OPINION
SMITH, Chief Judge.Plaintiffs have brought this suit under the Tucker Act, 28 U.S.C. 1491 (1982) and the Contract Disputes Act of 1978, 41 U.S.C. §§ 601-13 (1982).1 They seek refunds of alleged contract overpayments made under a standard stumpage rate adjustment clause included in various timber sales contracts. Under the typical Forest Service (Service) timber sale contract, such as those used here, contractors are selected according to the highest bid for a particular stand of timber. The bid price, however, is subject to adjustment depending upon changing timber markets. To share the risks of these changing markets the Service includes in each contract a stumpage rate (stumpage rate is the timber purchase price) adjustment clause. The stumpage rate is adjusted by operation of a specific formula tied to the performance of an index designed to reflect the selling prices of various species and grades of lumber manufactured in the western United States. The central dispute in this case involves whether the index referenced in the contract was adequate under the terms of the contract to reflect the prices experienced by timber firms located on the North Coast of California. A trial was held on that issue and the parties have filed post-trial briefs.2 After consideration of all the evidence presented at trial and the parties’ respective post-trial briefs the court enters *94judgment in favor of plaintiffs. The court holds that the index referenced in the stumpage rate adjustment clause included in each contract was an inadequate reflection of actual prices within the meaning of the contracts and that refunds are due plaintiffs.
Facts
The plaintiffs in this case are timber companies which have entered into timber sale contracts with the United States Forest Service for the purchase of timber located on national forest land. Each of the twenty-one sales in question are for Douglas fir timber located on the North Coast of California.3 The contracts were let between 1974 and 1984 and are generally of three to five years duration. The timber sale contracts in question are all on form 2400-6 (9/73). They were awarded to the companies which bid the highest amount for the timber determined to be included in the particular timber sale. As seen below the bid price is subject to adjustment during the term of the contract depending upon the prevailing market conditions. The projected amount of merchantable timber is also subject to overruns and under-runs and therefore may result in a change of the total contract price. For a thorough discussion of form 2400-6 (9/73) and the timber sale process see Sierra Pac. Indus. v. Block, 643 F.Supp. 1256 (N.D.Cal.1986).
Form 2400-6 (9/73) is divided into three sections: division A which contains the specific provisions; division B which contains the standard provisions; and division C which contains the special provisions. This case concerns the standard provisions B3.2 and B3.21. Section B3.2, the standard stumpage rate adjustment clause,4 provides:
Tentative Rates for those species and products listed in A5a are subject to quarterly adjustment in accordance with the following procedures: The calendar-quarter index average for each price index described in A6 is the arithmetic average of the three such monthly price indices preceding January 1, April 1, July 1, and October 1. The difference between said calendar-quarter index average and Base Index listed in A5a shall be the basis for quarterly escalation. To arrive at Current Contract Rates for timber scaled during the preceding calendar quarter, Tentative Rates for each species shall be: (a) reduced by such difference when the calendar-quarter index average is less than Base Index except that a reduction shall not result in a rate below Base Rate, or (b) increased by half of such difference when the calendar-quarter index average is greater than Base Index except that no increase shall exceed the difference between Tentative Rate and Base Rate.
Section B3.21 provides:
If an index described in A6 is no longer available or there is reason to believe that said index is inadequate to reflect product-price fluctuations, the unavailable or inadequate index may be replaced by another suitable index commonly acceptable in the industry. When there is no replacement index, Current Contract .Rate for the remainder of the sale shall be a Flat Rate derived from adjustment of Tentative Rate by the arithmetic average for the index for the proceeding 12 months, using the procedure described in B3.2 for quarterly adjustment. Such Flat Rate shall be subject to rate redeter-*95mination as provided elsewhere under this contract. (Emphasis added).
The plaintiffs allege that the index designated pursuant to the contract terms and discussed in detail below, became inadequate in late 1982 as an indicator of actual product price changes experienced by firms located on the North Coast. Plaintiffs thus seek to pay for the timber at a flat rate pursuant to provision B3.21.5 Application of the flat rate would result in refunds payable to plaintiffs.
Stumpage rate adjustment pursuant to the contract is a complicated process. The basic rate of payment is known as the tentative rate. The tentative rate is the bid rate included in the contract. Although the tentative rate always remains the same, it acts as the basis for calculating the current rate when the index for the quarter in which the logs were removed is available. The current rate is the rate at which the contractor is initially billed for the timber. It is derived from the difference between the index for the quarter of harvest and the base index. The base index is the index from the quarter prior to the contract award date. The current rate depends upon whether the index for the quarter of harvest is above or below the base index. If it is above, then the current rate is the tentative rate plus fifty percent of the difference between the current index and the base index. If it is below, then the entire amount is subtracted from the tentative rate and a refund is necessary. The contract specifies certain parameters for the adjustment. The current rate cannot be below a certain base rate specified in the contract. Conversely, increases cannot be greater than the difference between the tentative rate and the base rate.
As a general illustration of the process just described, the court has created the following hypothetical chart.
