Born Good or Bad? Polya helps

Were you born 'Good' or 'Bad'? The answer to this question can be given with help of mathematics!

Let's start with a simple model. When you were born, you had only a limited number of experiences. Let's assume you came to earth quite neutral, with one 'Good' (G) and one "Bad" (B) experience.
At this point in time, your (still unconscious) attitude and therefore expectation of a 'Good' (B) outcome of your next experience, will be 50%.

In line with the expression "You'll always reap what you sow" (Gal 6:7), or associative translated "You'll become what you X" (with X ='Think', 'Eat', 'Are', etc.)", your next experience will indeed turn out to be equally G or B.

Let's assume that providence decided, the outcome is G. Now you've become a more optimistic person. Your experience-bucket is filled with two G's and one B (experience), so your subjective 'colored' outlook on G's is 66,66% (2/3=[2 G's/(2 G's + 1 B)]) . You also look back on a relatively Positive Life Score of PLS=66,66% G's.
Would you have experienced a 'B score' instead, it would be the other way around and as a potential pessimist your outlook and PLS would have been lowered to 33,33% .

But happily you're a 66,66% (!) G-Score-optimist and life goes on. According to the same principles, the probability of scoring a new G-experience is now 66,66% instead of 50%.

As you may already notice, your PLS will more and more develop according your personal historical G- an B-experience track record.

A few questions that may rise, are:

• Does your Positive Life Score (PLS) has a limit? And if so, what's that limit?
• Once you're in a pessimistic phase, what are the changes of getting out?

Here's were the help of a great mathematician, George Pólya, comes in, by modeling the above situation in what is called:

Polya's Urn model
An urn contains G₀ Green (Good) and B₀ Black (Bad) balls. One ball is drawn randomly from the urn and is then placed back in the urn together with an (extra) ball of the same color.

Our Good&Bad exercise turns out to be a simplified two color Polya Urn Model (G₀=1,B₀=1) that is part of a large family of General Urn Models.

Properties
It turns out that this model has the following (translated)properties:

• On any given moment in your life if you do not know what kind of balls have been drawing before, the expectation of drawing a Good or Bad ball (experience) is always G₀ =G0/(G₀ +B₀) =50%.
  
  
• On any given moment in your life, gaining a Good or a Bad experience depends on the track record of G&B experiences in your life. So if you've experienced G Good experiences and B Bad experiences, your changes of experiencing a next Good experience are equal to the track record of your Positive Life Score : PLS_(G+B)=G/(G+B)
  
  
• The relative influence of a G or B experience on the PLS decreases rapidly as the number of total experiences increases. Your PLS has a definitive limit in (life)time with equal changes of outcome on the interval [0,1].
• As is clear from some simulations, the first 10 to 20 experiences in our life determine whether we'll become an optimist (PLS_(∞)> 0.75) or an pessimist (PLS_(∞)<0,25).
  
  
  
  
  
  
  
  
• Moreover, the first 5 to 10 experiences in your life already determine the direction of our PLS in life. This means that our parents and teachers have an important role in guiding us in our baby and youngster phase to a positive balanced number of experiences (a more than average PLS).
  
  For example if on a given moment in life you have had 4 Bad experiences and 1 Good, the probability of having a next Good experience is 20%. What's more frustrating is that the probability in this case to get in three steps to a 50% level is only about 3% (=1/5*2/6*3/7) . This illustrates the heavy responsibility of our parents and teachers.
  
  That's why it's for example so difficult to change your religion. Once the first 50 religion experiences have been brought in by your parents, it's hard to change from Budha to Allah or Christ, or the other way around.
  
  
• Once a more than average PLS is achieved, we're more likely to absorb a Bad experience without getting unbalanced. Parents and teachers can 'let go'.

Keep in mind, Polya's Urn is only a think-model to help you to become aware of the important mechanisms that play a role in becoming 'who you are' or 'what you'll be'.

Change?
Once you become experienced in life and your PLS direction has been set, you can only change this by either a Professional De or Re-programming (PDR) or a, what is called, Life Changing Experience (LCE). In PDR Bad experiences are taken away (i.e. out of the urn) and replaced by Good experiences, to regain trust and a higher confidence (PLS) level. In LCE's, your environmental or physical circumstances suddenly chance in such a way that you are forced to experience only just B (or just G) experiences. Another LCE is created by the change of context. What before were B experiences now turn out to be G experiences (or the other way around).

