Peter Principle

By Michael R. Munroe

Problem description• How does an organizations structure, turnover rate, and employee

selectivity impact its maximum performance?• This is relevant because it provides avenue to maximize productivity, or

evaluate organizational performance.• This will be simulated in MatLab – accounting for each relevant degree of

freedom and variability to allow numeric handling of results.

The Basic Model• Company

Six levels 160 employees

• Competence Uniform random Below 4 is culled Ranges from 0 to 1

• Promotion/Hiring Try first level below Try anywhere in the

organization Then hire from outside

• Ages Start is uniform random Lowest is 18, highest is 64

Accounting Notes

Accounted for• There is no such thing as time. An

Epoch is a metaphor for hire/advance/fire as driven by Performance review.

• Performance is measured in “Degree of Competence” and so is also an abstraction. It is applicable to ROI, education, contribution, .. Or whatever.

NOT Accounted for• Change in competence over time

(Improvement with experience, trends in source)

• Increase/Decline/Change in Contribution vs. level in company.

• Increase in cost vs. level in company.

• Leaving by any means other than retirement

The Basic Results

Observations:• From Epoch of zero to

48 system efficiency is increasing

• At about epoch 48 peak of 72.92 occurs.

• After 48 there is a trough that bottoms around Epoch 75

• After trough system stochastically orbits steady-state

0 50 100 1500.5

0.55

0.6

0.65

0.7

0.75

Epoch

Sys

tem

Eff

icie

ncy

Trend system efficiency (minCOP=40%, dwell=42)

0 20 40 60 80 100 120 140

0.72

0.722

0.724

0.726

0.728

0.73

X: 78Y: 0.7206

Epoch

Syste

m E

ffic

iency

Trend system efficiency (minCOP=40%, dwell=42)

X: 46Y: 0.7292

Questions, Knobs and Stats

Statistics• Central tendency and

Variation Mean and stdev Median and iqr

• Ensemble Size Paper: 50 elements Exercise: 10,000

elements

• “Knobs” Number of evaluation samples or

“Epochs” Dwell time (age) Competence floor

• questions Is there an organizational equivalent of the

10,000 hour rule? How does organizational performance change

with number of samples? How does changing the minimum

competence impact peak and steady state values?

Is there a metric like WIP-turns that relates organization structure to organization efficiency?

Varying Exit Age

As exit age increases:• Ramp to peak shallows• Peak height increases• Steady-State

competence increases• Post-peak decline

increases

Interesting points• Below age 34 there is

totally different phenomenology

• Differentiation based on “dwell time” starts to occur after epoch 4.

0 10 20 30 40 50 60 70 80 90 1000.68

0.7

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

Epoch number

Org

aniz

atio

nal c

ompe

tenc

e

Competence vs. Epoch for varying exit "age"

age 34age 39

age 44

age 49

age 54

age 59age 64

age 69

age 74

age 79age 84

2 4 6 8 10 12 14 16 18 20 22

0.7

0.72

0.74

0.76

0.78

0.8

0.82

Epoch number

Org

aniz

ational com

pete

nce

Competence vs. Epoch for varying exit "age"

age 34age 39

age 44

age 49

age 54

age 59age 64

age 69

age 74

age 79age 84

Median Efficiency vs. Exit Age

0

50

100

150

1020

3040

50

6070

0.4

0.5

0.6

0.7

0.8

0.9

Epoch

Mean System Performance vs. Max Dwell time and Epoch

Dwell Time

Sys

tem

Eff

icie

ncy

Observations• There is an

immediate ramp as dwell time increases.

• There is a “ridge” of max system COP, after which SS is achieved.

Notes:• Dwell time is 18 plus

number of “FOCAL” or reviews experienced before mandatory termination.

2040

6080

100120

140

20

30

40

50

60

0

0.2

0.4

0.6

0.8

1

Epoch

Variability (scaled IQR) of system efficiency

Retirement Age

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IQR of Efficiency vs. “Retire” ageObservations• There is a peak near

the origin.• There is a line-shaped

ridge proportional to age and epoch.

• There is a ridge of maximum variablity given epoch near the fourth “review” or age ~22.

Note• This is dimensionless

variablity – the axis is scaled.

0

50

100

150

0

0.2

0.4

0.6

0.8

10.5

0.55

0.6

0.65

0.7

0.75

Epoch

Mean of system efficiency

minCOP

Sys

Eff

Median Efficiency vs. Minimum COP

Observations• There is a peak of

variability around epoch 40, followed by a trough.

IQR Efficiency vs. Minimum COP

Observations• There is a peak of

variability around epoch 40, followed by a trough.

2040

60 80100

120140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.03

0.035

0.04

0.045

Minimum Competence

Epoch

IQR of system efficiency

Sys

Eff

0.03

0.035

0.04

0.045

Varying Minimum Competence

As competence increases• Steady-state increases• First ramp increases• Second ramp decreases• Peak Epoch occurs slightly

later

Interesting Points• Nature of the system

significantly transitions over 80%. General form and rate of increase changes.

0 50 100 1500.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

X: 136Y: 0.7374

Org

aniz

atio

nal c

ompe

tenc

e

X: 135Y: 0.7662

X: 135Y: 0.793

X: 135Y: 0.8198

X: 134Y: 0.8456

X: 133Y: 0.8695

X: 133Y: 0.8905

X: 132Y: 0.9054

X: 135Y: 0.9006

X: 47Y: 0.7456

X: 48Y: 0.7725

X: 48Y: 0.7979

X: 49Y: 0.8236

X: 49Y: 0.8482

X: 52Y: 0.8714

X: 55Y: 0.892

X: 58Y: 0.9066

X: 30Y: 0.9044

Epoch number

Competence vs. Epoch

min 10%

min 20%min 30%

min 40%

min 50%

min 60%

min 70%min 80%

min 90%

Min Competence vs. Steady State

As “filter level” increases:• Initial variation is

linear• Diminishing

returns starts kicking in

Interesting points• Around 0.85 is max

theoretical system efficiency.

• A 90% filter results in lower max than 80% filter

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

X: 0.8425Y: 0.9088

Minimum Allowed Competence

Max

Sys

tem

Com

pete

nce

Max System Competence vs. Min Competence Threshold

myy vs. x

fit 1

y max

Next Steps

• Company of youth Explore organization behavior between dwell time of

2 and 18 by computing ensemble median at 1 epoch intervals

• Variation, not just mean Explore time and parameter variation in IQR

• Structure vs. Peak• Pushed from beneath vs. Pulled from above

What does management actually contribute. Is the increase in pay a reasonable compensation for the return in value?

Backup

Source Material

Ignoble Prize• http://improbable.com/ig/winners/#ig2010Paper• http://arxiv.org/abs/0907.0455• http://arxiv.org/PS_cache/arxiv/pdf/0907/0907.0455v3.pdfPremise• Given - Performance in new position isn’t indicated well by prior performance.• Thus - People rise to highest level of incompetence• And – the best strategy for ignorance is random rewards.

Bottom line: There is a time and place for random rewards – its called ignorance.