Written by: Hazem Hassan

Publisher: Amira Haytham

The Area Under The Curve

Employee Based management sees the performance as one of the great idols of the management. Without performance, you are doing nothing. And as the traditional wisdom says “what you can’t measure, you can’t manage” so the question here is “if you can’t really measure your employee’s performance in terms of numbers, how will you be able to manage his/her performance?!!

Digital management is to translate each and every employee into numbers and curves not only that but to carefully analyze these numeric data to take the right scientific decision, and it uses the digging technique- and it is to well know and well define all the possible and impossible reasons behind the actions, which here is the performance- to get the main reasons behind the employee’s performance.

If there is a relation between the performance and the years of experience:-

The next lines show an example with some numbers to answer these questions.The area A is the Experience Validity (EV)

Definition: It answers this question” does the years of experience have a real effect/impact on the performance?” 

Calculation:

Calculate the area under the curve by 1- the manual ways; drawing squares/triangles/rectangles to fill the area in or by 2- integrating the curve equation based the X axis values.

Here we will calculate two areas under the curve:-

  1. The first area; don’t consider the curve direction/the curve turning points/the curve slope magnitude and it we will call it (+A) contains losses.
  2. The second area; consider the curve direction and the curve turning points and the curve slope magnitude and it we will call it (+/-A) doesn’t contain any losses.

Then find this ratio:-

= (+A) / (+/-A)

Kindly note that the numbers in the following example isn’t a live numbers

For example:-

The next chart represents the relation between the years of experience and the performance and the blue curve shows this relation with this equation: –     Y = 0.2848X + 5.7785

The blue line contains three parts; the first part goes up, the second part goes down and the last part goes up.

The first line

The area under this line is

= Rectangle area + Triangle area

= (5*5) PUY + (0.5*5*5) PUY

=37.5PUY

PU Performance Unit

Y Years of Experience

The line slope is +1

And by the integration we can calculate it too

The line equation is y = 5+x

 =5X +0.5X2 +C

At X equals zero

=C    it is the integration constant.

At X equal five

= (5*5) + (0.5*52) +C

=37.5 + C

The area under the line will be = 37.5 + C – C= 37.5 PUY

The second line

The area under the line is

= (3*6) + (0.5*3*4) = 24 PUY

The line slope is 1.33333

And by the integration it will be

Y = -1.333X+16.667

= -1.333X2/2 + 16.667X + C

At X equal five

= -1.333(52/2) + (16.667*5) + C

=66.71 + C

At X equal eight

= -1.333(82/2) + (16.667*8) + C

=90.776 + C

The area under the curve = 90.776 + C – 66.71 – C=24.066 PUY

The third line

The area under the line is

= (17*6) + (0.5*17*7) = 161.5 PUY

The slope is +0.4118

By the integration it will be

Y = 0.4118 X + 2.7059

 

=0.4118X2/2 + 2.7059X + C

At X equal eight

= 0.4118(82/2) + (2.7059 *8) + C

=34.8248 + C

At X equal twenty five

=0.4118(252/2) + (2.7059 *25) + C

=196.335 + C

The area under the curve = 196.335 + C -34.8248 – C = 161.5102PUY

 

+A = (area 1 +A 2 + area 3) = (37.5 + 24 + 161.5) = 233 PUY

+/-A = (area 1 -area 2 + area 3) = (37.5 – 24 + 161.5) = 175 PUY

Why the second area in +/-A is negative?  -Because the performance is demolishing, so this area isn’t a gain but a loss.

Experience Validity = (+/-A) / (+A) = 175/233= 75.107%

So regarding to this example numbers; the years of experience affects the performance by 75.107%

That really means “experience isn’t just sum of working years you spent, but a real performance you performed”

The curve starts from the point E to D to C to B.

The area ABCD is the losses ideal performance area, all the area under the line EA is the ideal performance area, the area under the curve EDCB is the actual performance area.

The ideal Performance Area= the Actual Performance Area +the Losses ideal Performance Area

The ideal area- in case the employee performance curve starts from the point 5PU and keeps on going up in the same direction and there is turning points- = (5*25) + (0.5*25*25) = 437.5PUY

Losses area = 437.5-233 = 204.5 PUY

Experience idealism = (+/-A) / (ideal Area) = 175/437.5 = 40%

The Positive Performance Area = green

The Negative Performance Area = red

The Losses Ideal Performance Area = brown

What do you need to go through all these hassle?

How?

Why?

Because

And