Consumers taste and consumption patterns are ever-changing which makes fashion products life cycle very short. And so, retail and fashion markets are very volatile and hard to predict.

HUUB’s business relies on being able to predict sales behaviours and thus the behaviour of our brands consumer. Indeed, stock optimization, prediction of quantities and optimization of orders are key to reduce costs, which will then reduce the bullwhip effect and improve not only our business but our brand’s as well.

As described by Lenort and Besta (2013), there are many potential benefits of using forecasting models on fashion companies:

• Possible reduction of the difficulties of the supplier production;
• Effectiveness improvement of the sourcing strategy of the retailer;
• The reduction of lost sales and markdowns and, so, the increase of profit margins.

Due to these short life cycles, historical data of the disaggregated product structure is ephemeral, hence the importance of forecasting different levels of aggregation. The strong seasonality also arises as one of the important behaviours to model.

The sales data generated by companies is thus highly dimensional, meaning that it is possible to aggregate and disaggregate it by a significant number of dimensions, e.g product structure, geography, etc.

Time series data in the retail world is particularly rich in dimensionality, and these dimensions can be aggregated in groups or hierarchies. Valuable information is nested in these complex structures, which helps to predict the aggregated time series data.

Aggregated time series data results in a few data points to learn from, which reduces the ability to apply more complex models. We used univariate statistical methods to build solid individual forecasts and reconciliate them optimally, using a grouped time series based on the product structure. The forecast for the most aggregated time series would capture nested information in the grouping structure and the optimal reconciliation methods applied would show more consistency in the forecast.

1.Data Preprocessing

Different approaches can be taken to pre-process time series data in order to stationarize, normalize, detrend and deseasonalize data. Pre-processing is an important stage as it has been shown that forecasting models perform better on pre-processed data (Makridakis, Spiliotis, and Assimakopoulos, 2018).

The Box-Cox transformation is used to modify the distributional shape of a set of data to stabilize variance and make the data more normal distribution-like so that tests and confidence limits that require normality can be appropriately used. It is defined by:

where λ is the transformation power parameter and y is a list of strictly positive numbers. Hence, the Box-Cox transformation can only be applied to positive data. A Box-Cox transformation with λ = 0 is equivalent to a simple logarithmic transformation.

2.Model Description

The Autoregressive Integrated Moving Average (ARIMA) or Box Jenkins methodology is one of the most popular and frequently used stochastic time series models.

The Seasonal Autoregressive Integrated Moving Average (SARIMA) model is the generalization of the ARIMA model for seasonality. In this model, the seasonality is removed by seasonally differentiating the series.

In other words, by computing the difference between one observation and the corresponding observation from the previous year (or season):

For a monthly time series, s = 12, for a quarterly time series s = 4, etc.

Mathematically, a SARIMA (p,d,q)×(P, D, Q)s model is formulated as:

where P, D, Q are the seasonal orders of the auto-regressive, integrated and moving average parts of the model, respectively, and s is the seasonal period.

3.Optimal Forecast Reconciliation

Univariate Time Series data rely only on time to express patterns. When there is aggregated data available, there are potential covariance patterns nested in the hierarchy.

Fliedner (2001) summarizes guidelines on using the more traditional hierarchical forecasting approaches, top-down, bottom-up and a combination of both, the middle-out approach.

The method proposed by Hyndman, Ahmed, Athanasopoulos, and Shang (2011) consists in optimally combining and reconciling all forecasts at all levels of the hierarchy. To combine the independent forecasts, a linear regression is used to guarantee that the revised forecasts are as close as possible to the independent forecasts while maintaining coherency.

The independent forecasts are reconciled based on:

where ˆ yT(h) is a matrix of h-step-ahead independent forecasts for all series, stacked in the same order as the original data, S is a summing matrix,

is the unknown mean of the most disaggregated series at the bottom level, and εh represents the reconciliation errors. The authors also proved that the resulting forecasts are unbiased, which is not the case in the top-down approach.

