art may inform whether the artisan would find a suggestion to combine in the teachings of an exemplar of prior art. Where the level of skill is high, one may assume a keener appreciation of nuances taught by the prior art. Similarly, appreciation of the differences between the claims in suit and the scope of prior art references — a matter itself informed by the operative level of skill in the art— informs the question of whether to combine prior art references. At bottom, in each case the factual inquiry whether to [1352]*1352combine references must be thorough and searching.
There is no question here that FSI presented sufficient evidence at trial from which a jury could have decided that one of ordinary skill in this case would have been motivated to combine Pratt and Morgan to produce a prima facie obvious invention. Specifically, FSI argued to the jury that the only elements of the asserted claims that are not clearly anticipated by Pratt are the finger-shaped marks that orient the ball with respect to the palm of the user’s hand. Referring to the “phantom lines” in Pratt as suggestive of finger placement on the ball, FSI argued that one of ordinary skill would have been motivated to substitute the finger marks from the Morgan ball for the circular marks on Pratt, or alternatively to place three sets of marks on the Morgan ball in the light of Pratt’s teachings. In addition, FSI argued that one of ordinary skill would have known to add the finger orientation means of the Morgan patent to Pratt by “filling in” the phantom lines in Pratt’s drawings and treating them as finger orientation means.
But the jury did not hear a one-sided ease on the issue of obviousness generally, and in particular on whether to combine Pratt and Morgan. As FSI conceded at oral argument, McGinley presented reasons to the jury to reject a combination of the references. McGinley argued many grounds -to support his contention that the asserted claims are not obvious in the light of Pratt and Morgan. To counter FSI’s claim that those references should be combined to render McGinley’s “means for orientation” obvious, McGinley pointed to specific differences between the prior art and the asserted claims. For example, Morgan does not disclose the required markings for at least three different kinds of pitches, as do the asserted claims. And Morgan does not disclose markings on a real baseball, as do Pratt and the asserted claims. We recount the gist of this testimony below.
The jury heard from Mr. Charles Quinn, FSI’s vice president of marketing and corporate representative at trial. Quinn testified in detail as to the express teachings of Pratt and Morgan, and as to the differences between these references and the asserted claims. For example, he conceded that the markings on the baseball in Pratt’s invention were circular, and therefore incapable of indicating orientation. Trial Tr. Vol. 2, p. 140. He also acknowledged that the “phantom lines” in Pratt’s drawings were not actually markings on a baseball. Trial Tr. Vol. 2, pp. 177-78. Quinn also pointed out that Morgan did not discuss implementing a baseball training device using a regulation baseball. Trial Tr. Vol. 2, pp. 172-73. Moreover, he acknowledged that Morgan taught only the provision of indicia for throwing a single type of pitch on each training device, instead of three sets of indicia as required in the asserted claims. Trial Tr. Vol. 2, p. 145.
The jury also heard from Mr. Richard Stitt, the attorney who prosecuted the '193 patent. Stitt testified at length about the prosecution history of the '193 patent and the fact that Pratt and Morgan were considered by the PTO throughout the entire pendency of McGinley’s application. .He confirmed that the “phantom lines” in Pratt’s drawings were not actually marked on a baseball. Trial Tr. Vol. 3, p. 56. Stitt also pointed out that the PTO never rejected the asserted claims as obvious in view of Pratt, and that it was never suggested by the PTO that the phantom lines of Pratt could easily be transferred to the actual baseball to arrive at McGinley’s [1353]*1353claimed invention. Trial Tr. Vol. 3, pp. 57-58.
Stitt testified that the PTO never rejected McGinley’s claims by saying that one could substitute the “elongate finger-shaped markings” shown in Figure 6 of Morgan in place of the “circular dots” in Pratt. Trial Tr. Vol. 3, p. 63. He also pointed out that the PTO could have issued an obviousness rejection of the asserted claims based on a theory of transferring Pratt’s phantom lines onto the baseball, but never did so. Trial Tr. Vol. 3, p. 185. Similarly, he testified that the PTO could have issued an obviousness rejection of the asserted claims based on a theory of combining Pratt with Morgan, but never did so either. Trial Tr. Vol. 3, p. 186.
