Complex products embody hundreds or thousands of patented components, all of which contribute a small amount to the overall value of the product. When one of those patents is infringed, how are damages to be assessed? That is problem is central to much of the high-profile litigation taking place internationally in the ICT sector concerning standard-essential patents (SEPs) subject to a commitment to license on fair, reasonable and non-discriminatory (FRAND) terms. Essentially the same problem was also raised, albeit in obiter, in Arctic Cat v BRP. As noted in Friday’s post, Roy J held that Arctic Cat’s 738 patent was not infringed. While it was therefore strictly unnecessary to consider damages, the case had not been bifurcated (“This is a case where bifurcation should have been more carefully assessed ), and Roy J went on to make a number of observations on the damages issue, though without arriving at any final figure. His discussion is of considerable interest as Canadian law has relatively few cases assessing damages for infringement when the invention is a minor part of a complex product.
The patentee sought damages in the form of a reasonable royalty for the use of the invention  and experts for both parties advanced a variety of methods for assessing those royalties. Ultimately Roy J concluded that most of the proposed methods were wholly unreliable, though one was inadequate as presented, but, with adjustment, could serve as a starting point . Roy J’s criticisms of the various methodologies all turned on one fundamental point: “the Court must strive to compensate the claimed invention solely with respect to damages that can be attributed to the invention” :
Where the invention is but one individual component of a multi-component product, the damages in the form of royalties must be in order to compensate the infringement of that individual component of the multi-component product that is captured by the invention. In effect, the royalty recognizes that the sales by the infringer are an illegal transaction which requires to be compensated. However, it is only the infringement that requires compensation.
The problem is that the invention is a method of tuning a two-stroke engine, in particular a snowmobile engine, for optimal performance by setting the ignition timing according to the exhaust temperature (see Friday’s post). How is the value of that invention to be separated from the value of all the other components of a snowmobile, or even of a snowmobile engine ? I will argue below that the method that found favour with Roy J is just as susceptible to this critique as those he rejected.
In the FRAND context, there are two basic approaches to setting a reasonable royalty, top-down and bottom-up. The bottom-up approach seeks to set a value on a patented technology directly, normally by looking to royalties on comparable licenses. This is referred to as a bottom-up approach because the cumulative royalty for the standard itself is established as the sum of the royalties from the individual technologies. The top-down approach, in contrast, starts by determining a value for the standard as a whole, and then apportions part of that value to the individual patented technology at issue. (For a review of the FRAND case law, see my paper with Tom Cotter, here.)
In this case, there were no comparable licenses, and all the methodologies fall, more or less, into the top-down category. The top-down methodology starts with the price or profitability of some product embodying the patented technology. This may be a final end-product sold to the consumer, or a smaller component thereof. In this case the candidates were the snowmobiles themselves, snowmobile engines, and the engine control module (ECM), which controls the ignition timing. A candidate methodology must then somehow apportion some part of that product value to the invention.
The plaintiffs’ expert, Mr Carter, proposed four methods. The basic flaw in all of these methods is that they used the value of the engine as a proxy for the value of the invention, when it is clear that the invention is responsible for only a portion of that value.