From the traditional hierarchical forecasting approaches, we selected the bottom-up approach to give us a reference. We tested it against different methods that consist of optimally combining and reconciling all forecasts at all levels of the hierarchy.

We need to estimate Wh, the forecast error variance of the h-step-ahead base forecasts. As it is challenging to estimate Wh, Wickramasuriya, Athanasopoulos, and Hyndman (2018) proposed five different approximations for estimating this parameter, some of which we implemented in our work.

1. The Ordinary Least Squares (OLS) provides substantial computational savings. The disadvantage, however, is that this specification does not account for the differences in scale between the levels of the structure.
2. The WLS (Weighted Least Squares) scales the base forecasts using the variance of the residuals.
3. MinT (Minimum Trace) assumes that the error covariance matrices are proportional to each other, and we directly estimate the full one-step covariance matrix based on the sample covariance.

4.Dataset

From a portfolio of brands under HUUB’s monitoring, we selected two to explore their sales behaviour, leveraging the grouping properties of their product structure. The time series of all HUUB brands have been analyzed in order to explore their sales behaviour. Only brands with more than two years of data and consistent sales on a weekly basis were considered for forecasting analysis.

For an initial study, we selected only the eCommerce sales channel of two representative brands. The aim of this data reduction is to narrow the scope of the problem since the purpose is to have a first approach and a strong baseline for the future.

The image above plots the selected eCommerce brands data series. The data is aggregated in weeks and ranges from the 11-12–2016 (Sunday) to 19–01–2019 (Saturday).

5.Grouped Time Series

Grouped time series are built based on a structure that disaggregates based on factors that can be both nested and crossed. When there is aggregated data available, there are potential covariance patterns nested in the hierarchy that we can leverage in the most aggregated series.

The structure used for this grouped time series starts at the top level with the time series that sums up all series at lower levels with different attributes. It is disaggregated by brand, brand 1, and brand 2, in a hierarchical structure.

We considered five different attributes:

• Gender (Male, Female or Unisex);
• Age group (Baby, Kid, Baby Kid, Teen or Adult);
• Product type (Clothing, Footwear, Accessories, Homewear, Beachwear, Swimwear, Swim accessories, Compound, Stationery, Underwear, Nightwear or Sports);
• Season of the product (Seasonal or Permanent).

Image 2 shows one of the alternatives to represent the group structure. It generates a total of 128 time series to be reconciled. When grouping time series, the complexity increases quickly, which requires significantly more computation resources to solve the problem.

For each of the time series, we applied the best possible model to forecast that individual series using the auto.arima() function from the R Forecast package (Hyndman and Khandakar, 2008; Hyndman, Athanasopoulos, Bergmeir, Caceres, Chhay, O’Hara-Wild, Petropoulos, Razbash, Wang, and Yasmeen, 2018)

Results

Based on the mathematical expression for the SARIMA function, we can deduce some parameters restrictions according to the size of the time series window.

The more general restrictions for the SARIMA model as a function of the time series length are:

Our time series has a length of T = 110 data points (weeks) and a seasonal period of 52 weeks. We want to test forecasting of 4 weeks, so we divide the time series into 106 data points for finding the best SARIMA parameters and coefficients, the training series, and 4 data points to test the forecast retrieved by that model, the testing series.

The length of the training series limits our SARIMA parameters in the following way:

Brand 1

The sales of brand 1 vary a lot with time, which reflects in a time series with high variance (see Image 1). This suggests that a Box-Cox transformation can make it more stationary.

A quantile quantile (Q-Q) plot shows the distribution of the data against the expected normal distribution, hence it is an effective diagnosis to determine whether a sample is drawn from a normal distribution. Image 3 shows the Q-Q plot of the Box-Cox transformed data with lambda=”auto” as well as the Q-Q plot of a simple logarithmic function, λ = 0.