Tentative bid rate = $100 per thousand board feet (MBF)
Base index = $50 per MBF
First quarter current index = $200 per MBF
Second quarter current index = $25 per MBF
Base Rate = $10 per MBF
Constraints—The current rate cannot be below the $10 base rate nor greater than $190 per MBF, which is the tentative rate plus the difference between the tentative rate and the base rate. If the current index is above the base index then the following would occur:
Tentative rate + V2 (current index — base index) = current rate [$100 + lk ($200 - $50) = $175 per MBF]
(Purchaser pays Forest Service $75 per MBF more than original contract amount for timber harvested during the first quarter).
If the base index is above the current index then the following would occur:
Tentative rate — (base rate — current index) = current rate [$100 - ($50 - $25) = $75 per MBF]
(Purchaser gets a refund of $100 per MBF because he has paid the current rate of $175 per MBF from the preceding quarter).6
The index designated by the contract through Specific Condition A6 and traditionally used in the area for quarterly adjustments is the 1971 Western Wood Products Association Dry Douglas Fir-Larch index (WWPA index). This index is maintained by the Western Wood Products Association (WWPA), a trade association of timber manufacturers operating in the western United States. The WWPA consists of both full members who vote on association policy and receive all services and associate members who subscribe only *96to the lumber grading service. Associate members have no vote on WWPA policy. The WWPA provides a broad array of services including product promotion and advertising, as well as statistical, forestry, and safety services. None of the plaintiffs in this case are full members of the WWPA, although should they seek to become full members they could. They thus have no say in policy decisions of the WWPA. There was some evidence at trial that WWPA was less concerned about their views of the adequacy of the index system than WWPA was about the views of its members. This, of course, is also the inference of simple logic.
As stated by the WWPA, the WWPA index is used to reflect “the trend of weighted prices for the entire area producing inland species.” To compute the WWPA index prices for the various lumber grade groups,7 the WWPA uses lumber sales data from participating mills within the specified region. It combines the grade group average prices into the index according to an “index log.”8 The index log is used to level out fluctuations in product mix and sales data on the assumption that it reflects the long term grade recovery of mills in the region. The index log was at the time of trial based upon a grade recovery survey completed in 1971. This survey records the percentages of each grade of lumber produced at the Mills from the logs they process.
The WWPA Inland region includes Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, South Dakota, Utah, Wyoming, those portions of Oregon and Washington to the east of the Cascade Mountain range, and the portions of California not in the Redwood region. The WWPA Coastal region includes those portions of Washington and Oregon to the west of the Cascade mountains. The Redwood region includes the North Coast of California but the WWPA’s activities in the region have been related solely to the grading9 of Sugar pine and Ponderosa pine. Lumber sales data for Douglas fir lumber shipped from mills located in the North Coast area are not used in the computation of the WWPA index.
The WWPA index is based upon lumber sales data collected from mills in the Inland region. Information used to compute the index is compiled from copies of invoices submitted to the WWPA by some 220 mills, accounting for 65-70 percent of the region’s production. From this footage cer*97tain key-items have been selected for use in the index. Sales data for green lumber are used in calculating the index level only after they have been adjusted into Clean Key Items10 under WWPA procedures. Some of these adjustments are the addition of flat dollar amounts per thousand board feet, while others increase the sale price by some fixed percentage. The majority of the reported sales are of dry lumber. Only wholesale transactions are used; footage used by companies, factory transfers, intra-company transfers and retail sales are not used for price reporting or in index calculations. On rail shipments, the mill price is arrived at by deducting from the delivered price the freight rate times new shipping weights that more accurately reflect actual weights. Sales made f.o.b. railhead, delivered nearest town, etc. are converted back to f.o.b. mill. All prices used are subject to a 2 percent cash discount; and any sales commissions or sales discounts are deducted.
The coastal forest zone is characterized by forests of Douglas fir and related species (except at higher elevations), and stretches from British Columbia through the North Coast of California. The old growth Douglas fir timber in this zone generally produces larger logs than old growth Douglas fir found in the Inland region. All of the contracts at issue here are for the sale of coastal Douglas fir timber. In general, coastal Douglas fir also produces larger, clearer logs with fewer knots than Inland Douglas fir. The amount of defect in North Coast old growth Douglas fir is substantially different than that in old growth Inland Douglas fir. Logs from old growth coastal Douglas fir generally produce a greater proportion of high grade lumber than logs from old growth Inland Douglas Fir.
The WWPA index includes data from the sales of lumber manufactured from Larch. Larch is not a commercial species on the North Coast of California and is not manufactured into lumber by the North Coast mills.
The plaintiffs have commissioned two separate studies of the alleged disparities between the WWPA index and the actual sales experienced by the plaintiffs. In one study, forester George Craig compared the WWPA index with an index created from actual data supplied by four North Coast firms representing nearly forty percent of the North Coast production of Douglas fir. He concluded that the WWPA index was inadequate as an indicator of North Coast product price fluctuations in 1983.