The first method proposed by Mr Carter was based on the profit difference between two of the defendant BRP’s snowmobile models, one of which did not practice the invention (the 800 P-TEC) and one which did (the 800 E-TEC). (The discussion of damages of course assumed, contrary to the holding on infringement, that the accused models did infringe.) Fundamentally, the method was based on the notion that the profitability difference between the E-TEC and the P-TEC snowmobile is a function of the invention . More specifically, Carter started with a long list of factors identified by a benchmark study as being of some importance to snowmobile purchasers. He identified three, namely engine power, reliability and acceleration, as being related to the invention, and he assessed the importance of these three factors relative to the entire list. As I understand it (the redaction of many key numbers makes Roy J’s description of the approach somewhat difficult to follow), and simplifying somewhat, this relative importance factor was then applied used to the profit differential between models to arrive at the increased profit due to the invention [362-64]. Roughly, it seems that the method assumed that the difference in profitability between the two models was attributable to improvements in all of the benchmark factors, and that the invention was responsible for all of the improvement in the three factors of engine power, reliability and acceleration. So, if there were say, a total of 35 factors, then 8.6% (3/38th) of the increased profitability of the snowmobile was attributed to the three identified factors and therefore to the invention. While the basic idea that the invention would affect the profitability of the snowmobile is at least plausible, Roy J identified problems at each stage of the analysis. There was no evidence of the effect of the invention on engine performance, and consequently there was no evidence that the invention was responsible for any improvement in engine power, reliability and acceleration [365-66]. As Roy J noted, “it is more than likely that factors such as reliability and engine power are affected by much more than the invention” . Indeed, there was no direct evidence of any improvement in any of these three factors; the improvement was imputed from the fact that the profit margin had increased. Moreover, the relationship between these three factors and improved overall profitability was tenuous. The importance of all the factors taken together adds up to more than 100% , which shows that there must be double counting, and the specific factors used to assess the royalty, eg acceleration and engine power, would appear to be correlated , which suggests an inflated royalty. Put another way, while the method apportioned some part of snowmobile performance to engine performance, it failed to adequately apportion the part of engine performance that was attributable to the patented invention. The second method proposed by Mr Carter was related and it was rejected for similar reasons. The expert did not strongly defend either of these approaches [369-70].
The third methodology compared the additional expected profit of BRP’s new 600 E-TEC engine, which did practice the invention, over a related model which did not, and then assessed the royalty as half the difference. While this method narrowed the focus by looking to the engine instead of the whole snowmobile, it assumed that the entire increased profit from the new engine was attributable to the invention. As Roy J said, with some understatement, “it is far from clear that the invention can be seen as explaining alone the profit. What is sold is a new direct injection engine. The invention would be merely an appendage” . That in itself is not a conclusive objection; it merely raises the problem of apportionment, which, while difficult, is not unsolvable, at least with a broad axe. But even crude apportionment was not possible because, as noted earlier, there was no evidence that the invention would actually contribute to any of the features valued by consumers, such as performance and reliability . Again, this method failed to adequately apportion the part of engine performance that was attributable to the patented invention.
The fourth method, which was preferred by Mr Carter, was to compare the profitability of the patentee’s snowmobiles over two model years, 2005, in which the invention was not practiced, and 2006, in which it was. Mr Carter attributed “the vast majority” of the difference in profitability between these model years to the patented invention . Again, the problem is that it appears implausible that the entire additional profit of the new model could be attributed to the invention alone, given that it is evidently a minor part of a complex machine (and keeping in mind that there was no direct evidence of how or whether it actually enhanced performance). But Roy J did not rely simply on the evident implausibility of this approach. He pointed out that the results of this method were internally inconsistent: for example, it implies that the profitability of black snowmobiles became better, as compared with green snowmobiles, over the two model years . It is difficult to see how this could be related to the invention (does the invention give an extra power boost to black snowmobiles in particular?), and in any event, no attempt was made to explain the discrepancy.
Roy J therefore rejected all of Mr Carter’s methodologies as being “so crude and deficient as to being of little assistance to the Court” .
Dr Urgone for the defendant, BRP, proposed three methods. While these methods all attempted to apportion some part of the value of the engine to the invention, the basis for the apportionment did not plausibly reflect the value of the invention relative to the value of the engine.
