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# Understanding the Crazy Math Apple and Samsung Use to Calculate Patent Damages

Apple argues billions while Samsung argues pennies. Re/code sorts things out for you.

Listening to how Apple and Samsung calculate damages often feels like Alice’s trip down the rabbit hole into Wonderland.

According to Apple’s experts, consumers would pay tens or even upwards of \$100 per phone for the patented features in the case. That is despite the fact that consumers typically pay \$200 or less for a smartphone, when factoring in a carrier subsidy. On average, Apple is seeking roughly \$40 for each of the more than 37 million Samsung phones and tablets it says infringe on its patents.

Samsung’s experts, meanwhile, say that even if its devices are found to infringe Apple’s patents, the damages should amount to just pennies per patent per device. Never mind the fact that Apple rarely licenses its patents, much less to a chief rival.

The one obvious conclusion is that if you have enough money — and these experts don’t come cheap — you can find math that supports almost any damage amount. It brings to mind the old expression that there are lies, damn lies and statistics.

But, with the case winding down, let’s look more closely at the numbers themselves and why they are so vastly different. Testimony in the case is due to wrap up on Friday, with the jury likely to begin deliberations by Monday or Tuesday.

In making its case, Apple relied heavily on a study from John Hauser, an MIT professor whom Apple also employed for the first patent case. Hauser did what is known as a “conjoint study” to place a value on features related to the patents in this case as well as to determine how the features affected a customer’s willingness to buy such devices.

Hauser’s study described certain features, including ones related to the case as well as unrelated “distraction features” and came up with some shockingly high values for the software features at issue here. For example, Hauser said his study found that consumers would be willing to pay \$102 more for a smartphone with automatic word correction or \$44 more for one with a universal search feature.

A second damages expert, relying heavily on Hauser’s study, concluded that Apple is due more than \$2 billion.

Samsung has blasted Hauser’s methodology, arguing that the type of study he did is inappropriate for valuing minor features and is tantamount to asking consumers which car they would buy based on a comparison of cup holders.

The Korean electronics maker trotted out a bunch of economics experts with entirely different methods of damage calculation. Its experts used an array of indirect methods, including eye-tracking studies and an analysis of product reviews, to justify its conclusion that each of the accused patents deserved a value of just 35 cents per phone.

One expert, Yale professor Judith Chevalier, used a range of different methods to arrive at the 35-cents-per-patent figure. She looked at what Android consumers typically pay for apps and an analysis of how often reviews mentioned the features in question, as well as the fact that Apple’s accounting method defers around \$10 for OS upgrades, each of which includes more than 100 features.

To bolster its case that the patents deserve lower valuations, Samsung is also seeking lower damages in its counterclaim that Apple products infringe on two of its patents — one related to FaceTime over cellular and another having to do with photo and video albums.

Samsung is asking for less than \$10 million in total damages. To arrive at that number, Samsung did some rather interesting math, of course involving multiple experts. The first expert used the 99 cents that Apple charged for FaceTime for the Mac as an example of what users might pay for a videoconferencing feature. Other factors used in the calculation included another expert’s calculation of relative demand for the chat feature and, oddly enough, the 70 percent cut Apple gives developers in the App Store. Samsung’s expert said that in this case Apple was like the developer of FaceTime and Samsung deserved, say, a 30 percent cut of the feature’s value if found to infringe Samsung’s patent.

On cross-examination Tuesday, Apple’s lawyers noted that Samsung has spent nearly as much on expert witnesses as it is seeking from Apple in its counterclaim. Even though Apple would rather not pay Samsung much if it is found to infringe, Apple is hoping to sway the jury that Samsung is lowballing its demands in an effort to suggests patents in general aren’t really worth that much.

Apple, by contrast, argues that its patented technology has significant value and that it has suffered greatly at the hands of Samsung. Apple, in various cases, has argued Samsung’s phones directly copy the iPhone and infringe on dozens of patents. However, companies are typically only allowed to sue over a few patents in one case. And, according to patent law, Apple can only collect damages for infringement of the patents it is actually suing over in a particular case.

So, instead of being able to argue that the total impact of Samsung’s copying is \$2 billion, the company must instead argue that the figure relates to just the value of the patents accused in the case.

Not surprisingly, Samsung doesn’t believe it owes Apple much, if anything. Indeed, when it comes to a certain type of damages known as “lost profits,” Samsung argues Apple actually isn’t entitled to any damages because it would not have had to keep its products off the market for a significant amount of time. Rather, it argues that even if it is found to infringe, it should only have to pay what is known as a “reasonable royalty.”

That’s where the Hauser and Chevalier numbers come in. Part of the royalty calculation involves what is known as a “hypothetical negotiation” in which the two parties are forced to come to the table and work something out. Not surprisingly, each side’s experts conclude that it is the other company that would essentially give in and pay what its client is seeking.

Expect both Apple and Samsung to use a significant part of their closing arguments, expected to take place on Monday, to make the case why their crazy math isn’t so crazy after all.