Similarly, a study by Professor J. Keith Gilless, an econometrician and a member of the forestry faculty at the University of California at Berkeley, reached nearly the identical conclusions. In his study Professor Gilless collected Douglas fir lumber sales data from a partially different group of four firms for the period from January 1980 through December 1983. He then conducted both a graphical and a statistical analysis of the indices.
The defendant presented a study by Professor John Beuter, a professor of forest management at Oregon State University. Professor Beuter’s study opposes the statistical and graphical basis of plaintiffs’ studies. Professor Beuter disagreed with plaintiffs’ conclusions and concluded that there was no significant problem with the WWPA index.
Discussion
The defendant has taken two positions in response to plaintiffs’ allegations of index inadequacy. First, it asserts that, as a matter of law, the sole discretion to determine index adequacy lies with the Service. Secondly, defendant argues that the index is indeed adequate.
Sole Discretion
In support of its argument that the Forest Service has sole discretion to determine index adequacy, the defendant relies upon testimony indicating the Service’s position as regards provision B3.21. In par-*98ticular, the Associate Chief of the Service, Mr. George Leonard, testified that it has consistently been the understanding of the Service that the Service makes the determination of index adequacy under its contracts. The testimony of Mr. Robert Gillespie, a retired Service Assistant Director of Timber Management was to the same effect. This position, however, is not borne out by the plain language of the contract or any reasonable reading. See, Mohasco Indus. v. Maxwell Co., 425 F.2d 436, 439 (5th Cir.1970) (“Since the language is, in the opinion of this court, free from ambiguity, we cannot give any effect to the testimony [on what] the parties intended ... ”). The contract provides no indication as to which party is empowered to determine adequacy. The only contract language relevant to the inquiry provides that if “there is reason to believe that said index is inadequate to reflect product price fluctuations, the inadequate index may be replaced by another index commonly acceptable in the industry. When there is no replacement index, Current Contract Rate for the remainder of the sale shall be a Flat Rate____” Thus, the only standard set out in the contract is embodied in the reason to believe language. This certainly suggests an objective standard rather than sole discretion on the defendant’s part. If the parties had intended for one of them to exercise sole discretion, then a contract provision could easily reflect that intention.
The history of this provision indicates little concerning this issue. The testimony was that the provision initially allowed the Service to determine inadequacy or adequacy but mutual agreement of the parties was required to chose a new index. That method was scrapped as unworkable and the present wording was incorporated. The contention that the Service retained sole discretion from the change, while a possible result, is not the only result. An equally plausible and more probable result of the change in light of the language used would be an interpretation that either party could declare an index inadequate if there was reason to believe that such was the case. Thus, the court concludes that the determination of index adequacy is objective. The court must make a determination of index adequacy in the event of a dispute such as this. This is clearly a court’s role in a dispute over the legal meaning of a contract term.
Was the Index Inadequate?
The main question presented by this case is the factual one of whether the index was inadequate under the contract. Plaintiffs contend that the WWPA index was inadequate while defendant disputes this. In support of their case, plaintiffs relied on the reports of their experts, Mr. George Craig and Dr. J. Keith Gilless. Defendant relied upon a report prepared by its expert Dr. John Beuter.
The Craig Report
In his report Mr. Craig compiled lumber sales data on greater than 490 million board feet of sales from four firms.11 He divided the sales data into eight grade groups (elements of index logs) corresponding to the grade groups used by the WWPA index. The table below compares the Craig study grade grouping and the WWPA grade grouping along with Dr. Gil-less’ grade grouping.12
GRADE DISTRIBUTION FOR DOUGLAS FIR & DOUGLAS FIR-LARCH
Grade Groups WWPA Index: Craig’s Index: Gilless’ Index
D & Better Select 4.23% 9.60% 9.04%
Shop 3.36 3.30 3.66
Common 5.20 0.00 0.00
Standard &-Better, # 2 & Better 44.37 43.12 55.14
*99Grade Groups WWPA Index: Craig’s Index: Gilless’ Index
Utility & Better, # 3 & Better 11.60% 18.57% 16.49%
Economy All 6.38 8.61 8.77
Studs (Except Econ) 20.30 1.41 1.54
Timbers 4.56 15.39 5.35
100.00% 100.00% 100.00%
The Craig study also showed that a significant amount of North Coast timber was sold green (94.53 percent was the average in 1982-83). In contrast, only 40.97 percent of the timber sold in the Inland area was shipped green (45.35 percent was the average for the first nine months of 1983).
The study also noted that the price of green Douglas fir 2 X 4 standard and better, random 8/20 foot lumber increased in price from the 2nd quarter of 1982 to the 2nd quarter of 1983 by 38.5 percent while Kiln dried lumber of the same grade increased 48.3 percent. The prices for utility grade lumber from the first quarters of 1982 to the first quarter of 1983 increased 71.2 percent for green or unseasoned and 90.3 percent for dry.
In addition, the comparison between the WWPA index and the North Coast index created by Mr. Craig indicated that a change in the relationship between the in-dices occurred in 1983. In 1982 the difference between the average prices was $42.86 and in 1983 the difference was $26.60. In terms of percentages, the Craig North Coast index was 124.6 percent of the WWPA index in 1982 and 112.1 percent in 1984. Thus, assuming the Craig index was reflective of actual North Coast prices, the WWPA index during this period increasingly reflected a higher price for lumber than the North Coast firms were obtaining in the market.