The first, “incremental cost-based apportionment,” compared two BRP engines, the SDI, without the invention, and the E-TEC, with the invention. The method took the percentage cost of the engine control module (ECM), which directly controls the ignition timing, relative to the cost of the whole engine for the E-TEC, and then did the same calculation for the SDI, and subtracted the latter from the former. This is baffling. As Roy J said “How the percentage of ‘y’ can be subtracted from the percentage of ‘x’ to obtain something useful remains a mystery in spite of the questions from the Court” . It’s a mystery to me as well. There is no particular relationship between cost and value. Suppose that the invention had actually reduced the cost of the ECM, which would be valuable as it would increase profit margins. This method would imply that the value of the invention was negative. In any event, even if cost could somehow be used as a proxy for value, this particular approach was grossly inadequate, for a variety of reasons pointed out by Roy J [390-93].
The second method proposed by Dr Urgone was “relative cost and inputs-based apportionment” -. This is the method that found most favour with Roy J. The method first derived the profit associated with the ECM itself by assuming that the ratio of profit of the ECM relative to that of the engine is the same as the ratio of their cost. That is the “relative cost” part of the method. The next task was to apportion the value of the invention itself from the profit of the ECM. To do this, Dr Urgone noted that there were 14 inputs to the ECM and only three of these were relevant to the use of the invention . Somehow, on the basis of the relative number of inputs, the method further apportioned the profits from the ECM. Unfortunately, perhaps due to the redactions, it is not clear to me exactly what the apportionment formula was. It may have been that 3/14ths of the profits from the ECM were attributed to the invention, but I suspect not. In any event, it seems clear enough that the apportionment would vary according to the number of inputs that were relevant to the invention relative to the total number of inputs: . As Roy J pointed out, one flaw with this approach is at the cost stage: “There is no indication of why the cost of the ECM would produce a profit directly proportional to the profitability of the whole engine” . There are also problems at the input apportionment stage. Roy J noted, that “what needs to be apportioned at this stage are the inputs in the ECM that relate to the invention, not those inputs already accounted for in the SDI engine” . Roy J suggested that a more refined approach, which differentiates between inputs needed for the new invention and those that would be needed for direct injection .
I am far more skeptical. Roy J pointed out that “crude calculations are oftentimes very sensitive to changes. Here, if instead of 14 inputs the number of inputs relevant to the new direct injection engine is rather 7, the increased direct profit attributable to the invention doubles to $13.56/unit” . But this reveals a more fundamental flaw with this approach. The basic intuition behind the approach seems to be that the value of the invention is somehow related to the number of new inputs to the ECM that are needed to support the invention. Perhaps there is some technical reason for this that is not apparent from the decision, but prima facie, I see no reason whatsoever why that should be so. Suppose no new inputs at all were needed. Perhaps exhaust temperature was already an input to the ECM for some other reason entirely – perhaps to throttle back the engine when the exhaust pipe was so hot as to be in danger of melting. If the ECM that practiced the invention and one that did not had exactly the same number of inputs, this would in no way suggest that invention was worthless. Conversely, the number of inputs might have had to be doubled, if the invention relied on a large number of new factors. Regardless of how many inputs it used, the invention would still be worthless if it did not result in any improvement in performance that consumers were willing to pay for. I simply cannot see how the number of inputs to the ECM could possibility be a proxy for the improvement in performance.
Dr Urgone’s third method was based on the idea that the more an invention is used, the more value it has . The BRP E-TEC engine used the invention only when the engine was operating at 70% throttle or more, which was roughly 5% of the time. If I understand correctly (and again redactions make the point a bit difficult to follow), because the invention was used 5% of the time, Dr Urgone then attributed 5% of the profit on the engine to the invention . The difficulty with this method is that there was no evident relationship between usage and profits . If the invention had been in use 100% of the time, then the 100% of the engine profit would have been attributed to the invention, even if it only contributed to a part of the engine performance . Roy J noted that the method posits notes that the invention is used only a small proportion of the time the engine is in use, and he asked rhetorically, “How is that a proxy for the value associated with the use of the invention?” 
In summary, Mr Carter used a variety of methods to arrive at the value of the engine, and then, quite implausibly, attributed all of that value to the invention. Dr Urgone nominally apportioned a part of the value of the engine to the invention, but the methods he used did not plausibly relate to the value of the invention.
