# Scale factor adjustments in preference share simulations

The Scale Factor, `k` is a number used to adjust the steepness or flatness of share preference in order to reflect the market shares in reality. You can adjust it under the of the preference share simulations.

## Example

Let’s assume we have a simulation with 3 products A, B, C, with partworth utilities, `x` = 1, 2, 7 respectively. In the example below, we have selected Scale Factor, `k` = 0.01, 0.5, 1, 2, 5, 100 to see the effect of different `k` to our preference shares.

Table illustrating the simulations with different `k`

 xk Preference share with Scale Factor k (normalised) Product Partworth Utility (X) Share of Choice k = 0.01 k = 0.5 k = 1 k = 2 k = 5 k = 100 k = 0.01 k = 0.5 k = 1 k = 2 k = 5 k = 100 A 1 10% 1.000 1.000 1 1 1 1 33.0% 19.8% 10.0% 1.9% 0.0% 0.0% B 2 20% 1.007 1.414 2 4 32 1.268 × 1030 33.3% 27.9% 20.0% 7.4% 0.2% 0.0% C 7 70% 1.020 2.646 7 49 16807 3.234 × 1084 33.7% 52.3% 70.0% 90.7% 99.8% 100.0% Total 10 100% 3.027 5.060 10 54 16840 3.234 × 1084 100% 100% 100% 100% 100% 100%

Bar chart visualising the simulations with different `k`

When `k` approaches `0`:

• Check column `k`=0.01
• We see that difference in preference shares are minimized. Despite Product B having twice the `x` (Utility) compared to Product A (2 vs 1), and Product C have more than triple the `x` compared to Product B (7 vs 2), we see that the preference shares with `k` –> 0 are divided almost equally at 33% among all three products.

When `k = 1`:

• Check column `k`=1
• The preference shares when `k` = 1 is exactly the same as share of choice normalised to 100%.

When `k > 1`:

• Check column `k`=2, 5, 100
• As `k` grows larger, the difference in shares are more distinct now and we see that almost everyone tend to select the single most preferred product. When `k` is sufficiently large, this approach is analogous to High Risk Simulations.

When respondents make choices in Conjoint surveys, they tend to make less errors compared to choices made in real life, as there tend to be more external factors affecting purchase decisions in real life, and this leads to relatively sharper preference share differences in simulations. In order to flatten it a little, we recommend scale factor `k` ranging between 0.3 to 0.8. Using scale factor below 0.2 would make the preference shares too flat and it will be difficult to see which product perform better than the rest.

## How to decide what scale factor value to use?

When you set up a low-risk preference share simulation on Conjointly, the default scale factor `k` = 1 and this should work for most scenarios. However, if you would like to change your `k` value, you can do so in Simulations tab → . Here are our recommendations of `k` value to be used for different scenarios:

kRecommendation
0.01We recommend to use very small `k` (value close to 0) in highly impulsive market, where people generally don’t care about brand/price/pack design.
0.5We recommend to use small `k` (ranging between 0.3 and 0.8) when there is some degree of impulsive behaviour. For example, Fast-Moving Consumer Goods, where attributes such as brand, price, promotion, pack design, claim do matter.
1We recommend to use `k` = 1 in situation where everyone makes rational decisions, not overlooking any important attributes on all purchase occasions.
2 to 5We recommend to use `k` = 2 to 5 when the market is closer to a high-risk context, where people tend to select single most preferred product even when it is only marginally more preferable than the next best product. For example, house, cars, computers.
50 or moreWe recommend to use `k` = 50 or more in life-and-death, urgent situations, where every minute detail of the product could fully sway preference. For example, surgeries for chronic diseases.