The more data points fall in a straight line, the more normally distributed they are. If they deviate from a straight line in any systematic way, this suggests that the data is not drawn from a normal distribution. Image 3 thus indicates that the logarithmic transformation effectively approximates the data to a normal distribution more than the Box-Cox transformation with lambda=”auto”. A λ = 0 Box-Cox transformation was therefore applied to the data.

Figure 4 presents the brand 1 time series after Box-Cox transformation. This series displays a clear seasonal pattern with a cyclic profile with a yearly, or half-yearly, period. A seasonal differentiating with a lag of 52 weeks (1 year) or 26 weeks (half-year) should, thus, improve the time series.

Indeed, the time series standard deviation decreases from 1.053 to 1.020 and to 1.028, after applying a 52-weeks and a 26-weeks difference, respectively, which improves the series in both cases. A first difference of the series increases the standard deviation and a unit root test also returns no first differencing, it is thus not expected to improve the modeling of the series.

The analysis of the ACF and PACF of the yearly differenced series indicate that a SARIMA (0,0,1)(0,1,0)52 model is a good candidate to reduce the data autocorrelations. This and other SARIMA models were tested and this was the model with the lowest AICc and BIC criteria.

A more complex model, SARIMA (6,0,0)(0,1,0)52, was favoured by the AIC criteria, however, according to the restrictions in Shang and Haberman (2017), this model exceeds the threshold limited by the size of the training series.

Moreover, particularly when the sample size is small, the AIC criteria favours higher order (more complex) models as a result of overfitting the data. The AICc is a correction of the AIC and more realistic criteria for smaller sample sizes, along with the BIC criteria. For these reasons, and since simpler models tend to be a better choice for accurately forecasting the general behaviour of time series, we chose (0,0,1)(0,1,0)52.

Brand 1 had a major peak of sales in the first quarter of 2017 which did not repeat in 2018 and which was almost 10 times above the average of the subsequent peaks (see Image 1). This sales peak was due to strong campaigning for an online collection launching. It was a one-time event and the peak affects the SARIMA models, increasing its prediction for the same period of subsequent years. We performed the same analysis having this outlier peak removed and its values interpolated. The time series forecasting RMSE was reduced by 22%.

However, to maintain the method’s automation capacity, we chose not to implement any outlier removal. Instead, external variables will be used to handle this type of event in a subsequent article.

Brand 2

The time series for brand 2 has a seasonal profile, which is also clear in the ACF and PACF at lag 52 (see Image 5). Since the series shows variations which change with time, a transformation can improve the series. Similarly to brand 1, the Box-Cox transformation with λ = 0 improved the normalization of the time series over lambda = ”auto”.

Since brand 2 displays a clear seasonal profile, it is not stationary and a seasonal difference can improve the series. Even though the standard deviation of the series increases from 0.64 to 0.68 after seasonal differencing, the series becomes more normalized.

The series is also more stationary after a first difference and the standard deviation decreases to 0.54. A second difference would increase significantly the standard deviation, so no more differencing was applied to the series. The ACF and PACF of the differenced series show a significant negative lag1 of ≈−0.3, which suggests a mild over-differencing.

This can be counterbalanced with one order of a moving average model applied to the series, which indicates that SARIMA (0,1,1)(0,1,0)52 is a good candidate model for the data.

Other models, including different differencing orders, were also tested and the AICc criteria, which favours a simpler model, was used to compare them. Based on that, SARIMA (0,1,1)(0,1,0)52 model was chosen out of all models.

Results for individual forecasts using the best fit models in the higher levels of the hierarchy

Global time series

A global time series is formed by the sum of brand 1 and brand 2 time series. The same pre-processing and analysis performed on brand 1 and brand 2 time series were applied to the global time series, in the same 4 weeks period range.

As expected, the global time series also exhibits a seasonal profile, with a cyclic behaviour and significant autocorrelations at lag 52. This entails a seasonal differencing, hence D = 1. The standard deviation of the time series increases when applying a first difference and the unit root test determined that the time series is stationary so needs no first differencing, both advocating for d = 0. The model that presented lower AICc criteria was SARIMA (0,0,1)(0,1,0)52. The fitting and forecast of the global time series by this model are shown in Image 6.