Mr. Craig’s report concluded that “[t]here can be no serious question about the inadequacy of the WWPA Inland Dry Douglas Fir-Larch lumber price index to serve as an indication of Douglas Fir product price fluctuations in Northwest California in 1983.”
The Gilless Report
Professor J. Keith Gilless from the University of California at Berkeley, also prepared a report concerning the adequacy of the WWPA index. Dr. Gilless performed both a graphical and statistical analysis. Dr. Gilless used data from four North Coast firms representing between thirty-five and forty-one percent of the annual Douglas fir production for the Redwood region.13 From this data, Dr. Gilless created a four firm index log substantially mirroring the index log created by Mr. Craig.14 Dr. Gilless then created a four firm index for the North Coast of California.
Graphical Analysis
The Gilless report first graphed the WWPA index and the four firm index. The graph indicates that the gap between the indices narrowed in early 1983. A second graph portraying a three month moving average of the difference between the in-dices indicates that the indices moved from a difference of nearly seventy-five dollars per thousand board feet in early 1980 to a difference of only twenty dollars per thousand board feet in early 1983. If the WWPA index and North Coast actual price trends were in sine then the price difference should have remained constant. A third graph documenting the monthly changes in the indices shows relatively consistent changes generally but also indicates a small drop in four firm prices in late 1980, and a larger drop in prices in late 1982. These three graphs are reproduced below.
*100[[Image here]]
*101 Gilless’ Statistical Analysis
In addition to the graphical analysis, Dr. Gilless also performed a statistical analysis of the relationship between the indices. In his initial analysis, Dr. Gilless attempted to discern whether or not the relationship was adequate. To accomplish this he developed what he called a Model I relationship, along with his own definition of the term adequate. He defined adequate as “[I]f the value of the WWPA index goes up or down by a given dollar amount, then a similarly constructed index for North Coast Douglas fir should change in the same direction and by the same amounts (allowing for some random disturbances).” The Model I relationship was defined as InCit = Betai + Beta2 (IWpa,t) + et, where Betai is the intercept parameter, Beta2 is the slope parameter, Iwwpa,t is the value of the WWPA index at time T, Inc,t is the value of the North Coast Index at Time T, and et is an independent random variable with a mean of zero. The linear regression analysis performed by Dr. Gilless resulted in a Betai of 63.9, a Beta2 of .904, an R2 of .58,15 and a Durbin-Watson statistic16 of .194. Dr. Gil-less testified that Beta2 is the slope coefficient by which the value of the WWPA index is multiplied. He noted that a Beta2 close to one would imply a one to one movement between the indices. He then testified that the Beta2 of .904 was close to one given the standard errors inherent in the estimation process. However, he also testified that the Durbin-Watson statistic of .194 meant that the Model would consistently over or under predict the North Coast prices. Dr. Gilless then concluded that:
[If] my criteria, my definition of adequacy holds, this model should be a good predictor of North Coast lumber prices. The result of my analysis showing this high degree of serial correlation would lead me as an econometrician to say this Model I relationship does not capture the underlying relationship between these two indexes [sic]. They do not move together in the way I said was adequate.
The next portion of Dr. Gilless’ statistical analysis is his investigation of the relationship between the indices. Dr. Gilless developed his Model II test to investigate this relationship. Thus, the Model II relationship took the form InCjt = Betai + Beta2 (Iwwpa,t) + Beta3 (Digso) + Beta4 (D1983) + et. The difference between Model I and Model II is the addition of the Betas and Beta4 parameters along with the dummy variables,17 Dig8o and D1983. Dr. Gilless tes*102tified that the significance of this Model would be in whether Beta3 and Beta4 are significantly different from zero. If so then, according to Dr. Gilless “the gap between the two indexes and the situation of an adequate relationship, has been unstable.” 18 According to Dr. Gilless’ report and testimony, the Model II relationship was estimated as: Betai = 74.1, Beta2 = .854, Beta3 = 24.0 and Beta4 = — 17.9; the standard errors of the Betas where 8.85, .045, 2.40, and 2.14 respectively. The R2 was 0.95, thus 95% of the variability of the four firm index was explained by Model II. The Durbin-Watson statistic was 1.05 which indicated some correlation problems. All of the Betas were significantly different from zero and Beta2 was close to l.19 According to Model II then, the relationship between Dr. Gilless’ index and the WWPA index was unstable.
It is worth noting that Dr. Gilless’ conclusions as regards each Model are consistent with each other and with his general conclusion that:
[t]he relationship between the WWPA index and prices on the North Coast does not appear to have been a stable one between 1980 and 1988. In light of the evaluation criterion chosen for this analysis, it does not appear to have been “adequate” as a measure of North Coast Douglas Fir lumber price fluctuations. The WWPA index demonstrated much greater strength than North Coast prices in late 1980 and again in late 1982, and North Coast prices did not subsequently recover from the resulting erosion relative to the WWPA index.
