The Commercial Environment: Pt 2 - The Subtle Deviation



 Some things you hear once and they stay with you forever…

"This is the best strategy document I have ever read."

Some things you wish you could remember…

"Honestly, did I leave the front door unlocked all night again? Ah well, it's a safe neighbourhood."

Some things are statistical definitions…

"

Sample Size (n) - The number of data points you have collected

n = Σ data points n = sample size Fig 1: Sample Size

Expected Value (μ) - The most likely result

μ = 1 n Σ i=1 n x i μ = expected value n = number of observations xᵢ = each individual observation Fig 2: Expected Value

Standard Deviation (σ) - How spread out your results are around the expected value.

σ = 1 n Σ i=1 n (x i − μ) 2 σ = standard deviation n = number of observations xᵢ = each individual observation μ = expected value Fig 3: Standard Deviation

Standard Error (SE) - how much your sample mean is likely to vary from the expected value, given your sample size.

SE = σ n SE = standard error σ = standard deviation n = sample size Fig 4: Standard Error

Sample Mean (‘x hat’) - The average of your observed results over a given period

= 1 n Σ i=1 n x i x̄ = sample mean n = number of observations xᵢ = each individual observation Fig 5: Sample Mean

Confidence Interval (CI) - A range within which the true expected value is likely to fall, given your sample size and standard deviation.

CI = ± Z* · σ n CI = confidence interval x̄ = sample mean Z* = critical value (e.g. 1.96 for 95%) σ = standard deviation n = sample size Fig 6: Confidence Interval

Critical Value (Z*)- The number of standard deviations from the expected value that defines the boundary of your confidence interval.


Confidence Level Critical Value (Z*) 50% 0.674 75% 1.150 95% 1.960 Fig 7: Critical Values Table
"

…to name just a few.


Hold onto them until the end of the post.



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THE COMPARATOR LOOP

Commercial environment output −ve +ve Comparator Value · Z-test |x̄ − μ| / (σ/√n) > Z* Sales Cycle Time · Z-test |x̄ − μ| / (σ/√n) > Z* Volume · Z-test |k − λ| / √λ > Z* Decisions · Z-test |k − λ| / √λ > Z* Hi Exp Lo Hi Exp Lo Hi Exp Lo Hi Exp Lo Exp — within expected range, no action required diagnostics step 1: identify external inputs. step 2: measure. Hi — above expected range Exp — within expected range Lo — below expected range Fig 8: Comparator Circuit Diagram

In PT1 - An Uncontrolled System, the comparator goes under-examined. For comic effect, I favoured a snide jab at my fellow salespersons over a proper functional description.

I should correct this…

 In the minimalist model, the comparator functions qualitatively, taking in the feelings of the salesperson on the basis of the feedback of the outcome. When the outcome is good, the salesperson takes all of the credit, the glory and the bonus.

  The opportunity for deeper understanding of the commercial environment is missed.

When outcome is bad, the feedback is refracted through the emotional prism of a salesperson’s disappointment (the most righteous disappointment there is) and possible feelings of threat. The feedback is liable to be lacking objectivity, to be seen as lacking objectivity, or both.

  The opportunity for deeper understanding of the commercial environment is obscured.

 In the maximalist and hybrid systems the comparator is doing a quantitative assessment, where it measures actual data from outputs, compares it with known data from previous outputs and then concludes on whether the outputs are high, expected or low.


  The opportunity for deeper understanding of the commercial environment is omnipresent.


* * *


 Some things you discover…

"When I saw the size of the bonus I nearly spat my ginseng all over the place!"

Some things discover you…

*** Ne’er-do-well tries door***

Door: ‘Cccrrreeeeaaaakkk’

. . .



Some things are mathematics…


* * *

“But, what does the

comparator actually do?”


THE MATHSY BIT

Well, firstly, there is a distinction to be drawn in the proposed measurements data.

Some data over any given period can be expected to form a normal distribution and will have an average value, a standard deviation and a clearly defined sample size.

 Other data, however, are themselves an individual datum. To generate a normal distribution from these, you would have to measure the same data simultaneously across multiple timelines.