The baseline models performance summary is presented in Table I

Models were chosen based on the AICc resulting in the best fit on the training data. This also guarantees that we choose the simplest possible models.

High Ljung-Box (LB) p-value indicates a reasonable resemblance of residuals with white noise, further approving the models.

The RMSE was used to understand forecasting accuracy within a 4 weeks horizon, but it was not the main criteria used to select the models as it could lead to overfitting of the training data.

Grouped Time Series Forecast Reconciliation

The best individual forecasts were used as input for the reconciliation process. Independent (base) forecasts, used as baseline, bottom-up and the three approaches considered as the optimal reconciliation methods: OLS, WLS, and MinT.

Table II shows the performance metrics in the out-of-sample data: independent (base) forecasts, used as baseline, bottom-up and the three approaches considered as the optimal reconciliation methods.

All approaches were tested using a horizon h of 4 weeks, which was identified by HUUB as the most relevant period range to be forecasted, given the weekly data granularity.

The results are presented for the three most aggregated time series, despite the fact that the grouped time series yielded results for all the possible combinations. This is also a major advantage for the business, allowing to drill down to more granular dimensions, with the reassurance that the forecasts are consistent across these dimensions.

Overall, the results show that the best performing method for each series can leverage nested information in the group structure and add consistency to the outcome. This is supported by the RMSE of WLS in brand 1, which has a very significant improvement when compared to the baseline.

In terms of brand 2, WLS results were very close to the baseline, which can be explained by the simpler grouping structure for this brand, i.e. it is essentially concentrated in one product type, one gender, one age group, one season.

For the global time series, the baseline model performed slightly better than the reconciled best model, with an RMSE 5% lower than WLS. This could be due to this time series having a less irregular profile where a SARIMA model can perform better.

Overall, the RMSE indicates that WLS is a robust method for the forecasting of seasonal time series, outperforming the very ineffective bottom-up, but also the simpler OLS and the new MinT approach.

So, what’s the best model to use?

This work explored the optimal forecasts method for grouped time series to forecast the weekly sales of two fashion brands under HUUB’s monitoring. The data were disaggregated according to five selected attributes: brand, gender, whether the item is seasonal or permanent, age group and product type. This disaggregation resulted in a grouped structure with 128 individual time series.

These series were individually fit by the best SARIMA model found by the auto.arima() function and were then reconciled following the optimal forecasts method. We’ve explored three different cases of the optimal forecasts methods: OLS, WLS, and MinT, as well as the simple Bottom-up approach.

The forecast performance of the three most aggregate series was evaluated and compared to the forecasts obtained by baseline SARIMA models. Each of these baseline SARIMA models was found by manually analysing the time series ACF, PACF and through stationarity and differentiating tests to determine the best model parameters and coefficients.

The comparison of the performance of the optimal forecasts method and the baseline SARIMA models showed that WLS was the most robust forecasting method.

What’s next?

Our research intentionally focused on univariate time series models, providing a strong baseline and framework to build more complex forecasting models.

Preliminary work with a higher-level disaggregation with more attributes has shown a significant improvement of the RMSE of the global time series forecast. We will present these findings in the next article.

One possibility worth of exploiting is the use of hybrid models, that combine statistics and machine learning, already proven to generate better results than statistical ones (Makridakis, Spiliotis, and Assimakopoulos, 2018). Another aspect that our work will further explore is the use of multivariate models since they can add significant information on the volatile and unexpected behaviour observed in the data.

Our research is a strong baseline and framework to build more complex forecasting models and a first approach to leverage the hierarchy of retail data.

Cite us on your work using our code: arXiv:1903.09478 [stat.ML]

Check the complete set of references in the article. Want to read the complete version? Click here to download it!

HUUB is disrupting the fashion supply chain and continuously evolving brands! Find out more here.