Stitt also testified that he flew to the Patent Office in Washington, D.C., with McGinley for an interview with the Examiner to discuss the differences between Pratt and Morgan and the claimed invention. Trial Tr. Vol. 3, pp. 142-145. Finally, he explained in detail why neither Pratt nor Morgan alone or in combination with each other would provide the claimed “means for orientation.” Trial Tr. Vol. 3, pp. 150-52.
In addition, McGinley relied heavily on the presumption of validity to which his patent is entitled by the terms of 35 U.S.C. § 282, mainly in the context of Stitt’s tutorial concerning how McGinley’s patent was prosecuted, and in McGinley’s opening statement and closing argument to the jury. As noted above, throughout the trial, McGinley pointed out that both the Pratt and Morgan references were before the examiner who tested McGinley’s patent for validity. Indeed, those two references were discussed in an interview between the applicant and the examiner. The examiner rejected McGinley’s claims as anticipated by Pratt, and made no mention of any concern as to obviousness in view of Pratt alone or of a combination of Pratt and Morgan. The Board of Patent Appeals and Interferences reversed the examiner’s anticipation rejection, holding that Pratt failed to teach McGinley’s means for orienting the baseball relative to the palm of the hand. In due course, McGinley’s patent issued and became clothed with the statutory presumption of validity, with no obviousness challenge having been mounted against it, either on the basis of Pratt alone, or of Pratt in combination with Morgan.
The jury in this case was expressly charged that the patent in suit is entitled to the presumption of validity, and that FSI could only overcome that burden with clear and convincing evidence to the contrary. It is well established in our case law that FSI’s burden in this case was especially heavy:
When no prior art other than that which was considered by the PTO examiner is relied on by the attacker [FSI], he has the added burden of overcoming the deference that is due to a qualified government agency presumed to have properly done its job, which includes one or more examiners who are assumed to have some expertise in interpreting the references and to be familiar from their work with the level of skill in the art and whose duty it is to issue only valid patents. In some cases a PTO board of appeals may have approved the issuance of the patent.
American Hoist & Derrick Co. v. Sowa & Sons, Inc., 725 F.2d 1350, 1359, 220 USPQ 763, 770 (Fed.Cir.1984), cert. denied, 469 U.S. 821, 105 S.Ct. 95, 83 L.Ed.2d 41 (1984).
Perhaps McGinley’s best argument to save his claims from prima facie obviousness in the light of Pratt and Morgan is his contention that those references together teach away from their combina[1354]*1354tion. We have noted elsewhere, as a “useful general rule,” that references that teach away cannot serve to create a prima facie case of obviousness. In re Gurley, 27 F.3d 551, 553, 31 USPQ2d 1130 (Fed.Cir.1994). If references taken in combination would produce a “seemingly inoperative device,” we have held that such references teach away from the combination and thus cannot serve as predicates for a prima facie case of obviousness. In re Sponnoble, 405 F.2d 578, 587, 160 USPQ 237, 244, 56 C.C.P.A. 823 (1969) (references teach away from combination if combination produces seemingly inoperative device); see also In re Gordon, 733 F.2d 900, 902, 221 USPQ 1125, 1127 (Fed.Cir.1984) (inoperable modification teaches away).
McGinley argues in his brief that Pratt itself teaches away from combining the finger orientation of Morgan, because Pratt, by teaching only the placement of finger tips on the baseball, leads away from placing a full finger orientation on the ball. Such may be the case, but we have no assurance that the jury heard that argument. At oral argument in this court, however, FSI confirmed that McGinley argued to the jury that adding the finger marks of Morgan to Pratt’s baseball, by “filling in” the phantom marks to create structure that defines orientation as claimed, would require obliteration of the claimed rotation arrows, a feature that is necessary in order to permit the Pratt invention to operate properly. FSI also confirmed at oral argument that the jury heard McGinley’s argument that to combine the finger placements of Morgan onto the Pratt ball would also render the Pratt ball inoperable, by eliminating the multicolored equatorial band, a claimed feature of the Pratt patent also required for successful operation of Pratt’s invention.