I wonder if Roy J was attracted to Dr Urgone’s second method, despite all the problems he identified, because it focused on the smallest unit, namely the ECM. In the US FRAND case law context the general rule is that royalties should be based not on the entire product, but instead on the “smallest salable patent-practicing unit” (SSPPU): LaserDynamics 694 F.3d 51, 67 (Fed. Cir. 2012); CSIRO v Cisco, 809 F3d 1295, 1302 (Fed Cir 2015). Roy J remarked that the SSPPU approach “is gaining traction in the U.S.” , and in this case
 the comparison of the contribution margins between whole snowmobiles of different years was unreliable. Comparing engines and the added profitability due to the invention was an improvement. It may have provided more enlightenment if the analysis had focused on the ECM (or ECU) where it may have been possible to be more precise as to the actual use. In other words, a better focus on the smallest patent-practicing unit may have brought more adequate clarification on the real damages incurred by AC.
Similarly, he disparaged Dr Carter’s favoured method in part because it assumes “that comparing snowmobiles, and the snowmobiles of his clients at that, as opposed, for instance, to a smaller, or the smallest saleable unit that is part of the snowmobile, can produce reliable results” .
I suggest that considerable caution is required before embracing the SSPPU approach. In Ericsson, 773 F3d 1201, 1226 (Fed Cir 2014), the Federal Circuit explained that the SSPPU principle is justified on two distinct bases. One is fear of misleading the jury: “care must be taken to avoid misleading the jury by placing undue emphasis on the value of the entire product.” This rationale is wholly inapplicable in Canada. The second is the substantive point that when the value of the end product is not driven by the patented technology, assessing the royalty on the basis of the entire product may capture some of the value contributed by non-patented aspects of the product and thereby fail to apportion the profits between the patented and unpatented features. But as the Court noted in Ericsson at 1226, the same net royalty can be achieved either by using a small component which embodies only the patented invention as the base, or by using the entire product as the base combined with a lower royalty rate. And more recently, in CSIRO v Cisco, 809 F3d 1295, 1303 (Fed Cir 2015), the Federal Circuit has remarked that a rule which would require all damages models to begin with the smallest salable patent-practicing unit “is untenable.” The ultimate goal is to determine the value of invention. To the extent that focusing on the SSPPU aids in that goal, doing so is desirable, but not otherwise. In this case, for example, Dr Urgone’s second method derived the profit associated with the ECM itself by assuming that the ratio of profit of the ECM relative to that of the engine is the same as the ratio of their costs. That effectively starts with the profit margin on the engine, and apportions some of that value to the ECM on the basis of the assumption that profitability is correlated with cost. I see no particular basis for that assumption, particularly IP context, where the invention is effectively information. An ECM that is a stock microprocessor may cost very little, and yet if it is cleverly programmed according to a patented invention, it may make a major contribution to the performance and value of the engine, even though it contributes only a small part of the cost. In this case, focusing on the ECM adds a layer of distortion, rather than a layer of clarity. Indeed, for that reason the ECM would not be the focus of the analysis under the US SSPPU approach, because it is not a “saleable” unit. When the unit is independently sold, at least we know the value of the unit itself, though further apportionment to arrive at the value of the invention is normally required. But there is no point to focusing on a small unit when it is not sold separately, so that determining its value creates a new problem in itself.
In this case it seems to me that one of the first or second of Mr Carter’s methods had the most promise in principle, suitably adjusted. (Though I recognize that I do not have the benefit of the full record.) At least they focused on features that add value to the snowmobile. If it were possible to put a value on these features, and then connect the feature to the invention, a rough but reasonable apportionment might have been possible. But the basic problem facing the patentee on the facts is that there was no evidence at a technical level that the invention contributed to the performance of the engine , . Without any factual evidence as to whether and how the invention actually affected the performance of the product in a way that is valued by consumers, it is difficult to see how any apportionment methodology, no matter how sophisticated, could arrive at an even roughly satisfactory apportionment.
