HP-2020-000016 - [2025] EWHC 1451 (Ch)
Chancery Division of the High Court

HP-2020-000016 - [2025] EWHC 1451 (Ch)

Fecha: 16-Jun-2025

Mr Colley’s quantum models

Mr Colley’s quantum models

606.

Mr Colley’s expert reports calculated the potential profitability of Worldeez, using two alternative models. The first model was a Bertrand simulation model, with various different assumptions as to the success of Worldeez within that model. The alternative model was a simpler model of profitability using the financial projections prepared by Cabo for Nickelodeon.

607.

As already noted at §501 above, Mr Colley’s evidence was not that Cabo would in fact have achieved the success modelled in any of the permutations of his simulation model, or the Cabo projection model. Rather, his models sought to provide an indication of the profits that Cabo could have obtained if it had achieved the level of commercial success assumed in the variants of his simulation model or the Cabo projection model. Whether or not Cabo would have achieved those levels of commercial success was, Mr Colley accepted, a matter for the court based on the factual evidence and the evidence of the toy experts.

608.

There is no dispute that a Bertrand simulation model can be a useful model to quantify damages arising from a competition law infringement. The use of simulation models (including Bertrand models) is discussed in the Commission Staff Working Document “Practical Guide: Quantifying harm in actions for damages based on breaches of Article 101 or 102 of the Treaty on the Functioning of the European Union”, C(2013) 3440. In particular, the Practical Guide notes that:

i)

The Bertrand model of competition describes a market with a relatively small number of firms (and high barriers to entry) that compete on price and not output quantity. Under this model, prices are set simultaneously by firms based on beliefs about the prices their competitors will charge. Prices increase with the degree of product differentiation (§98).

ii)

Bertrand oligopolies in markets with differentiated products will normally lead to prices and volumes somewhere between perfect competition and monopoly levels, with the exact outcome depending on the number of firms in the market and barriers to entry, the degree of differentiation, and other characteristics of the market such as demand characteristics and the capacities and cost structure of producers (§99).

iii)

Simulation models can be used to simulate the sales volume and market share a foreclosed competitor would have attained if an exclusionary infringement had not taken place. It should be constructed to replicate the most significant factors influencing supply (in particular the competitive interaction between firms and their cost structures) and demand conditions (§§100 and 103).

iv)

Although such models rely on a simplification of reality, they may provide useful insights regarding the likely damages. Their reliability depends, however, on the right assumptions being made, particularly as to the likely conditions of competition and consumer demand in the non-infringement scenario (§104).

609.

Mr Colley started from the premise that a Bertrand simulation model was a reasonable approach to the modelling of damages, bearing in mind the inherent difficulty of estimating Worldeez’ performance in the counterfactual scenario. His chosen model was a differentiated product Bertrand model, which assumed that equilibrium prices could be significantly above marginal cost, because of the quality differences between products.

610.

In order to populate that model, Mr Colley looked at five comparator brands in the market in 2017–2018: LOL Surprise, Shopkins, Hatchimals Colleggtibles, Num Noms, and Mash’ems/Fash’ems. He used the actual world retail prices and market shares (by both revenues and volumes) in those years to derive a “quality index” for each of those brands. Mr Colley described the quality index as reflecting the “consumer appeal of a brand” based on factors such as the features of the products and age of the brand. It was, however, common ground that the quality index also inevitably reflected other non-price factors that affected sales volumes, such as marketing and supply chain issues. As Mr Colley accepted in his oral evidence, “quality” in this context did not mean purely product design quality, but was rather a measure of the commercial success of the products in the market, in terms of sales volumes.

611.

Mr Colley then defined hypothetical quality indices for Worldeez, based on his calculations of the quality index for the comparator brands, weighting those comparators in different ways. The simulation model then predicted how Worldeez would have performed in the market if it had achieved the assumed quality level, taking into account its actual world prices, marginal costs and the simulated competition from the other brands if Worldeez had been present on the market. In short, therefore, the models predicted what Worldeez’ revenues might have been if Worldeez had achieved the same commercial success as the brands in the comparator sets chosen, with the various different weightings he selected.