We are satisfied that McGinley presented sufficient evidence as well to counter FSI’s alternative argument that it would have been obvious to place three sets of marks on the Morgan ball in light of the teaching of Pratt. First, a reasonable jury could have determined from examining the Morgan reference that the finger placement indicia on Morgan are too large to allow the inclusion of more than a single set of markings. This point is important, because Morgan expressly requires markings on the ball to accommodate the placement of two full fingers and a thumb to simulate throwing a single pitch. The jury could have certainly concluded that one of ordinary skill would not attempt to place markings for two additional pitches on Morgan’s ball. Two more sets of markings as shown by Morgan itself would require markings for two additional sets of fingers and thumbs. On the other hand, two sets of markings as shown by Pratt would lead to confusion as to the correct means for orientation on Morgan’s ball. Any such configurations, ie., Morgan’s invention with markings for throwing three different pitches, would risk, if not achieve, obliteration of the clear and unmistakable markings shown on Morgan’s ball to teach the throwing of a single curving pitch. Moreover, a reasonable jury could have considered that all of the embodiments described and illustrated in the Morgan reference are expressly limited to teaching a student pitcher to throw a baseball with a “particular curve or break,” and that none of the embodiments discuss or suggest using a conventional baseball as opposed to a hollow shell comprising two metallic or plastic hemispheres glued or otherwise bonded together. The jury also could have concluded that Morgan — with its full finger and thumb imprint markings on the ball — teaches away from a means for orientation using the smaller tear-drop markings disclosed by McGinley or the [1355]*1355small truncated finger-shaped markings used in FSI’s accused baseballs.
Given the strength of the teaching away point, we think it remarkable that FSI makes no attempt whatsoever in its brief to counter McGinley’s argument. The jury’s verdict that the claims in suit are not obvious is supported by the evidence brought forward by McGinley to resist FSI’s contrary evidence. Here we have the classic example of sufficient evidence to support each position argued to the jury. The key issue, namely what the references teach and whether they teach the necessity of combination or the requirement of separation, is a fact issue. When the jury is supplied with sufficient valid factual information to support the verdict it reaches, that is the end of the matter. In such an instance, the jury’s factual conclusion may not be set aside by a JMOL order.
Given the multiple bases upon which the jury’s verdict in favor of McGinley can be sustained over FSI’s arguments for combining the references, we must conclude that FSI fares no better in arguing a combination of Pratt into Morgan than it does in arguing a combination of Morgan into Pratt. The jury was thus entitled to reach its verdict of nonobvi-ousness on the ground that one of ordinary skill in the art would not deem the asserted claims of the '193 patent obvious in light of Pratt and Morgan in combination. That being the case, it is illogical to think that one of ordinary skill in the art would have deemed McGinley’s claims obvious in the light of Pratt alone. If one of ordinary skill is not taught by Morgan to extend Pratt’s circular markings into the phantom lines, that person would not be taught by the phantom lines alone to do so. Nonetheless, we think the district court erred as well in its decision that McGin-ley’s asserted claims were obvious as a matter of law in view of Pratt alone. A21-22. According to the district court’s reasoning, no reasonable jury could have failed to conclude that an ordinarily skilled artisan would have been motivated to transfer the finger-shaped “phantom lines” shown in the Pratt reference onto the actual Pratt baseball itself, thus providing 'the missing “means for orientation” that is admittedly otherwise missing in Pratt.
