Measuring Sales Performance using Simple Statistical Models
Published: 2023-02-01 16:25:45

Measuring sales performance is a crucial aspect of running a successful business. Accurately tracking and analyzing sales data helps companies understand their strengths and weaknesses, perform forecasts, identify trends, and make informed decisions that drive growth. In this article, I will illuminate how some simple statistical models can be used for measuring sales performance. Whether it is a small or enterprise sales team, simple quantitative techniques can be used to provide valuable sales insights or draw attention to areas of need. **After reading this article, you will see various examples how simple models are applied in real life scenarios.**

*Note: All the images in the article were generated by Artificial Intelligence using **Stable Diffusion 2.x**[^1]. The pictures depicting "salespeople & teams" were generated by artificial intelligence (AI) and any likeness to anyone is a coincidence.*

## Price's Law - Top Sales Performers Account for 50% of Sales Output

![Sales Price's Law](https://raw.githubusercontent.com/bartczernicki/Articles/main/20230129-MeasuringSalesPerformanceUsingSimpleStatisticalModels/Image-SalesPricesLaw.png)

**Price's Law**[^2] is a statistical principle that describes the distribution of productivity in organizations. It states that a small proportion of employees will produce a disproportionately large amount of output. In the context of sales performance, this law suggests that a small number of salespeople will be responsible for a significant portion of total sales. According to **Price's Law**[^2], approximately 50% of the total output of a sales team will be generated by the square root of the total number of employees in the team. For example, if a sales team has 100 members, approximately 10 of them will generate 50% of the total sales. Conversely, if a sales team is large 10,000 about 100 salespeople will account for 50% of the sales outcomes. This means that **Price's Law** estimates overall top performance drops as the size of the sales team increases! To state this another way:  
- In a sales team consisting of 100 sales members, 10 top performers will account for 50% of outcome; 10% of the sale force are top performers.
- In a sales team consisting of 1,000 sales members, 32 top performers will account for 50% of outcome; 3.2% of the sale force are top performers.
- In a sales team consisting of 10,000 sales members, 100 top performers will account for 50% of outcome; 1% of the sale force are top performers!

Basically, with a larger the sales team structure, less of them are contributing to the overall success. **Price's Law** is one of the core reasons enterprise organizations split up their sales teams into various sales areas. For example, you may have a sales team focused on various technology domains, geographical regions or even industry verticals. This allows multiple top-performing teams to emerge across various sub-sales areas. 

Another quick way to operationalize **Price's Law**[^2] for sales performance is to use it to understand that a sales organization will naturally skew sales outcomes to the top performers. This is attributed to the nature of how sales accounts are allocated, the manifestation of "luck versus skill" and other conventions that govern sales. Furthermore, this principle has important implications for sales performance management. By understanding **Price's Law**, sales managers can focus their efforts on identifying and supporting the top-performing salespeople, who are likely to have the greatest impact on sales results. Additionally, **Price's Law** can be used to identify areas for improvement in sales performance. For example, if a large portion of sales are generated by a small number of salespeople, the manager may focus on developing and implementing training programs to improve the performance of the rest of the team.

It is important to note that while **Price's Law**[^2] can provide useful insights into sales performance, it's a statistical principle and should not be used as a rigid rule or the sole measure of sales performance. Other factors, such as market conditions, customer behavior, and product features, can also impact sales results and should be considered in sales performance evaluations. For more information, please consider watching this video presentation on **Price's Law**[^3].


## Regression to the Mean - That new Rockstar Salesperson will likely perform closer to the Historical Sales Average

![Sales - Regression to the Mean](https://raw.githubusercontent.com/bartczernicki/Articles/main/20230129-MeasuringSalesPerformanceUsingSimpleStatisticalModels/Image-SalesRegressionToMean.png)

**Regression to the mean**[^4] is a statistical phenomenon where the average of a population is calculated as the expected value of the population, and outliers (values that are much higher or lower than the average) tend to return towards the average in the long run.  

In the context of hiring a new salesperson, **regression to the mean** can come into play when a new hire has a history of exceptional sales performance. If the new hire's sales quota is based solely on this past performance, it's possible that their future performance will not match their previous success. This is because their past performance was likely influenced by various factors such as luck, temporary market conditions, and other external circumstances. For example, if a new salesperson has previously exceeded their sales quota by 100%, it's unlikely that they will always consistently perform at this level going forward. Instead, their future performance is likely to return closer to the average of the sales team, and possibly even below the average. This is regression to the mean at work.  