The Best Forecasting Model For Sales Demand [Part I] was originally published in HUUB on Medium, where people are continuing the conversation by highlighting and responding to this story.

Focusing purely on results, without considering this kind of approach, might lead to an amazing product that, in the end, will fail at first try. It creates the distrust feeling in users that makes an amazing technology deployment to be postponed for years.

Although we like to try everything, this is exactly what we want to avoid. On one hand, at HUUB, we are focused on supporting our people with amazing technologies that will extend their capabilities, instead of replacing them. On the other hand, we don´t fall into the disconnection issue of building something that uses state of the art technologies but fails to prove that it adds value for our co-workers.

An HUUBnormal pragmatism is the key for artificial intelligence with value

Just like your eyes get used to a bad eyesight so do companies to their performance when they rely on gut feeling and we all know what happens if you close your eyes while driving your car. We like to think artificial intelligence as the missing glasses in both strategic and tactical decision levels and once on, everything will start being much clearer. As we like to put money where our mouth is, take the following examples in consideration:

Email classification. Our Account Management team spends most of their day communicating with our brands for multiple reasons: going from returns handling to stock issues. As it is our goal to have a much more active role in giving insights to the brands managers, we had to do something. With this mindset, we created a text classification algorithm based on a set of historical email conversations. Our model then learns to classify future emails according to a set of topics. This allowed us to have full visibility over the most frequent problems that a given brand has and guide our operational and strategic focus to fix them. In the end, the goal is met, to relieve and leverage our account management team.

Order to box. We love to work with retail brands, but this comes with very specific issues that have to be fixed in order to become competitive in the Supply Chain Management industry. Take this as an example, a given brand attends a fair and sells its trendy apparel to multiple boutiques. It will start producing the items and three months later HUUB will be shipping them, splitting the items at the reception moment. So far so good, but how do we know how many boxes need to be prepared to accommodate the items bought by each boutique? Imagine the time and money lost preparing the wrong set of boxes and then moving all items to a new set. To solve this probelm, we created a volume estimation algorithm that, based on regular item features like category, fabric, supplier and size, calculates its volume and outputs the optimal pack set for a specific order. This allowed us to save around 20% of preparation times and 15% in shipping costs, depending on the service.

Operational planning. When you manage multiple Supply Chains from multiple customers with suppliers in all corners of the globe, different service level agreements and more than 65 destination markets, having business rules planning operations is not an option. With just a few brands, a team of analysts might be enough, but with more than 30 it becomes humanly impossible to understand all contexts and prioritize operations. Our approach was to look at all pieces of the Supply Chain Management processes and create an abstract mathematical model that fits all possible variables and constraints of the planning process. After building the abstraction, we were able to customize the model using the business rules of all our brands and output on a daily basis the most optimal plan for the following two weeks. This allowed us to save costs with not optimal activities and at the same time prepare the company for to scale.

We are focused on people and on the support of our business growth. We leverage the combination of math, statistics, machine learning and deep convolutional neural networks, as our weapons to tackle the obstacles that we face on our path.

Well, we also like to push the limits…

At HUUB, we take food very seriously. Being part of a startup, we are not lucky enough to count on a canteen. So you either bring your own food or you need to eat outside of our facilities.

The routine is the following, around mid-day, we start our active discussion on what to eat, where to eat and who wants to join the horde of nomad eaters of our company. Not having too many co-workers makes this as easy as standing up and shouting out loud who wants to go. But this is too easy for an artificial intelligence backed industry 4.0 company.

What if we could build an integrated system? One that, based on the daily menu of a restaurant, generates a slack-based poll and, at a given time, automatically calls the restaurant to reserve the required food and tables? Well, we did it. And guess what, every day we save 20 min of all our nomad eaters.

Based on our historical data, I think you should use the key…

Thinking analytics is nowadays a multiple dimension problem, companies must think descriptive to understand its figures and keep track of the company performance. Even so, with the recent innovations that democratized machine learning and artificial intelligence, companies should start thinking about prescriptive and optimization.