What is a court to do when faced with such weak evidence of damages? Roy J held that the burden is on the patentee to show what the royalty should be, and in particular “to give evidence that will separate from the profits realized by the infringer the damages that are as a result of the infringed invention.” . Roy J held that “the Plaintiff has not discharged that burden” . It might seem to follow that in this case, the patentee had not carried its burden and damages should therefore be assessed as zero. Roy J noted that Grenier, in his chapter on damages, in Intellectual Property Disputes (Dimock, ed), 17-4.1, suggests that the plaintiff who does not establish the royalty by “conclusive evidence” might be awarded nominal damages. Roy J rejected this view, saying an award of zero or nominal damages was appropriate “only in the extreme cases in view of a violation of a valid patent” . Roy J noted that “In this case, I would have concluded that there is not a complete absence of evidence. There was an absence of satisfactory evidence” . This raises two points. First, there is really no support for a standard that damage must be established on the basis of “conclusive” evidence. That proposition is not supported by either of the cases cited by Grenier in the paragraph referred to by Roy J (namely Teledyne v Lido (1982), 68 CPR(2d) 204, 208-09, and Reading & Bates,  1 FC 483). More interestingly, if we take it that the plaintiff has to prove its loss on the ordinary balance of probabilities, the difficulty is that the loss is not a binary concept, like validity. It is straightforward to say that (in)validity must be established on the balance of probabilities, as the evidence will weigh one direction or the other, and the balance of probabilities sets the tipping point. But the loss is a number, falling along a continuum. Even with the most rigorous methodology, the specific number arrived at probably does not exactly reflect the true loss. Certainly, the better the methodology, the more likely it is that the number arrived at will fall in the reasonable vicinity of the true loss, but that is a difficult notion to reflect in the concept of burden of proof, which rests on a paradigm of a binary decision. In any event, the courts have long relied on the metaphor of a “broad axe” .
With that said, I’m not sure the broad axe implies that the court must always assess some damages for infringement of a valid patent, no matter how inadequate the evidence. In this case, Roy J entirely rejected the evidence of the patentee, saying it had not carried its burden , and he concluded by indicated that he would have assessed a royalty based on a method proposed by the defendant’s expert:
 However, it would also be inequitable to assess the damages at zero. A more appropriate approach could have been the blunt, but practicable, relative cost and inputs base apportionment, with adjustments. A royalty higher than that proposed by BRP would in all likelihood have been appropriate.
The relative cost and inputs-based apportionment was BRP’s method. Apart from the point that, in my view, this method was entirely unreliable, suppose that BRP had not presented any evidence at all. Would Roy J have awarded more than nominal damages based on the patentee’s inadequate evidence? Moreover, Roy J said BRP’s method was appropriate “with adjustments.” But it is not clear how the court can make the adjustments without evidence from the experts. Fortunately, Roy J did not have to address this questions in light of his conclusion that the patent was not infringed.
In my view, this might well be a case in which a purely nominal award would have been appropriate. Roy J's fundamental objection to a nominal award seems to have been that if we know that the patent is valid and infringed, it would be “inequitable” to assess the damages at zero simply because of the difficulty of carrying out an accurate apportionment , . To my mind, this point would have been more compelling if we had some evidence that the invention actually contributed something, at a technical level, that consumers valued. As Roy J remarked several times throughout his decision, there was no evidence as to what the invention actually did, even in the plaintiff’s snowmobiles. Apportionment is inherently a very difficult problem, and if we know the invention does something useful – drastically reduces dropped calls in a phone, for example – it is reasonable to say that damages should not be refused entirely simply because it is difficult to determine the precise value of an admittedly valuable invention. But if there is no evidence that the invention is actually valuable at all, even at a technical level, I see nothing inequitable about awarding nominal damages.