There is a super simple statistical regression formula (illustrated below) that can be used. Many social sciences studies show that cognitive correlation regarding performance is usually in the 20% (0.2) - 30% (0.3) range. This means that using a job interview performance as the key driver of future sales outcomes will only likely explain 20%-30% of future sales outcomes. In fact, only 3% of 708 cognitive studies showed correlations of 50% or more on future performance from a single cognitive driver (like a job interview)[^5]. Basically, you need more factors to judge a correlated future performance.

![Sales - Regression to the Mean](https://raw.githubusercontent.com/bartczernicki/Articles/main/20230129-MeasuringSalesPerformanceUsingSimpleStatisticalModels/Image-RegressionToMeanCalculation.png)

In the job interview scenario shown above:  
- A new "rockstar salesperson" interviews for a sales position. A sales leader estimates that they will produce triple than the current team
- If for example, historically on average a salesperson performs at $1 million/year, tripling this new "rockstar salesperson's" performance would lead to a sales performance expectation of $3 million/year
- The **regression to the mean** formula states that it is more likely this new "rockstar salesperson" will be closer to the average and not optimistic outlier. Their sales performance should be estimated closer to the average: $1 million/year + $2 million/year * 30% = $1.6 million/year
- The sales leader can certainly forecast for the salesperson to perform considerably better. However, using the **regression to the mean** calibrates the estimate conservatively. Note that using the **regression to the mean**, the larger the initial estimate ($2 million/year vs $1 million/year), will result in a bigger the regression to the mean as a percentage change.
- For decisions & judgements based on a single driving factor, you want to use the cognitive correlation coefficient of between 0.2 - 0.3. If you are very optimistic and confident, you could perhaps use something slightly higher (0.4). What if you don't want to rely on cognitive intuition/cognitive expertise? The good news is that if you have actual data, the correlation coefficient (r) can be easily calculated[^6].


To avoid making an overly optimistic sales forecast for a new salesperson, it's important to consider multiple factors when assigning a performance quota, such as the salesperson's skills, experience, and the market conditions that they will be operating in. However, when considering one main factor (job interview/resume) it is best to calibrate the performance expectations closer to the average. This can help to ensure that the new hire's sales performance is sustainable and in line with expectations.


## Law of Large Numbers - Consistent Patterns & Trends will emerge with enough Sales Engagements

![Sales - Law of Large Numbers](https://raw.githubusercontent.com/bartczernicki/Articles/main/20230129-MeasuringSalesPerformanceUsingSimpleStatisticalModels/Image-SalesLawOfLargeNumbers.png)

**The law of large numbers**[^7] is a statistical concept that states that as the sample size increases, the average of the sample approaches the population mean (ground truth). For example, to test the performance of a system of flipping a coin heads or tails, a few coin flips could be performed. After enough sample flips the "ground truth" of 50% emerges (50% probability of a coin landing on a head or tail). In the beginning of the chart below, note there are some wild swings in the estimate, but the trend converges to a 50% probability eventually with a large enough sample. Law of large numbers can apply to even large complex systems if similar processes are used, and the events are more or less independent.

![Sales - Law of Large Number of Coins](https://raw.githubusercontent.com/bartczernicki/Articles/main/20230129-MeasuringSalesPerformanceUsingSimpleStatisticalModels/Image-LawOfLargeNumbersCoins.png)


In the context of sales processes, the **law of large numbers** can be used to find trends and make more accurate predictions about future sales performance or the "ground truth" performance of sales. For example, if a company wants to predict the average daily sales for a new product, it can collect data on the sales of that product over a period of time and use that data to calculate the average daily sales. The longer the period of time for which data is collected, the larger the sample size and the more reliable the average will be as an indicator of future sales performance. This allows for much better forecasting.

In addition to predicting future sales performance, the **law of large numbers** can also be used to identify trends in sales processes. For example, if a company notices that sales are consistently higher on certain days of the week or during certain months of the year, it can use this information to make strategic decisions about product promotions, staffing levels, and other factors that affect sales.

It's important to keep in mind that the **law of large numbers**[^7] only works if the metrics you're tracking don't change a lot from one time to the next. For example, if the number of sales changes a lot from month to month, it will be harder to see a clear trend. That is why it's important to keep track of your sales over a long time, and to be careful when interpreting the results. These trends can manifest themselves as consistent historical probabilities that can be used as input into other forecast models.