Other Testimony
The testimony of Mr. Orville Olsen, a former CEO of McNamara & Peepe Lumber Company, indicated that the company was severely harmed by the breakdown in the relationship between their company’s actual sales prices and the price reflected in the WWPA index. Mr. Olsen testified that he and Mr. Joe Grosser, a principal with J & D Timber Company, prepared some graphs from published lumber sales data indicating that the prices paid for timber were rising while prices received for products were falling. One of the graphs, plaintiff’s exhibit 77, showed the WWPA index rising from 225.67 on May 31, 1983, to 248.34 at the end of July. The actual price as derived from Random Lengths, an accepted trade publication monitoring actual prices,20 went from 240 down to 220 during the same period. Mr. Grosser confirmed the testimony of Mr. Olsen that the lumber prices were moving in one direction while the prices of the final products were moving in the opposite direction. Additionally, Dennis Scott, a certified public accountant and vice president of Eel River Sawmills, testified that the WWPA index, through its failure to track actual prices, was imposing substantial unrealistic costs upon the mill. Mr. Charles Barber, a registered forester and an employee of plaintiff Reservation Ranch, testified that his tracking of the index and standard and better prices from Random Lengths indicated divergence in prices throughout 1983. The testimony of Joseph Tomascheski, the Vice President of Timber Resources for Sierra Pacific Industries, corroborates the other testimony on the functioning of the WWPA index during 1983.
Defendant’s Position
The defendant controverts plaintiffs’ position that the index was inadequate by presenting its own expert on the matter, Professor John Beuter. Dr. Beuter’s analysis attacks the roots of both of the plaintiffs’ studies although focusing more *103directly on Dr. Gilless’ study. Dr. Beuter’s attack on plaintiffs’ studies suggests that better indices were available for comparison than the Craig and Gilless indices. Also in his view, the studies focused wrongfully upon the indices ability to predict prices rather than on an ability to account for changes in the indices.
Dr. Beuter created several new indices based individually upon the years 1980, 1981, 1982, 1983, and the average between 1980-83. He concluded that the WWPA index is not as effective a measurement as the indices based upon actual prices when measured by common criteria such as the mean absolute deviation21 and the mean square deviation.22 But, he noted that the differences in effectiveness of the WWPA compared to the other indices is small.23
Dr. Beuter’s report attacks the plaintiff’s statistical analysis from a philosophically sound position. Namely, he correctly points out that all indices are only approximations of reality. They are not reality. If they reflected reality perfectly they would not be indices but compilations of the actual numbers. The very purpose of an index is to provide a short$hand approximation for a complex, ever changing reality. Thus, like the Greek philosopher Xeno’s paradox, one can always imagine an index a little more perfect than any existing one. And also one more perfect than that one, but still imperfect. With this argument defendant questions the very meaning of “adequacy,” at a philosophical level. To paraphrase Burke, “while this may be metaphysically true it is practially false.” The contract recognizes that some indices may be inadequate, and the contract must be interpreted to define that line of inadequacy. Therefore, the philosophical soundness of Dr. Bueter’s report will not defeat plaintiffs’ claim of inadequacy. Plaintiffs’ analysis appears to the court to be reasonable and backed up with other non-statistical evidence sufficient to carry plaintiffs’ burden of proof.
Although Professor Beuter’s report questions the validity and usefulness of the plaintiffs’ statistical reports, the court does not believe that Dr. Beuter’s report at all addresses the plaintiffs’ other evidence of index inadequacy. Dr. Beuter’s general conclusion that all is well with the index does not persuade the court to disregard all of plaintiffs’ credible evidence of index inadequacy not contained in Dr. Gilless’ statistical analysis. The graphical evidence presented by both Mr. Craig and Dr. Gil-less reflects a convergence24 of the WWPA index and their respective indices.25 Mr. Craig concluded that this convergence of the indices resulted in a breakdown of the previously existing relationship in late 1982. Further, the essentially uncontro-verted testimony of plaintiffs’ non-expert witnesses is ultimately convincing that the index was not performing its intended function properly. They showed that the index performance had a significant economic impact upon the profitability of their respective companies during 1983. The inadequacy language of the contract must ultimately be related to this type of impact.
The testimony of defendant’s other witnesses on the question of adequacy does *104not help its position. Dr. James Pharo, the chief appraisal specialist for the Service, and an economist, testified that the smaller the sample size, the less accurate the statistical prediction. This testimony’s purpose was to show that Dr. Gilless use of a thirty-five to forty-one percent sample was inadequate. The court notes, however, that Dr. Gilless testified convincingly that a forty percent or even much smaller, sample size would be adequate where the product in question was nondifferentiated.26 Further, Dr. Pharo testified that out of 357 sales to seventy-four firms in the North Coast region, the only complaints were those filed in this case. While this testimony may be significant on the question of the perception of other firms, the bare statistic does not answer many of the court’s concerns. For instance, what percentage of timber sales went to the other firms, and were the other firms harvesting timber during the time that the index was improperly functioning? The court has previously noted that the four firms providing sales data for Dr. Gilless’ report represented between thirty-five and forty-one percent of the annual Douglas fir production for the entire Redwood region. This leaves the remaining fifty-nine to sixty-five percent of the Douglas fir market for the other seventy firms doing business in the North Coast area.27 Accordingly, Dr. Pharo’s testimony does little to undercut Dr. Gilless report.