It should be noted that the “phantom lines” shown in Pratt are virtually identical to the finger-shaped markings on Fig. 6 of the Morgan reference, except that the Morgan markings are “filled-in” and actually marked on the ball. Therefore, many of the arguments mentioned above with respect to Morgan apply with equal force with respect to the Pratt phantom lines. Specifically, as FSI conceded at oral argument before this court, the jury heard McGinley’s argument that transferring large finger-shaped markings (such as those illustrated in Fig. 6 of Morgan or in the phantom lines of Pratt) would render the Pratt invention inoperable by interfering with the multi-colored equatorial band. Thus, according to this evidence, one of ordinary skill in designing baseballs for use as pitching trainers would not be motivated to modify Pratt by filling in the phantom lines to express palm-oriented finger placement on the ball. As mentioned above, the jury also heard extensive testimony concerning the prosecution history of the '193 patent, including the critical facts that (1) Pratt was before the PTO during the entire pendency of the patent application, and (2) although the PTO continued to reject the asserted claims as anticipated by Pratt until McGinley won an appeal before the Board on that point, the PTO never rejected the asserted [1356]*1356claims as obvious in view of Pratt alone. Surely, relying on the presumption of regularity that applies to all administrative agencies such as the PTO, the jury could have reasonably concluded that if the PTO believed that an obviousness rejection based on Pratt alone was warranted, such a rejection would have been promptly been made. Also, just as was the case with the Morgan markings, the jury could have reasonably concluded from an examination of the references that the Pratt phantom lines are so large that it would not be feasible to include three sets of them on a single baseball, as required by the asserted claims. Because substantial evidence supports the jury’s implicit factual finding that no motivation to modify Pratt in that manner has been demonstrated in this case, the district court’s ruling that Pratt alone renders the asserted claims obvious as a matter of law was erroneous.
Due to the “black box” nature of the jury’s verdict, it is impossible to determine which of the above pieces of evidence, alone or in combination, carried the day in the jury room, and how much weight was assigned to each piece. All that can be said with certainty is that— as a whole — the evidence enumerated above (all of which was admittedly before the jury) constitutes substantial evidence to support the jury’s verdict. We recognize the concerns of the dissenting opinion that it is difficult to sort out the weight to be given factual determinations in an obviousness inquiry from the degree to which the district court should override permissible found-facts to sum-up the legal conclusion of obviousness vel non. But when a dispositive element of the factual equation, here whether to combine or modify key references, so clearly could have been decided by the jury in McGinley’s favor, it is not our place to elide the -vagaries of a black box jury verdict by overriding the jury’s decision. Our law does not compel the use of special verdicts in these cases, and so long as the parties are content to give the jury unfettered room to operate on dispositive factual issues within the scope of a general verdict request, we must be mindful of our role as an appellate court and respect the verdict reached, notwithstanding what may seem to some to be an invention of little novelty.
For the reasons set forth above, we conclude that the district court erred when it ruled on JMOL that no reasonable juror could have ruled that FSI failed to make out a case of obviousness by clear and convincing evidence.
V
Denial of McGinley’s Motion to Amend Complaint
More than one year after McGinley had filed its initial complaint against FSI in this case, and almost two months after the deadline that had been set by the district court for filing a motion to join additional parties, McGinley sought to add his own company and oral exclusive licensee, S.C. Products, Inc. (“SCP”), as a plaintiff. Apparently, McGinley and SCP are “one and the same,” and McGinley is the sole shareholder of SCP. However, in a technical corporate sense, the RCIB was sold by SCP, not by McGinley.
The district court denied McGinley’s motion, and articulated the following bases for its decision:
The court, in its May 10, 1999 telephone conference, found that both parties have been equally dilatory in preparing this case for trial, and therefore denied the plaintiffs motion for an extension of the deadline to file amended pleadings. The [1357]*1357plaintiffs current motion to amend comes nearly two months after the deadline for such motions. The court believes that, had the plaintiff diligently sought to bring the matter to trial, the plaintiff could have brought this motion to amend within the deadline specified in the scheduling order. For example, the plaintiff did not complete depositions of defendant and its representatives' — the very depositions on which he in part bases his motion to amend — until the week of May 17, 1999, some six weeks after the deadline for motions to amend.