HUUB is bringing this mindset to the Supply Chain Management industry. It is increasingly demanding more and more agility to answer consumers expectations. So, in a nutshell, we offer solutions that generate insights and optimize processes that have been stuck in manual operations for too many years.

By the way, we are offering tickets to join us on this amazing trip, revolutionizing, with pragmatism, the data analytics world! Do you have what it takes? Check our jobs.

Thank you!

Between the future and the present, lies the pragmatism was originally published in HUUB on Medium, where people are continuing the conversation by highlighting and responding to this story.

We’re about to start a journey through space and time. Let’s imagine that we represent the evolution of Marketing in temporal and space dimensions. We realize that nowadays Marketing is living in a Flatland for most companies, meaning that it’s stuck in an inferior dimension.

So, let’s plan a rescue mission and bring marketing to our three-dimensional world:

For starters, let’s use imagination and represent this journey through design. Wherever you are, whatever you’re doing, I’d like you to imagine Marketing as a geometric figure passing through time and evolving from zero to three dimensions.

1. The term ‘marketing’ — Zero dimension — PointLand:

According to etymologists, the term ‘marketing’ first appeared in dictionaries in the sixteenth century where it was referred to the process of buying and selling goods/products in a market. During this time, there was no awareness of the one dimension word (the contemporary definition) and marketing was just a representation of a process.

2. Contemporary definition — One dimension — LineLand:

The contemporary definition of Marketing first appeared in 1897 as a process of moving goods from producer to consumer with an emphasis on sales and advertising, where Marketing was based in on observation skills. This was a big leap forward in the marketing evolution, almost like what happened when Thomas Edison invented the light bulb and the world stopped living in the darkness.

At this moment it was recognize that the capacity to influence someone was directly related to psychological behavioral analysis.

This was also the moment where creativity came out of the box to make the difference, when it was realized that to be able to influence someone, you should create the right and distinctive message. Like what was made in the tobacco industry in 1946 with the marketing campaign of Camel: “More doctors smoke camels than any other cigarette!”

3. Marketing (old way) — two-dimensional — Flatland:

Welcome to the Flatland, the dimension where Marketing appears as a square and it’s supported by 4 main pillars, two of them travelled from the previous dimension, Psychological Behavior analysis and Creativity, and two new ones: Data Analytics and Knowledge.

In this dimension we reach that moment where we realize that science needs mathematical proof to become a scientific fact and without knowledge, you’re just a guy with good soft skills that haven’t found the right path.

Most of the companies that we know live in this dimension. For a long time, this square was the state of the art in terms of Marketing Strategy, but a revolution came and it seems that very few companies were ready to embrace it. Today companies are stuck in this dimension, where concepts and execution standards worth more than A/B testing. Where behavior analysis is made based on very small data sets (in a world where data it’s at arm’s [and smart] length). Creative people just have one shot to became viral and Analysts don’t use creativity to find KPIs (Key performance Indicators) that matter. Instead they are just focused on vanity metrics such as App Downloads and Facebook likes.

Marketing society is living in a big bubble, which in an extremely ironic way has no creativity to see the three-dimensional world. I know this is not easy, it’s like trying to imagine ourselves living in a four-dimensional world.

Nevertheless, the portal from the Flatland to the next dimension is open. It’s time to pack our things and travel through time and space.

4. The Marketing of today (new way) – Three-dimensional - Spaceland:

This portal was opened after a big-bang explosion, I call it the Digital Revolution. It’s urgent to apply depth to the square and consequently evolve marketing from a square to a cube. I believe that the factor that will allow us to achieve this depth is Digital Maturity. Digital maturity is about adapting the organization to compete effectively in an increasingly digital environment, which goes far beyond implementing new technologies at a high pace. To get there you need to align the company’s strategy, its workforce, culture, technology, and structure to meet the digital expectations of customers, employees, and partners. Digital maturity is, therefore, a continuous and ongoing process of adaptation to a changing digital landscape.