Mr. Fred Reseburg, Director of Economic Services, and Comptroller of the Western Wood Products Association, the producer of the index in question, also testified that the WWPA index was adequate. He said that the WWPA’s understanding of index adequacy is “that it properly reflects the price movement of lumber of the same species.”28 He then went on to note that the WWPA watches three elements when evaluating index adequacy. According to Mr. Reseburg, they are the grade recovery as compared to the index log, the arithmetic average movement in comparison to the index, and complaints from industry or the Forest Service. He also observed that any suspect conditions would have to exist for about a year before the WWPA would begin to fine tune an index. When asked whether the WWPA index was adequate as an indicator of product prices on the North Coast, Mr. Reseburg indicated that he believed it was adequate because the markets were the same.
The court has trouble accepting the defendant’s conclusions that the index was adequate, and Mr. Reseburg’s testimony underscores the trouble. Initially, the court observes that the three criteria laid out by Mr. Reseburg have been met in this case with respect to index inadequacy in the North Coast area. The grade recovery for these firms does differ from that which forms the index log for the WWPA index. An inspection of the grade groupings reproduced previously in this opinion shows that, among other differences, the WWPA index is based upon 20.30 percent of production being studs while only 1.41 to 1.54 percent are studs on the North Coast. Similarly, the WWPA index logs shows only 4.23 percent of D and Better Select while the North Coast logs show that 9.04 to 9.60 percent of its production is in D & Better Select.
The plaintiffs have also shown a disparity in the arithmetic averages between the WWPA index and the North Coast experience. Both Mr. Craig’s and Dr. Gilless’ graphical analysis of their respective indic-es show dramatic convergence of the indic-es and Dr. Gilless’ graph of the monthly changes shows the rather erratic behavior of the indices. Further, there is ample evidence in the record of the complaints of industry about index performance relative to the North Coast. Mr. Reseburg’s testimony that the conditions discussed above would have to exist for a year before the WWPA considered changing the index un*105derscores plaintiffs’ problem in light of the significant economic damages that can be done by an inadequate index in a relatively short time. The period of time involved here appears to be somewhere between six months and one year. This time frame is sufficient for an index to become inadequate and to cause significant economic damage to those holding contracts tied to it. The WWPA’s lack of sensitivity to this problem is perhaps not surprising in this case due to plaintiffs’ non-membership.
Mr. Reseburg’s testimony that he thought the index was adequate is also controverted by other evidence. His reasoning that the logs were selling in the same market place was refuted by much testimony that the markets for North Coast lumber were in southern California, admittedly a depressed market in 1983. The inland region sold its lumber into the Midwest, East, South and portions of the West outside of California where demand was higher. In addition, testimony indicated that because of the high quality of old growth Douglas fir on the North Coast a substantial amount was exported as clear timber.
There is also evidence that the North Coast firms could have become full members in the WWPA. The implication being that these North Coast firms could have then had a voice in the policy of the WWPA. Such evidence does not, however, influence the court’s decision in a way adverse to plaintiffs’ position. Other firms in the North Coast had sent information on Douglas-fir sales to the WWPA. The WWPA admitted that it did not use the information in calculating the WWPA index. The burden of this evidence, in fact, supports plaintiffs’ position. If the WWPA index did not more adequately reflect North Coast realities because of non-membership in the WWPA by plaintiffs, this underscores the inadequacy of the WWPA index with respect to plaintiffs’ in this case.
Further, the court will not suppose that the relatively small voice which the instant plaintiffs would have had in the policies of the WWPA would have caused the WWPA to include the plaintiffs’ product price information in the index. Furthermore, such efforts would most probably have been futile at best. There is much evidence that the WWPA index is in effect an inland index. It is, or was, geared nearly completely to the markets found for Dry Inland Douglas fir shipped to markets outside of California. The market for the old growth Douglas fir found on the North Coast of California is either California, or overseas for much of the clear timber manufactured.
If the instant contract were pegged to performance of an index without relationship to adequacy then both parties would assume the risk of poor index performance. However, when a contract is pegged to adequate index performance, the parties must have contemplated that the index performance would somehow be measured for adequacy or inadequacy. The adequacy of an index in this situation can only be determined by the closeness with which it tracks real economic variations. Short term or seasonal aberrations should not be included when determining adequacy, rather, relatively long term aberrations such as those experienced by plaintiffs in this ease are representative of an inadequate relationship. When an index constantly causes a contractual party to lose money because of presumed market changes not experienced in actual sales, then the underlying usefulness of the index must be questioned. No index can track dollar for dollar individual firm actual prices for then it would not be an index. However, changes in the index should be reflective in terms of direction and amplitude of changes experienced by any significant group of firms such as those represented in this case. Here the WWPA index and the actual prices as taken from Random Lengths went in opposite directions as WWPA presumed prices rose and actual prices on the North Coast declined. Consistent tracking above or below actual prices should not give rise to much concern, however, complete reversals of the relationship, or long term divergence or convergence of the indices do indicate a problem with adequacy of the index. This is particularly true when the area inadequately represented is a discrete and un*106represented part of the industry covered by the index.
