Beta Distribution & Decision Modeling Analysis

In this decision we will be using a modified brand image coefficient (BIC) that reflects the product mix scenario. We are using this modified BIC because we recognize a higher conversion rate does not always equate to a stronger brand equity-especially in the luxury market. More virtual products may drive increased interaction, but can also dilute overall brand identity by appearing too trend-driven or can shift customer perception away from the authenticity Flourish is known to have. Our model reflects this tradeoff by keeping conversion rates reflective of potential increased engagement and purchases when the right balance of virtual products in introduced, while also scaling the brand image coefficient downward, sometimes resulting in a negative BIC (brand image damage), for mixes that overemphasize virtual goods and risk weakening Flourish's luxury position.

Managers expect BIC to be lower overall when compared to the metaverse decision based on internal and external information collected from and about luxury customers and AR experiences. AR is often associated with functionality and convenience which are not values always at the core of a luxury brand. It may be seen as more utility-driven, regardless of product mix, and less groundbreaking than the metaverse decision. 

We expect the conversion rates and number of visitors to in the AR store to be less than the metaverse store. We also expect the conversion rates to vary based on the product mix offered. 

We anticipate the physical good only decision to have moderately high conversions as its best aligned with the traditional luxury consumer and their expectations. 

The 80/20 physical to virtual mix represents a conservative yet innovative option that could lead to the highest conversions without compromising the brand's modern image while still maintaining customer alignment. It is a balanced mix that will appeal to customers who are open to innovative digital experiences but still associate luxury primarily with physical goods.

However, the 50/50 mix leans more into the virtual goods, which could be a potential risk to the brand's premium brand image and number of successful purchases. A higher offering of virtual goods may reduce value traditionally tied to luxury brands and could lower purchases and overall conversion rates with Flourish's existing customer base. The uncertainty around customer's embracing virtual goods makes this option riskier in terms of brand image impact.

Given this information, we used binomial distribution to establish our probabilities of each conversion and product mix combination. 

The conversion rate probabilities give a clear picture of what we can anticipate from each product combination. For the Physical Goods Only option, around 11.8% of outcomes fall into the low conversion level, 79.9% fall into the moderate level, and approximately 8.3% fall into the high level. This indicates a highly consistent, predictable performance in which most consumers convert at a moderate rate, which are ideal for maintaining a trusted, traditional luxury experience.

In the 80/20 Physical/Virtual mix, we observe an even better profile of around 9.2% of outcomes are low, 84.0% are moderate, and 6.8% are high. This balance implies that, while there is a slight introduction of digital products, the risk of underperformance is minimal, and the strategy is effectively matched to engage customers while staying true to the brand's core values.  

On the contrary, the 50/50 mix indicates a greater degree of uncertainty. Around 14.3% of the results are in the low conversion level, 76.5% in the moderate level, and around 9.3% in the high level. The increased likelihood of low conversions indicates that focusing more on digital products may not resonate as well with your core luxury customers, thus compromising the brand's unique appeal.

From these probabilities and our modified BIC, we can build our distribution tree

According to the analysis, the proposed AR shop represents a strategic opportunity for Flourish to increase its digital presence, brand image, and improve its relationship with current high-end clients. The decision tree shows that the AR project should be launched once the metaverse investment is successful. Given the probability-weighted brand image impact of various product mixes, the 80/20 physical/virtual mix emerges as the best option and when paired with the metaverse decision, results in a total brand image impact of 848, over the 800 required minimum for Flourish management. Even with a lower modified BIC, we expect the conversions to stronger with this scenario, as it strikes a delicate balance between encouraging innovation while preserving the established luxury brand identity.

However, we can see if management were to pursue more virtual goods in their AR store, they risk actually diluting the brand image. As seen in the 50/50 product mix, the brand image impact score gained from the metaverse investment is actually brought down by the AR store to 830. While this is a marginal difference, Flourish managers should not consider increasing virtual goods much beyond the 80/20 mix at the risk of negatively impacting any brand image impact gains from the metaverse decision.

Risk Profile

Our decision tree outlines the optimal decision for Flourish managers is to create an AR Storefront. Based on our risk profiles, we can analyze the optimal product mix within the AR Storefront and determine what products will allow Flourish to optimize brand image. "50/50 Physical/Virtual" product mix in the AR storefront has a lower expect Brand Image Impact with the most likely result being 830. This option provides the brand the least return, and thus is not the optimal choice.  Offering "Physical" products only produces reasonable return on Brand Image Impact and is expected to produce a minimum BII of 841.5, with the most likely scenario being 846.25.   This provides a reasonable option in terms of the brand image. Next, the "80/20 Physical/Virtual" has stochastic dominance over all the other available options. This is evident as it produces a higher Brand Image Impact score in all the tested scenarios. This scenario is most likely to produce a score of 847.48. In each estimated market condition the product mix of 80% physical and 20% virtual items produces the best resulting Brand Image Impact score. 

In our analysis we focused on three product mix options for the AR storefront and focused on how each aligns with Flourish's brand image and digital customer expectations.

• 50/50 Physical/Virtual Mix is a bold digital move with potential to reach all new customer segments. However, the increase in virtual goods dilutes brand exclusivity and overall image while alienating loyal clientele and results in a loss of brand image impact score. We would suggest to Flourish management to reduce the amount of virtual product offerings overall.

• Physical Only offers familiar, tangible luxury experience with minimal risk to the brand. It requires the lowest investment and ensures steady conversions and results in modest brand image and engagement.

• 80/20 Physical/Virtual Mix strikes a balanced approach, introducing some digital innovation without straying from the brand's original products. This option is what we recommend as it is ideal for attracting tech-savvy customers while maintaining core luxury values, making it the most aligned with Flourish's identity.

We recommend moving forward with the 80/20 mix, which enhances digital innovation while keeping brand prestige safe. It results in the highest addition of brand image impact. 

To ensure success, we recommend Flourish prototype and beta-test the AR experience with high-end clients before full rollout. Post-launch, we recommend tracking key metrics across conversion rates, engagement, and brand image perception through direct customer feedback, social media monitoring, and overall satisfaction surveys. This ensures the AR platform delivers immersive value without compromising the luxury identity.