612.

Mr Colley’s primary calculations were made using several different comparator sets:

i)

Base Case 1 specified a Worldeez quality index calculated as the average of the five comparator brands.

ii)

Base Case 2 assumed that Worldeez’ market performance would have been more similar to that of LOL Surprise and Hatchimals Colleggtibles than the other three comparator brands. This model therefore calculated the Worldeez quality index by doubling the weight given to the LOL Surprise and Hatchimals Colleggtibles quality indices, compared to the weight given to the quality indices of the other three comparators.

iii)

The two base case assumptions were then tested using various sensitivity analyses, one of which gave Worldeez the same quality index as the Hatchimals Colleggtibles brand.

613.

Mr Colley used his simulation model to predict Worldeez’ counterfactual sales volumes and revenues in 2017 and 2018. He then extrapolated from those predictions to estimate volumes and revenues in subsequent years, as well as licensing revenues and international sales, based on various assumptions set out in his evidence. His profitability calculations assumed that the cost of goods would be as in the Nickelodeon projections.

614.

The alternative profitability model based on the Cabo projections was far simpler. It was not a simulation model but simply calculated lost profits taking the Cabo projections as a starting point, extending that to further years, further retailers (Argos, Amazon and Claire’s), and adding in licensing revenues and international sales, on the same assumptions for those as used for his simulation models.

615.

When cross-examined on the relevance and reliability of his profitability models, Mr Colley emphasised that the purpose of his evidence was simply to model different versions of success in the counterfactual, and that it was not for him to opine on the chances of Worldeez achieving those levels of success. He accepted that his simulation modelling was only relevant if the court concluded that Worldeez would have achieved sales volumes comparable to those of the comparators used his model. Since the Cabo projections model assumed even higher sales volumes than considered in the simulation modelling, Mr Colley accepted that if the court considered that Cabo would not have achieved the commercial success assumed in in the simulation models, that would also undermine the utility of the Cabo projection model:

“… it’s got to be reasonable that if your main concern looking at the simulation results is that you don’t think that Worldeez was going to be of sufficient quality to … compete with those comparators that were achieving that certain level of sales, and the Cabo forecasts imply an even higher level of sales, it would be difficult how you could sort of square the one with the other.”

616.

In its opening submissions Cabo relied on all three of Base Cases 1 and 2 and the Cabo projections model. The version of the DTM originally provided to the court for the trial therefore included, in the input cashflow assumptions, a midpoint of the two Base Cases, the Cabo projections model, and an average of the Base Case midpoint and the Cabo projections model. By the time of the closing submissions, however, Cabo had abandoned Base Case 2. As for the Cabo projections model, the most that was said was that it was a “further data point to which weight should be attached”, on the basis that it provided some insight into the evolution of the business which Cabo and Singleton were expecting at the time. Notably, however, the inputs for the final version of the DTM did not include either Base Case 2 or the Cabo projections model: in reality, therefore, both were abandoned by Cabo as providing any useful quantum model for the court.

617.

Instead, Cabo’s closing submissions relied on the following three versions of the simulation model, which were the versions included in the final version of the DTM:

i)

Base Case 1as described above.

ii)

A scenario giving Worldeez the same quality index as Hatchimals Colleggtibles.

iii)

An average of Base Case 1 and the Hatchimals scenario.

618.

Assuming a five-year lifecycle for Worldeez, and using Cabo’s costs stack, Cabo provided the following estimates for its losses (in millions of pounds), on two alternative bases. The first was that Cabo would have been successful at securing both international distribution for Worldeez and licensing deals (in both the UK and overseas), and did not therefore make any adjustment for the probability of those outcomes. The second was that the loss calculation should be subject to probability adjustments to reflect an 80% probability of international distribution and a 65% probability of licensing deals. The calculations also included future revenue streams reflecting future unknown product, as well as interest. The figures are shown in the following table, with brackets indicating the probability-adjusted figures.