Another question to be asked when an index is allegedly inadequate is whether it still fulfills the intent of the parties. In this case the answer must be no. The index was designed to split the risk of rising or falling markets.29 To the extent that it tracks actual prices (i.e., prices rising and index rising or prices falling and index falling), then the index fulfills its stated purpose. When the index is rising but actual prices are falling, it no longer fulfills its function and one party receives a windfall not intended or contemplated under the contract between the parties.
The court finds that the WWPA index at issue here became inadequate to reflect North Coast product prices beginning in December of 1982. The plaintiff is therefore entitled to refunds calculated at a flat rate as specified in the contract. The defendant is directed to calculate the appropriate amounts of refunds due plaintiffs under these contracts and to submit those calculations to the court within 30 days of the issuance of this opinion. Plaintiff may register any objection to the defendant’s calculations no later than 30 days after the service upon plaintiff of defendant’s calculations. The court will enter final judgment upon final agreement or determination of the amounts due under these contracts. Interest pursuant to the Contract Disputes Act will be calculated from the dates the claims were received or from the date payments were made, whichever is later.
. The Court’s April 10, 1989, opinion in this case is withdrawn and this opinion is substituted in its stead pursuant to plaintiffs Motion to Amend Opinion. The current opinion does not change the substance or holding of the initial opinion.
. Portions of the factual part of this opinion draw verbatim from uncontested portions of the parties’ post-trial materials.
. For purposes of this opinion the North Coast of California includes the counties of Del Norte, Humbolt, Mendicino, and certain portions of Siskiyou, Trinity and Glenn counties.
. Stumpage rate is the timber purchase price. As noted it is usually adjusted, either up or down, depending upon the prevailing market rate relative to the designated index. Mr. George Leonard, the Associate Chief of the Service, identified the purpose of stumpage rate adjustment as:
To adjust the stumpage prices charged under the timber sale contract so that they respond to general trends in the market. It provides an opportunity for operation of the timber sale contracts over a greater range of the market cycle and it provides a mechanism for sharing the risk and the benefits of upward movement of the market and of protecting the purchaser on downward movements of the market.
Transcript of Proceedings at 522-23.
. There has been no contention by plaintiffs or defendant that a suitable replacement index exists.
. This result ignores the constraint placed upon the process by standout provision B4.223 which provides:
Cash deposits requested to cover estimated charges for timber subject to escalation under B3.2 shall be based upon Current Contract Rates and related deposits in effect during previous calendar quarter, except when the most recent applicable monthly index differs from the previous quarterly index average by more than 5%. In such event, request for deposits shall be based on a rate adjustment of half of such difference, rounded to the nearest 10 cents.
. Grade Groups represent the various qualities of lumber cut from a log. Dr. Gilless’ report identified several grade groups in its glossary. For example, “Shop” is "Lumber that is graded for the number of sizes of cuttings that can be taken from it, for the manufacture of other products such as door and window parts.” "Standard and Better” is defined as a mix of lumber grades suitable for general construction. The “ & Better” signifies that a portion of the lumber is actually of a higher grade than standard (but not necessarily of the highest grade). The proportion of higher grades included is a factor in determining market value.
. The plaintiffs proposed order described the "Index Log" in this manner:
[The] WWPA uses lumber sales data reported by participating mills within the specified region to compute average selling prices for specified lumber grade groups, and combines these grade group average prices into the index according to the proportions of an "index log.” The index log assumes a fixed distribution of lumber grade groups, and is based on information collected in grade recovery studies of mills located in the appropriate region. The index log is used to level out fluctuations in product mix in sales data on the assumption that it reflects the long-term grade recovery of mills in the region. As of the date of trial, the index log for the Inland Dry DF-L Index was based upon a grade recovery survey conducted in the Inland Region in 1971. WWPA has stated:
The index log is used to provide a consistent weighing of grade prices. If grade prices were not weighed by an index log, the monthly average price would vary, depending upon the volume reported and processed by the Western Wood Products Association each month. For instance, if low volume of Shop and Better and high volumes of lower grades were actually shipped and reported each month, the average prices would be low. If, during a following month, a high volume of Shop and Better were reported along with a small volume of the lower grade, the average price would be substantially higher. Thus, use of the index log against grade prices eliminates the variation caused by fluctuations in the mix of grades reported month to month. This procedure provides a trend of average prices not dependent upon volume sold.
. Grading is the process of dividing a log into the various grade groups.
. Clean Key’Items are a method of adjusting Douglas fir-Larch information for green timber to the Dry Douglas Fir-Larch Index.
