What Is the Expected Value of a Father?
In the human sense, a father is expected to support his children, be present in their lives, and treat his wife with respect. He should lead by example and act with love, patience, and integrity. But that is only one perspective. What if we examine fatherhood through the lens of quantitative thinking?
I’m Johannes, 18, and I’m working toward a career in Quantitative Finance. To stay accountable and share insights along the way, I’m documenting my learning journey daily.
Today is Day 2, and I explored one of the most foundational concepts in probability and finance: the Expected Value Formula.
In simple terms, expected value is the weighted average of all possible outcomes. It is a tool used by investors, analysts, and quants to guide decisions under uncertainty. The formula is:
\(\large E[X] = \sum_{i=1}^n p_i \cdot x_i
\)
Here:
- \( E[X] \) is the expected value of a random variable \( X \)
- \( p_i \) is the probability of the \( i^{th} \) outcome occurring
- \( x_i \) is the value associated with the \( i^{th} \) outcome
In this context, \( x \) is a random variable, but I will assign it specific values based on traits of a good father.
The question is: how can we make this practically applicable to fatherhood?
To calculate the expected value of a father, I identified six core traits that, in my view (plus a bit of internet scrolling), define a truly valuable dad:
- Presence and Involvement
- Support and Encouragement
- Guidance and Discipline
- Emotional Intelligence
- Role Modeling
- Unconditional Love and Respect
These are the six most crucial traits that contribute to the value of a father. I will now assign each of them a probability \( p_i \) and a corresponding impact value \( x_i \) to compute an expected value for fatherhood.
The Expected Value of a Father can be broken down by several key aspects. For “Presence and Involvement”, the probability \(p_i\) is \(0.85\) with a score \(x_i\) of \(9\), yielding a product \(p_i \cdot x_i\) of \(7.65\). “Support and Encouragement” has a \(p_i\) of \(0.80\) and an \(x_i\) of \(8\), resulting in \(6.40\). For “Guidance and Discipline”, the \(p_i\) is \(0.75\) and \(x_i\) is \(7\), totaling \(5.25\). “Emotional Intelligence” is assigned a \(p_i\) of \(0.70\) and an \(x_i\) of \(9\), making \(p_i \cdot x_i\) equal to \(6.30\). “Role Modeling” has a \(p_i\) of \(0.65\) and an \(x_i\) of \(8\), leading to \(5.20\). Finally, “Unconditional Love and Respect” has the highest probability at \(0.95\) and a score of \(10\), giving a product of \(9.50\).
Let me break down how I assigned each probability \(p_i\) and impact score \(x_i\). I used simple logic: how often the trait realistically appears in great fathers I have observed or read about (this gave me the probability), and how much long-term influence it carries (this gave me the impact score).
1. Presence and Involvement
A father who shows up consistently, mentally and physically, creates emotional stability.
\(p = 0.85\) because many fathers try to be present.
\(x = 9\) because that presence builds trust and security.
2. Support and Encouragement
A father who believes in his children changes their inner narrative.
\(p = 0.80\) since not all fathers express this well.
\(x = 8\) because support builds confidence and direction.
3. Guidance and Discipline
This is about clear boundaries and practical wisdom.
\(p = 0.75\) as it varies across parenting styles.
\(x = 7\) because good guidance influences future decisions.
4. Emotional Intelligence
Many fathers struggle to express or regulate emotions.
\(p = 0.70\) since this trait is less common.
\(x = 9\) because emotional maturity teaches children how to handle pressure, failure, and relationships.
5. Role Modeling
Children learn more by observing than by listening.
\(p = 0.65\) since not all fathers are aware of their example.
\(x = 8\) because character is often copied unconsciously.
6. Unconditional Love and Respect
This is the foundation for everything else.
\(p = 0.95\) because most fathers love deeply, even if they struggle to show it.
\(x = 10\) because being loved unconditionally shapes identity.
And now all that remain is the final calculation, which I will do here:
\(\begin{aligned}
E[X] &= (0.85 \cdot 9) + (0.80 \cdot 8) + (0.75 \cdot 7) + (0.70 \cdot 9) + (0.65 \cdot 8) + (0.95 \cdot 10) \\
&= 7.65 + 6.40 + 5.25 + 6.30 + 5.20 + 9.50 \\
&= \boxed{40.30}
\end{aligned}
\)
This means the expected value of a high-quality father is
\( E[X] = 40.30 \)
though personally, I would easily give a score of \( 40.31 \) or higher even if that is mathematically impossible with this model.
This serves as a clear introduction to the expected value formula, which is commonly applied in valuation and portfolio construction.
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