How to Evaluate Sales Consultants in a B2C Business

10 min readAug 3, 2022

In any business situation, it is essential to minimise uncertainty, to verify any potential business success or business failure objectively and to adapt respective cost structures accordingly. Bayesian statistics helps to do exactly that.

Suppose, for a moment, that you are a B2C business and someone offers you to take care for your sales process in order for your customer transformation to be increased significantly. Sounds great but how do you evaluate such a service?

The Offer

So far, business was not so bad. Currently, on average 3 % of those persons coming along your business via various sales channels can be transferred into real customers.

As typical for B2C businesses, you are chased by various so called coaches and sales consultants telling that they have the very system to scale your business and to increase your customer basis considerably.

And considerably in this case means improving the customer transformation to at least 20 %.

How can such a service be evaluated?

Is it enough that those consultants bring you 20 new customers out of 100 persons approached for once in one trial while you yourself just can get 3 new customers? Is this already proof enough? On the other hand, is it really bad luck that the “boosted” sales process did not bring the results promised but the scaling concept will prove itself in the sales periods following up?

When does a B2C business know that the hired coaches/ sales people are worth their consulting fee?

There is a way to test the ability of your hired sales consultants. It comes from the corner of Bayesian statistics.

This article is about taming uncertainty in a business context by utilising relatively easy statistical tools and adapting a business’ cost structure accordingly.

Bayes — in general

In general, Bayesian statistics works like this that we do want to know something about a “thing” based on some data we observe. This is called the posterior belief.

Though, we do not have all the information and therefore we do not know exactly how this topic of interest (this “thing) behaves. In other words, there is uncertainty with respect to e.g. the behaviour, the amount, its pure existence and similar.

An example would be: What is the probability of having cancer (= the thing we want to know) provided that typical symptoms for this disease are showing up (= the data we observe).

On the other hand, we do know the data which was observed. So, in Bayes statistics tables are turned and it is asked: What is the likelihood of observing this data provided the thing we want to know e.g. exists, reached a certain amount and so on. And this likelihood is put into connection to what we believed about this thing before we saw the data. The latter is called the prior belief.

To go further with the example:

posterior … probability of cancer provided that we have symptoms
likelihood … chances of seeing the symptoms provided that there is cancer
prior … probability of cancer in general (and before we see new data/ evidence)

P(Cancer|having Symptoms) = P(having Symptoms|Cancer) x P(Cancer)

Keep in mind that the data we observe is just a sample. And a sample is just a part of something bigger, called the population representing the overall information. It rarely happens that we evidence a whole population. In most cases it is always a smaller or bigger sample of the overall information.

Hence, the sample data can give us a certain hint what the population is doing. But we never know exactly how the population is eventually built up. This is the root of the prevailing uncertainty.

Evaluating Assignments

Coming back to our business problem, we take over those principles of Bayes statistics. And as we have some kind of counting problem, i.e. counting the number of clients transformed, we apply a certain form of Bayes models: the Beta-Binomial Bayes Model.

Let’s start with the prior.

The Prior Belief

The basic business situation is that the customer transfer rate is around 3 % on average. This is our prior belief: 3% on average, that’s it!

In statistical terms (and keeping the counting problem in mind) this prior belief can be expressed as Beta distribution.

P(client_transfer_rate) ~ Beta(5, 150)

So, this means that we have an expected client transformation rate of approximately 3 % on average per period of time or per trial. Of course, on a single case basis it is not always 3 %. Sometimes it is just 1 %, next time it may be 4 % of new clients and so on — but on average the transfer rate is 3 %. Exactly this consideration is reflected in the Beta distribution above and shows the uncertainty in the business development.

As can be seen in the graph below, on a single case basis around 90 % of those single cases are between 0 and 5 clients transferred per period of time/ per trial.

Overall it is a rather strong prior belief in what is happening with the B2C business at the moment.

The Likelihood

The sales coach hired did promise an increase of the customer transfer rate to 20 % per period/ per trial. Provided that the success rate of the hired consultant is really 20 % (this is the “thing” we eventually want to know) and we put our fate on a sample size of 100 persons approached per sales period/ per trial, then this can be expressed with the following Binomial distribution:

P(consultant_success_rate) ~ Bin(100, 0.2)

With this, we acknowledge that the expected customer transfer rate is 20 % on average. Though, also here we face an element of uncertainty and the single transfer rate is floating between approximately 10 % and around 35 % with changing chances of materialising.

All this is based on a sample size of 100 people within a certain sales period/ within a trial. This is important to notice because the sample size has influence on the level of uncertainty on the one hand.

On the other hand, it also defines the weight the likelihood has compared to the prior belief when defining the posterior. And our prior belief is quite strong as we saw above.

The Posterior

In this stage, both of the worlds, which is

the current situation of customer transfer rate representing our prior belief in what is currently possible in our business and
a higher success rate regarding the customer transfer rate as promised by the sales consultant and represented by the likelihood,

are combined to update our knowledge regarding the customer transformation possibilities.