Given that logistical challenge, we will use two separate statistical models instead.

One Sample Z-Test

|x̄ − μ| σ / n > Z* x̄ = sample mean μ = expected value σ = standard deviation n = sample size Z* = critical value Fig 9: The Z Test

Above, we have an inequality.

This inequality compares the measured mean to the expected mean, and by selecting a critical value from the table in Fig 7, we can say with a defined degree of confidence after n samples whether the difference between the measured and expected means are statistically significant signal, or background noise, where for larger confidence intervals we need a larger sample size.

Fig 9, below, gives us a more intuitive understanding of the maths,

50% CI −0.67 SD expected value +0.67 SD sample mean Fig 9: Normal Distribution with 50% Confidence Interval

If the sample mean is as shown in the graph, then we can say with more than 50% confidence that this is a significant change in the expected conditions.

One Sample Poisson Test

|k − λ| λ > Z* k = observed number of events λ = expected number of events Z* = critical value Fig 8: Comparator Circuit Diagram


Above, we have an inequality.

This inequality compares the measured number of events to the expected number of events and by selecting a critical value from the table in Fig 7, we can say with a defined degree of confidence after n events whether the difference between the measured and expected means are statistically significant signal, or background noise, where for larger confidence intervals we need a larger sample size.

Fig 10, below, gives us a more intuitive understanding of the maths,

50% CI sample mean 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 expected number of events Fig 10: Poisson Distribution with 50% Confidence Interval

If the sample mean is as shown in the graph, then we can say with more than 50% confidence that this is a significant change in the expected conditions.

Comments

The Z-test and P-test sections may look pretty similar (some would say, almost indistinguishable).

There is good reason for this. We are assuming a normal approximation for the P-Test and we are assuming that the event counts from the last comparable fiscal period are the mean.

“That’s a big assumption, Ian, what if last year was an anomaly?”

Good question - remember, we are creating a trigger to further investigation. If there is a significant shift in event counts between expected and measured, then this should be investigated, and only through the investigation would we find if last year was anomalous.

“50% is a really low confidence interval”

Again, good point - but remember what we are doing. Anything above 50% means that it is more likely than not that the difference in mean is due to something structural. This is the earliest possible early warning signal - you exist in a competitive environment, the earlier you understand the commercial environment, the better you can adapt, the stronger your competitive position.



* * *


Some things are used to measure you.

***Swag bag, full of awards, clinks into the night time***

Some things help you to see the truth

***Swag bag, full of plunder, clinks into the night time***





Some things are comparison parameters…



* * *

“Great. But, what does the

comparator actually do?”

The Metrics

With these statistical models, the comparator can assess real time order data from different parameters against the expected values from the last comparable fiscal period with the assumed same commercial environment, which could be last year, the same quarter last year, last quarter or others, depending on your business.

Name: Order Value

Definition: The booked value of each order won

Test: Z-Test

Example Signals: Market is improvement, increasing scarcity of competitive supply (high) decreasing availability of budgets, new entrants in customers market (low)

Name: Order Volume

Definition: The number of orders won

Test: P-Test


‍ ‍Example Signals: More decisions in market, improved coverage, competitor has weakened (high) Market contracting, coverage reducing, or win ratio falling (low).

Name: Sales Cycle Time

Definition: The time elapsed between first meaningful commercial engagement and a buying decision

Test: Z-Test

Example Signals: Market caution, more stakeholders, regulatory uncertainty, or sales engaging earlier (high) More efficient process, customers more decisive, or sales being brought in later with less specification influence (low)


Name: Total Buying Decisions

Definition: The total number of opportunities you were involved in that reached a buying decision

Test: P-Test

Example Signals: Market generating more activity, or your coverage has improved. (high) Change in buying behaviour, budgets squeezed, customers deferring, or sales not getting involved in enough winnable opportunities. (low).




* * *




Some things are falling into place.

Some things are still a little out of sight





Some things are better left for next time…




* * *



 In the next post, I will give you a free comparator and show you how to use it.

The opportunity for a deeper understanding of the commercial environment is yours.




Next
Next

The Commercial Environment: Pt1 - An Uncontrolled System