## Statistical Distributions - How Negative Binomial Can be used to Measure Call Center Sales Goals

![Sales - Call Center](https://raw.githubusercontent.com/bartczernicki/Articles/main/20230129-MeasuringSalesPerformanceUsingSimpleStatisticalModels/Image-SalesCallCenter.png)

There are various statistical distributions that have a small set of parameters that are very effective tools in estimating processes. One such distribution is the negative binomial distribution. A **negative binomial distribution**[^8] is a way to understand what happens when you're counting a certain number of events, but the number of events you need to observe is unknown (and you need to predict it). In the context of sales performance, you can use a negative binomial distribution to make predictions about the number of sales you'll make and given the number of sales attempts it will take, given consistent performance number.  

To use a **negative binomial distribution**[^8] in a sales scenario, you need to know two key inputs: the number of desired successful sales and the consistent probability of making a sale. You can use past sales data to find the average number of successful sales (trends from law of large numbers), and use market research or other information to estimate the probability of making a sale.  With this information, you can make predictions about the number of sales you'll make. Assume the following call center sales scenario:
- There is a sales bonus given out every month if a salesperson closes 20 deals in a month in a call center
- The probability of closing a sales deal is consistently shows a 10% probability from a sales call; every sales call there is a 1 in 10 chance of closing business
- How many sales calls does the salesperson need to make to earn the monthly sales bonus?

Using an **online negative binomial calculator**[^9], it can probabilistically estimated that to close **20 deals in a month from a 10% sales conversion**:  
- 1.6%  probability it will take up to 100 sales calls to achieve the monthly sales bonus
- 25.5% probability it will take up to 150 sales calls to achieve the monthly sales bonus
- 70.6% probability it will take up to 200 sales calls to achieve the monthly sales bonus

It is probably common sense that more sales calls (attempts) will help achieve the desired sales conversion number. However, the **negative binomial distribution** helps illuminate a numerical forecast and put probabilities on the forecast. This provides an incredible amount of information to the sales leadership or the sales individual to plan their monthly success accordingly.

## Summary

Simple statistical models can play a significant role in sales performance management, as they allow companies to make data-driven decisions that can help improve their overall sales results. One of the key benefits of using simple statistical models is that they can provide a more objective view of sales performance, as opposed to relying solely on human intuition or ad-hoc methods. This can help to eliminate bias and minimize the impact of personal opinions, leading to more accurate and reliable results.

Moreover, these models are also relatively straightforward to implement, and require only basic statistical knowledge and a minimal investment in terms of time and resources. This makes them a cost-effective solution for companies looking to improve their sales performance, especially for those with limited budgets or resources.

However, it is important to note that these simple statistical models should not be used as the sole measure of sales performance. While they provide valuable insights into key drivers of sales, they are not designed to provide sophisticated sales forecasting, which requires more complex models and algorithms. Therefore, companies should complement these models with other methods, such as market analysis and customer insights, to get a more comprehensive view of their sales performance and make more informed decisions.

## Footnotes
[^1]: Stable Diffusion on Hugging Face: https://huggingface.co/spaces/stabilityai/stable-diffusion 
[^2]: Price's Law: https://salesmetry.com/blog/2021/01/22/prices-law-competence-is-linear-incompetence-is-exponential/  
[^3]: Price's Law - Jordan Peterson Video: https://www.youtube.com/watch?v=8z3OZ7QuJE0  
[^4]: Regression to the Mean: https://www.statisticshowto.com/regression-mean/  
[^5]: "Noise: A Flaw in Human Judgement" Daniel Kahneman (page 151): https://www.amazon.com/Noise-Human-Judgment-Daniel-Kahneman/dp/0316451401  
[^6]: Calculate the Correlation Coefficient: https://www.statisticshowto.com/probability-and-statistics/correlation-coefficient-formula/  
[^7]: Law of Large Numbers: https://www.investopedia.com/terms/l/lawoflargenumbers.asp  
[^8]: Negative Binomial Distribution Details: https://dlsun.github.io/probability/negative-binomial.html  
[^9]: Online Negative Binomial Calculator: https://homepage.divms.uiowa.edu/~mbognar/applets/nb1.html