This upgrade of knowledge is represented by the posterior belief. See the graph below with:

the blue area representing the pior belief
the red area representing the likelihood, and
the purple area in the graph representing the posterior belief

Indeed, the posterior was moved compared to the prior belief. But it is not even close to the 20 % which were promised. Instead the expected value of customer transformation is around 10 %. Especially two issues led to this result:

We had a relatively strong prior belief in those 3 % of customer transfer rate.
The sample size with which the “promise” was tried out amounted to just 100 persons approached per sales period/ per trial. This is not quite a sample size for a B2C business.

Therefore, let’s try this with a sample size amounting to 1,000 potential customers per round:

This time the results are much closer to the consultant’s committment. The expected customer transformation is at approximately 18 %. Also the level of uncertainty (represented by the broadness of the shape of the respective curves in the graph) is much more minimised compared to the sample size of just 100 potential customers.

Going Down the Timeline

So far, we updated once and examined where our posterior belief ended up. But it does not stop there!

In fact, we have a certain picture of the business situation (i.e. prior belief of a transfer rate of 3 %). Sales consultant gives us a first result based on its capabilities (likelihood of bringing a 20 % transfer rate) and we update our picture of the market possibilities (posterior belief of a transfer rate of 10 % respectively 18 % depending on the sample size).

And now, this current posterior belief is the new level of prior belief for the next sales period/ next trial. By repeating this several times, in other words the consultant has to bring results several times, a more clear picture of whether the consultant is worth the money should approach.

Let’s test it.

We were lucky and took a consultant which has the capability of getting us a transfer rate of 20 %. But this fact we do not know yet which is the cause of all our uncertainty!

Consultant delivers 15 rounds of potential customers. Each round has a sample size of 100 persons.

Based on the consultants capability (which is a transfer rate of 20 % and which we still do not know yet…) we get the following results (trial results are randomly derived based on a binomial distribution with sample size = 100 and a success rate of 20 %):

As mentioned before and as it gets clear with this timeline, the expected value of the transfer rate of the hired sales consultant is 20 % in the long run (which we do not know yet!). But this does not mean that single events (that is each period or each trial) does not result in other outcomes (e.g. 17 %, 12 % and so on). In fact, in our case the consultant has quite a bad start.

The following graph shows the constant upgrade of our belief in the capabilities of our consultant during those 15 trials.

The bold line is the new expected transfer rate after each trial moving up from somewhere close to 9 % after the first trial to 17 % after 15 trials.

Those thin lines represent the borders of a 95 % credible interval and stand for the uncertainty in our belief. Given this, after 15 trials we are 95 % confident that the real transfer capabilities of the consultant are between 15.3 % and 18.9 %. Also, be aware how the level of uncertainty decreases with each trial:

The consultant failed for the moment. After a bad start in the beginning and based on the small sample size, there was too less time for the consultant to prove its ability. Though, the success trend is upwards. So, we could decide to give the consultant another couple of trial periods in order to see where things are heading to.

Increasing the Sample Size

We test the consultant in the same way. This time, the sample size with each trial is 1,000 potential customers.

Here is how our posterior belief is upgraded over those 15 sales periods/ trials:

This time — although the consultant still had a bad start — we understand very fast where the capabilities of the consultant are heading to. The 20 % transfer rate is already hit after the 3rd trial and irrespective of the single outcomes in each trial the overall picture is much more stable.

Of course there is still uncertainty (see the 95 % credible interval). Though, the level of uncertainty is already much more minimised with a much faster downward pace during the trials.

I guess, you should stick to this sales expert.

Bad Sales Coach

Let’s take the case of a sales consultant which somehow manages to get you a transfer success rate of 20 % right in the beginning of the assignment but then moves back rather quickly towards its real sales abilities (e.g. 8 % transfer rate).

Following results per trial based on a sample size of 100 each:

Results with a sample size of 100 per each sales period/ trial:

Results with a sample size of 1,000 per each sales period/ trial:

In both cases, the evaluation model tells you that something is wrong with your sales consultant.

The just gradual upgrade of the posterior belief prevents us from believing in the transfer results of 20 % right from the beginning. The higher uncertainty range (represented by the 95 % credible interval) also tells you to take results with more grain of salt in the beginning and to be cautious with an early evaluation of your consultant.

On the other hand, the real picture behind the sales promises is revealed very fast and drops accordingly towards the real 8 %.

Conclusion

Either one relies on promises made, or one incorporates measurements to see if an assignment is working out or not.

In this case a bit of statistics helped to reduce the uncertainty which came with the announcement of getting much more new clients.

Based on the implemented statistical measurements, it is possible to agree on an appropriate fee structure with an external consultant which on the one hand reflects any potential success or failure and on the other hand gives the opportunity to objectively verify the business development.

In other words, it helps to tame uncertainty in a business context and is the basis for adapting a suitable cost structure, in this case for potential sales consultants.

References

Calculations and visualisations done with R