A district court’s decision to grant or deny a motion for leave to join a party involves a procedural question that raises no special issues relating to patent law, and therefore Tenth Circuit law applies in this case. Sun-Tek Indus., Inc. v. Kennedy Sky Lites, Inc., 856 F.2d 173, 175, 8 USPQ2d 1154, 1156 (Fed.Cir.1988). In the Tenth Circuit, this issue is reviewed for an abuse of discretion. Scheufler v. Gen. Host Corp., 126 F.3d 1261, 1270 (10th Cir.1997). In this case, we can safely conclude that the district court did not abuse its discretion. Trial courts are given broad latitude in managing and scheduling eases, and therefore the stated bases for the district court’s decision to deny McGinley's motion are entirely reasonable. See Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 9 L.Ed.2d 222 (1962) (stating that undue delay may form a proper basis for a court to exercise its discretion to deny a plaintiffs motion to amend its complaint).
VI
Denial of FSi’s Motion for New Trial on Willfulness
FSI argued at trial that it did not willfully infringe the '193 patent on the basis that it allegedly had a reasonable, good faith belief that the patent was invalid. FSI did not rely upon-advice of counsel to demonstrate this belief. Instead, FSI sought to demonstrate its good faith belief, through the testimony, of its corporate representative and vice president of marketing, Charles Quinn, who was to testify as to FSI’s understanding of the Pratt and Morgan patents. At trial, the district court prevented Quinn from testifying as an ordinarily skilled artisan in the invalidity portion of the trial, since he was. not qualified as an expert under Federal Rule of Civil Procedure 26.
After the jury verdict, along with its motion for JMOL of invalidity, FSI argued in the alternative that it was entitled to a new trial on willfulness, without citing any particular basis for' granting the motion, other than referring to evidence presented at trial tending to show that FSi’s infringement was not willful. In its briefs on appeal, FSI argues for the first time that it is entitled to a new trial because' it was denied a fair opportunity to present its allegedly “key piece of exculpatory evidence” at trial (i.e., Quinn’s testimony as to FSi’s understanding that the '193 patent was invalid in view of Pratt and Morgan). The district court denied the motion for a new trial on willfulness, stating as follows:
[E]ven if the Federal Circuit were to reverse this court on its JMOL determination, the jury’s willfulness finding should not be set aside nor should defendant be entitled to a new trial. The crux of this opinion is that the '193 patent is obvious as a matter of law; if the court is deemed to be incorrect in that conclusion, that is, if there actually was a question of fact for the jury on obviousness, then, as plaintiff discusses in his responsive papers, the evidence presented supports the jury’s conclusion that the infringement was willful and, also, the verdict was not so contrary to [1358]*1358the weight of that evidence as to mandate a new trial.
The denial of FSI’s motion for a new trial is a procedural issue not unique to patent law, and is therefore reviewed in this case under the Tenth Circuit’s abuse of discretion standard. Smith v. Ingersoll-Rand Co., 214 F.3d 1235, 1242 (10th Cir.2000); accord Shearing v. Iolab Corp., 975 F.2d 1541, 1544, 24 USPQ2d 1133, 1136 (Fed.Cir.1992).
We conclude that the district court did not abuse its discretion in denying FSI’s motion for a new trial. Because FSI failed to make any offer of proof under Rule 103 of the Federal Rules of Evidence, nothing in the record indicates what Quinn would have said on the stand if asked. Sorensen v. City of Aurora, 984 F.2d 349, 355 (10th Cir.1993) (finding no abuse of discretion in denying new trial where party failed to establish sufficient factual record for appellate court to consider propriety of excluding testimony). Moreover, we are satisfied that — even without being allowed to present Quinn’s allegedly exculpatory evidence — FSI took advantage of its fair opportunity to present evidence concerning FSI’s independent development of the accused 2705 baseball and its alleged acts of good faith to the jury.
VII
Conclusion
For the reasons stated above, we reverse the grant of JMOL in favor of FSI and order the jury’s verdict reinstated. We leave undisturbed, however, the district court’s other judgments, rulings, and orders on appeal, thereby affirming the remaining questions raised by McGinley and the cross-appeals presented by FSI. The case is returned to the district court for further proceedings not inconsistent with this opinion.
Costs
No costs.
REVERSED-IN-PART AND AFFIRMED-IN-PART