What if?
There are many other aspects that could be studied in relation to the Polya model. For example:

• What would be the effect if an experience is not just only Good or Bad, but a mix.
• What if a 'Good experience' doesn't trigger extra positive confidence (an extra G) but a negative experience (an extra B).

The answer in both cases is that almost always the PLS-limit=50% !, in other words: You'll become average.

But how does a little bit of extra Bad (or Good) influence the PLS limit? If you want to experiment and learn more about Good and Bad, go and visit Polya's Urn Experiment or look up the Math behind Polya's Urn

Math helps us to discover who we are or what we become...

Our Beat

From the moment we were born, 'our beat' has been set.

No matter what we do or say, 'our beat' in life go's on. No matter who we are or pretend to be, we're not able to oversing or shout down 'our beat'.

In every phase of life we play a different tune. As baby sometimes clumsy, but charming. As a child ambitious, but still fuzzy. As adult classic and convincing, as if we have become 'our tune' instead of 'our beat'.

But we're neither the notes we play, nor the space between them. Our tune plays on the background and 'our beat' keeps leading, whether we like it or not. Others may help us to find out in life what other tunes fit 'our beat', but they wont be able to change 'our beat'

Until finally 'our beat' slows down and we have to face our final moment, when 'our beat' transforms our tunes, guided by angels, in a new universal image, that'll beat(le)s you.

You won't stay beatless, and you can't beat 'your beat' in life, but you may try.

Now with this in mind listen to the next song. Can you distinguish the tune from the beat, the baby form the adult, life form death?


Try me 2 |

Your life in 5.16 minutes...
(Play it loud on professional stereo equipment)

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Client Lifetime Value (CLV)

In a Harvard Business Review called "Why satisfied customers defect", Jones & Sasser explain that even a 80% 'satisfied clients score', is no guarantee for sustainable success.

Common management misconceptions are:

1. A client satisfaction level below complete or total satisfaction is adequate.
2. It's not profitable to invest in changing customers from 'satisfied' to 'completely satisfied'.

Their conclusion is that, in most cases, 'complete customer satisfaction' is key in order to secure customer loyalty and generate sustainable financial performance.

Loyalty & Satisfaction
Despite of what sometimes intuitively is assumed, the relationship between loyalty and satisfaction is in most cases not linear, but depends on the competition level of a specific market segment.

In a Dutch presentation, called "CRM Myths", direct marketing professor Janny Hoekstra confirms this relationship and shows that even 'satisfied clients' are in the so called 'indifference zone'.

The 'art of client management' is obviously to create 'Apostles' and to avoid creating 'Terrorists'.

So stimulate, instead of discourage, your clients to give you feedback and to complain, because this is the only way to create new apostles.

NPS
A relatively new and, according to Harvard (The One Number You Need to Grow), probably better method to measure client loyalty is the 'Net Promoter Score' (NPS). Simply score your clients on a 0-10 points scale on the question: "Would you recommend company X ?'

Now simply calculate the NPS score (%) as:
NPS = Promoters% (rating 9&10) - Detractors% (rating 6 or less)

NPS scores of 75% or more prove world class loyalty.

Loyalty effect
Another, intuitively driven, perception is that the more customers are loyal, the more they generate profit.

In general this seems true, however as Hoekstra shows: not every 'more loyal' client is also per definition 'more profitable'.

Just like Reinartz (Insead) stated in his article : 'Not all custumors are equal'.

Reinartz defines different client groups called: Butterflies, Strangers, True Friends and Barnacles.

Each group urges a different approach in a Customer Client Strategy.

Investing in 'True friends' appears essential and eventually pays out.



Customer Lifetime Value
Actuaries that combine marketing an actuarial sciences could help by defining and calculating what is called: The Customer Lifetime Value (CLV)

The CLV of a specific client(group) could be defined as the discounted value of the yearly margin (m = profits - costs), with discounting rate (i) and the (client) retention rate (r).

CLV:Rule of thumb
In the strongly simplified case with constant margin, the CLV - as a rule of thumb - could be defined as the margin (m) multiplied with the so called margin multiple = r/(1+i-r).

Example: Discount rate = i =12%, Retention rate = r = 90%, results in a CLV of approximately 4 times the yearly margin.

As is clear from the formula and table above, the choice and impact of the discount rate is only significant in combination with a high (>90%) retention rate.

Modeling and creating Client Value is not only in the interest of the shareholder, but moreover a case of creating creating added value for clients, in particular 'best satisfied clients'.

More info at: Modeling CLV(insurance), Customer Metrics