# Elastech

Elastech is a plastics firm which has invented a new kind of squash ball – which they are convinced will soon dominate the global market.

They would like us to estimate the size of the US squash ball market, where they will start selling their new balls first.

This is a simple estimation question and is really just a test of the candidate’s ability to structure their approach to the question and make reasonable assumptions.

## Structuring the Problem

The candidate should begin by asking reasonable questions to gather additional information and by explicitly structuring their approach to estimating the market.

Other values will have to be assumed by or come from the general knowledge of the candidate.

The candidate could break down this estimation in multiple ways - and might choose to represent this breakdown mathematically and/or as a tree structure.

Here, we leverage the facts that:

Number of squash balls sold = number of players x number of balls per player

Number of balls per player = number of packs purchased x number in pack

We also note that age will be one of the most important drivers as to how likely an individual is to participate in squash. Thus, we segment the US population into age brackets likely to capture different levels of participation.

This breakdown is best represented as an issue tree, as shown in Exhibit 1.

## Leading the Analysis

The candidate should now work through the different elements of their structure to arrive at an estimation.

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### Segmentation

The candidate should make a rational segmentation of the US population based on reasonable assumptions.

Here, we make the following reasonable assumptions:

- Average life expectancy is 75.

- The population is linearly distributed as a function of age – that is, the population pyramid is a simple column, and there will be the same number of individuals of any two ages.

- The demanding nature of squash means that almost nobody plays it below the age of 16 or above the age of 60.

From here, the population aged between 16 and 60 is segmented into three 15-year age cohorts.

The following additional assumptions are then made for each cohort:

*16-30*

This is when individuals are most likely to play squash – at school, university, for a team or for leisure. We assume 10% of this age cohort will play squash at least once per year.

*31-45*

Participation in squash will decline somewhat in this age group along with participation in sporting activity generally. However, squash remains a popular activity – especially amongst certain socio-economic groupings. We assume 5% of this age cohort will play squash at least once per year.

*46-60*

Participation will fall significantly as many individuals find that injuries etc make it no longer viable for them to participate in squash. We assume 2% of this age cohort will play squash at least once per year.

### Number of Players

With these assumptions, we can calculate an estimated total number of squash players in the US.

Total number of individuals in each cohort = (15/75) x 330m = 1/5 x 330m = 66m

Total number of players = number from cohort 1 + number from cohort 2 + number from cohort 3

Total number of players = (0.1 x 66) + (0.05 x 66) + (0.02 x 66) = 0.17 x 66 = 11.22m

### Number of Balls

The number of balls bought per year by squash players will vary wildly. Casual players will often simply use those available for public use at courts and buy none. Serious players may buy dozens per year.

Here, we assume that the average player will have cause to buy quash balls twice per year. When they do, they will simply buy one pack.

We can then very simply calculate the average number of squash balls per year purchased by each player:

Number of balls bought per player = number of packs bought x number of balls in pack

Number of balls bought per player = 2 x 3 = 6

## Squash Ball Market Size

We can now conduct the final calculation to find our estimate for the size of the US squash ball market in terms of the number of balls sold.

Number of balls sold = number of players x number of balls bought per player

Number of balls sold = 11.22m x 6

Number of balls sold = 67.32m (round to 67m)

**
We can, therefore, inform Elastech that we estimate the US squash
ball market at approximately 67 million balls sold per year.**

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