We are talking about a living organism. The four pillars are in constant evolution and interaction with each other. Companies from today can’t reach this perspective because they are still living in the Flatland.

Artificial intelligence (AI) came to serve Marketing. We see it in several platforms available in the market, which allow companies to optimize their strategies and enhance their abilities. Say you wanted to decide which costumers to contact first in your outbound Strategy, why should you target them just based on your gut feeling or on your target definition? See for instance the Einstein platform from Sales Force.

Einstein uses all the data that you were gathering along this years and the one you will gain along the way and learns from it. Then applies knowledge to deliver predictions and recommendations based on your unique business preposition.

When analyzing the https://www.optimail.io/ platform, you’ll see that it helps you build your campaigns and work on the outputs so they can learn, adapt and improve. We are in a presence of a email marketing platform on steroids.

Nowadays, when we talk about psychological behavior analysis we need to think in big data, not the simple ´observation model’. As a matter of fact, the principle is the same, to study patterns in consumer behavior, but this time using larger datasets. By using this approach companies are allowed to move to more accurate prediction models. The beauty of this approach is that the more information it receives, the better it gets at producing results. We, as humans, are inherently flawed in our ability to predict accurately. How do you think Facebook can predict and select the type of content you will be more interested in engaged?

Achieving this knowledge about our channels, our campaigns and our targets enables us to start automating our processes. There are already platforms that allow you to setup and customized some of your marketing campaigns, see for instance http://www.activecampaign.com/. Their powerful automation platform is very user-friendly and easy to use, it’s where you should start the automation experiences.

Nowadays, achieving digital maturity is critical for every company to succeed. This means: follow the innovation, follow the technological evolution, test everything you can and learn from everything to achieve something greater.

To conclude I would like to bring some questions to debate.

Shouldn’t we already be trying to envision Marketing in a fourth dimensional world? It’s even possible to design Marketing like a hypercube?

I believe we can and we are working on it. Join us on our journey.

Marketing is living in a Flatland was originally published in HUUB on Medium, where people are continuing the conversation by highlighting and responding to this story.

So, we often draw, create short stories or just picture hypothetical scenarios.

Picture this one.

Your startup is a rock rolling in a field, the speed represents the company’s growth rate and the size its valuation. The growth of the diameter of the rock is achieved by the collisions with other rocks along the way. This process can also create erosion.

The push from founders, investors and employees are the only forces applied to the system that moves the rock forward, accelerating as per Newton’s Second Law. Nevertheless, we have to remember inertia and friction. Inertia is the pain to make things move in the beginning. Friction represents all growth obstacles, namely your churn rate.

Therefore, you have to consider 3 main variables to work with:

1. Management is the sum of the magnitude of the projection of all forces applied in the strategy’s direction. Then, it can be broken down in two perspectives: direction and magnitude. If you guarantee that everybody is onboard with your startup’s strategy, you achieve direction and efficiency. The magnitude of the summed forces comes from peoples’ motivation.
2. Strategy gives the direction that each individual has to take when pushing. If someone is highly motivated but pushes in a 45º direction relative to the defined strategy, it causes a deviation. To solve it, you have two options: reroute the direction of this force (using point 1) or, if you are unable to do it, balance this force with perpendicular ones that, summed up, have the same magnitude (using point 1 with other teams/people).
3. Legacy is the outsider, barely recognized as important and easily forgotten. As presented before, the rock is losing small pieces of itself along the way (the erosion process). These will be carried on everyone’s back, increasing the friction as a consequence and subsequently reducing the rock’s speed. The best possible example is today’s tech world, where microservices’ architectures help to reduce dependencies. This decoupling represents the power to decide which small rocks you leave behind and what you will develop next.

Like a triangle in a Cartesian coordinate system, you cannot change one vertex’s coordinates without affecting all the angles.

A Startup story: the Allegory of the Rock was originally published in HUUB on Medium, where people are continuing the conversation by highlighting and responding to this story.