. The lumber firms supplying data for Mr. Craig’s report were Eel River Sawmills, Inc., Harwood Products Co., McNamara & Peepe Lumber Co. and Sierra Pacific Industries. Of these, only McNamara & Peepe Lumber Co. is not a party to this litigation. The sales data covers the period from 1982 through 1983.
. For purposes of comparison, Dr. Gilless’ grade grouping is reproduced here rather than in the section of the opinion discussing his report.
. The firms were Areata Lumber Co., Eel River Sawmills, Inc., Harwood Investment Co., and Sierra Pacific Industries. All four of the companies are plaintiffs in this action. Eel River, Harwood, and Sierra Pacific also provided data for Mr. Craig’s report.
. Dr. Gilless’ index log was reproduced previously along with the WWPA index log and the Craig index log.
. R2 is known in statistical language as the coefficient of determination. It is defined as “a measure of the variation explained by the estimated regression equation. It is a measure of how well the estimated regression equation fits the data.” Anderson, Sweeney & Williams, Statistics for Business and Economics, 510 (3d Ed. 1987).
. The Durbin-Watson test is a test for serial correlation. The statistic known as the Durbin-Watson statistic has a value between 0 and 4. As the court understands it, a value close to zero indicates positive serial correlation, a value close to two indicates no serial correlation, and a value close to four would indicate negative serial correlation. See Pindyck & Rubinfeld, Economic Forecasting, 158-64 (2nd Ed.1981). Serial correlation occurs "when the error terms from different (usually adjacent) time periods ... are correlated ... serial correlation occurs in time-series studies where the errors associated with observations in a given time period carry over into future time periods. For example, if we are predicting the growth of stock dividends, an overestimate in one year is likely to lead to overestimates in succeeding years.” Id. at 152.
. Dr. Gilless testified that:
A "dummy variable" is a variable that you use to account for something that’s qualitative rather than quantitative in nature in the form of in this case two different periods in time. You could also use a dummy variable as I did in one of the previous papers I had in my Vitae to express colonial associations. Either Indonesia was a colony of the Netherlands or it was not. That’s expressed by recording these variable values as zeros or ones. So in this case we can say that I’m estimating the relationship which says we’ll see if the relationship between the WWPA and the North Coast Index looks like North Coast Index equals Beta 1 plus Beta 2 times the WWPA Index in the middle period, late 1980 through late 1982 and looks like Beta 1 plus Beta 3, as a different intercept term, plus Beta 2 times the WWPA Index during that first year of the period and Beta 1 plus Beta 4 plus Beta 2 times the WWPA Index in the final period. So that when you estimate this the Beta 1 term now tells you sort of the difference between the two graphs in the middle period and Beta 3 parameter tells you sort of the changes in the intercept that would be reflective of early in the period, the Beta 4 parame*102ter the change from that middle period intercept reflected the later period data.
Transcript of proceedings at 378.
. Transcript of proceedings at 378-379.
. Dr. Gilless went on to correct the Model II relationship for autocorrelation problems. The corrected equation was substantially similar to the original Model II equation. However, the corrected equation had an R2 of .88 and a Dur-bin-Watson statistic of 2.15, therefore, no serial correlation problems were indicated.
. Mr. Olsen testified that he did not use his actual mill data because the Random Lengths data was almost identical. Transcript of proceedings at 88.
. "A measure of forecast accuracy [mean absolute deviation] is the average of the sum of the absolute value of the forecast errors.” Anderson at 619. The "mean absolute deviation measures the variation in a data set by determining the mean of the absolute values of the deviations from the mean.” Neil A. Weiss & Mathew J. Hassett, Introductory Statistics, 76 (2nd Ed. 1987).
. As the court understands it, the mean square deviation is the average of the squared deviations from the mean.
. The WWPA index also had the smallest mean deviation from the actual figures when compared to the other indices created by Dr. Beuter.
. By convergence, the court means that the WWPA index, which was below the four firm index on the graphs, began rising while the four firm index created by both of plaintiffs expert witnesses began to fall. The three graphs provided in the discussion of Professor Gilless' report present this well.
. The court has little, if any, reason to question the validity of the underlying indices created by Mr. Craig and Dr. Gilless. Both men were credible and both index logs were closely related. Also, both men created four firm indices which closely tracked each other and converged with the WWPA index in December of 1982.
. Nondifferentiated, according to Dr. Gilless, means that there is no brand identification. In other words, if a 2 x 4 is a 2 x 4, a smaller sample size is needed to determine the direction of price. Transcript of Proceedings at 363.
. Two of the remaining firms, J & D Lumber Company and Reservation Ranch, are also plaintiffs in this action.
. Transcript of proceedings at 914.
. Mr. George Leonard testified that the purpose of the index was:
To adjust the stumpage prices charged under the timber sale contract so that they respond to several trends in the market. It provides an opportunity for operation of the timber sale contracts over a greater range of the market cycle and it provides for a mechanism of sharing the risks and benefits of upward movement of the market and of protecting the purchaser on downward movements of the market. Transcript of proceedings at 523.