The Actuary Song
As I was browsing through ITunes, I came across the Actuary Song, taken from the musical “I Love You Because”. Well, I had no idea there was an actuary song, as you can imagine. It turned out there were actuary two others songs on ITunes about actuaries. But I will focus for the moment on the Actuary Song. The Actuary Song is about a girl Marcie who broke up with her boyfriend and her friend Diana gives her some advice about finding Mr Right. I have lived happily as an actuary now for a number of years and I had never heard actuarial principles were used on the dating scene. If only I had known this, maybe I could have applied some of my mathematical skills to assess the likelihood of certain relationships.
So here is what I learnt from the Actuary Song... The Rebound Time (RT), that is the time (in years) you need before you start another long-term relationship, depends on the Relationship Length (RL) of the previous relationship. The first year is worth 6 months of RT, the next is worth half of that and so on... So RT = ½ + ¼ +... + (1/2)^RL
That leads to the formula: RT = 1 – (1/2)^RL.
As you can see, this can be made a continuous function, starting from 0 for RL = 0, with a limit of one year for RL → ∞ . This is yet another discovery for me, the rebound time after a break-up is maximum one year! Well, that means I have wasted some time in my life. But that’s alright; let me continue to explore the Actuary Song theories.
The next thing is the Adjusted Relationship Length, or ARL, which is supposed to take into account different factors that may alter the perception of the length of the previous relationship.
The ARL uses the NBI, that is the number of boyfriends index. You may be glad to learn that:
NBI = 4 / (3 + #BF)
So for a first boyfriend, #BF = 1 and NBI = 1. There is no adjustment made.
After boyfriend say number 21, #BF = 21 and NBI = 1/6. The RL is adjusted by 1/6. In other words, it feels like the relationship was 6 times shorter than it actually was.
The ARL also uses the Who Broke Up factor. If they broke up with you, WBU = 5/4. If you broke up with them, then WBU = 3/4. In other words, you cut down you RT if you break up first.
Finally, the Bitterness Factor, but I have to say that I didn’t quite understand how it works in the ARL calculation. But we already have a very interesting formula that can be summed up as below:
ARL = RL x NBI x WBU
Where:
NBI = 4 / (3 + #BF)
WBU = 5/4 if they broke up with you or 3/4 if you broke up with them.
And hurrah, your rebound time is:
RT = 1 – (1/2)^ARL
Now I have to say I was quite impressed by the cleverness of this formula. So much so that I think we can do much more than that. I believe we can figure out a formula to calculate the probability of finding Mr or Ms Right given a set of assumptions. I believe we can calculate the expected length of a relationship using variables such as your communication skills, your financial situation and your good looks. I believe we should start gathering the data right now and ask people to fill questionnaires on their relationships.
Or maybe I will let you do that. The danger here is the ‘Observer Effect’, where the one doing the research changes its outcome. If my formula tells me I may stay with a girl and marry her, and the girl finds out about my actuarial model, there is a chance she might call me an unromantic nerd and never see me again! That is what I will call self-destroying prophecy... A self-destroying prophecy is when an actuary destroys all his chances with a good girl because his stochastic model predicts there is a 76.5% chance they will get married. So I am back to square one, confronted by the thought romance may be governed by non-parametric random variables. Someone help me.
So here is what I learnt from the Actuary Song... The Rebound Time (RT), that is the time (in years) you need before you start another long-term relationship, depends on the Relationship Length (RL) of the previous relationship. The first year is worth 6 months of RT, the next is worth half of that and so on... So RT = ½ + ¼ +... + (1/2)^RL
That leads to the formula: RT = 1 – (1/2)^RL.
As you can see, this can be made a continuous function, starting from 0 for RL = 0, with a limit of one year for RL → ∞ . This is yet another discovery for me, the rebound time after a break-up is maximum one year! Well, that means I have wasted some time in my life. But that’s alright; let me continue to explore the Actuary Song theories.
The next thing is the Adjusted Relationship Length, or ARL, which is supposed to take into account different factors that may alter the perception of the length of the previous relationship.
The ARL uses the NBI, that is the number of boyfriends index. You may be glad to learn that:
NBI = 4 / (3 + #BF)
So for a first boyfriend, #BF = 1 and NBI = 1. There is no adjustment made.
After boyfriend say number 21, #BF = 21 and NBI = 1/6. The RL is adjusted by 1/6. In other words, it feels like the relationship was 6 times shorter than it actually was.
The ARL also uses the Who Broke Up factor. If they broke up with you, WBU = 5/4. If you broke up with them, then WBU = 3/4. In other words, you cut down you RT if you break up first.
Finally, the Bitterness Factor, but I have to say that I didn’t quite understand how it works in the ARL calculation. But we already have a very interesting formula that can be summed up as below:
ARL = RL x NBI x WBU
Where:
NBI = 4 / (3 + #BF)
WBU = 5/4 if they broke up with you or 3/4 if you broke up with them.
And hurrah, your rebound time is:
RT = 1 – (1/2)^ARL
Now I have to say I was quite impressed by the cleverness of this formula. So much so that I think we can do much more than that. I believe we can figure out a formula to calculate the probability of finding Mr or Ms Right given a set of assumptions. I believe we can calculate the expected length of a relationship using variables such as your communication skills, your financial situation and your good looks. I believe we should start gathering the data right now and ask people to fill questionnaires on their relationships.
Or maybe I will let you do that. The danger here is the ‘Observer Effect’, where the one doing the research changes its outcome. If my formula tells me I may stay with a girl and marry her, and the girl finds out about my actuarial model, there is a chance she might call me an unromantic nerd and never see me again! That is what I will call self-destroying prophecy... A self-destroying prophecy is when an actuary destroys all his chances with a good girl because his stochastic model predicts there is a 76.5% chance they will get married. So I am back to square one, confronted by the thought romance may be governed by non-parametric random variables. Someone help me.
Thank you for this maths. I wanted to use some of it for the programme for our production of I Love You Because (theatre1.org.uk). Ok if we do that? I'll give you a credit?
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