If we’re counting just exclusive relationships, the list gets short. I’ve been in several relationships since my divorce, but not hit the Exclusive button (one I’d have liked to, the other two didn’t get close). I’m excluding relationships before I was 18, a dim memory.
So:
#1 - 2 1/2 years
#2 - 25 years
I’m 53
I’m 55. Numbers above are exclusive of my current relationship – I’m married now.
I know it’s been a long time, but the reason I asked was so I could do some statistical analysis, and perhaps attempt to find a function representing the likelihood that a romantic relationship is successful, given its current length.
A “romantic relationship” is a general term including flings, long-term relationships, and marriages, and the time at which it ends is measured by the time elapsed the first date and final breakup or divorce.
Let event D represent the event that a romantic relationship is doomed, or destined to end (by breakup or divorce) at some point.
Let event D’ represent the complement of event D, the event that a romantic relationship is successful, and is destined to never end (by breakup or divorce).
I decided to discard the data points in which a romantic relationship ended due to death, as it’s unknown whether those relationships were doomed or successful. So, I’m defining a romantic relationship “ending” as a romantic relationship that ends by breakup or divorce, for good (breaks in the middle don’t count and are simply included in the time elapsed). Of the remaining data points, the mean time length was 36 months.
The romantic relationships representing the data for which the mean time length was 36 months, were of course all doomed romantic relationships, because the time they lasted was finite. The histogram of this data displayed an exponential relationship between the time at which a doomed romantic relationship ended and the number of doomed romantic relationships.
Thus I decided to model the probability that a doomed romantic relationship lasts up to a certain time, with an exponential probability distribution. Let T be a continuous random variable representing the time in months where 0 < t < infinity. The general form of the probability density function of an exponential probability distribution is f(x) = λe^(-λx). We assume that the mean or expected value of the time at which a romantic relationship ends given it’s doomed E[T | D] is equal to 36, based on the given data. Based on this fact, λ = 1/36, and the probability density function for the time at which a doomed romantic relationship ends is given by f(t | D) = (1/36)e^(-t/36).
This gives us a cumulative distribution function of F(t | D) = 1 - e^(-t/36). and a survival function of S(t | D) = e^(-t/36).
The cumulative distribution function represents the probability that a doomed romantic relationship will end by T = t. The survival function represents that probability that a doomed romantic relationship will “survive” or not end until at least T = t.
We can interpret F(t | D) to represent the ratio of doomed romantic relationships “filtered” or S(t | D) to represent the ratio of doomed romantic relationships still remaining, at T = t.
Let b represent the ratio of doomed romantic relationships to successful romantic relationships at T = 0. The ratio of doomed romantic relationships to successful romantic relationships at T = t is given by d(t) = bS(t | D). d(t), the ratio of doomed romantic relationships to successful romantic relationships at T = t, can be expressed as the probability that a romantic relationship is doomed given T = t: P(D | T = t) = bS(t | D).
The probability that a romantic relationship is successful given T = t is simply the complement of P(D | T = t) or P(D’ | T = t) = 1 - b*S(t | D).
Unfortunately, b is currently unknown. b can essentially be interpreted as the probability that a first date with someone will lead to a “successful romantic relationship with them”. If the average number of first dates person goes on until they find their life-long partner, E[F] is found, it will be possible to calculate b by treating E[F] as the expected value of a geometric probability distribution representing the probability that it will take F first dates to find one life-long partner. However, because the average number of first dates a person goes on is unknown, this is not a possibility.
However, P(D’ | T = t) = 1 - bS(t | D) is not a completely useless function. We know that 0 < b < 1 (inclusive) as no more than 100% and no less than of romantic relationships can be doomed. P(D’ | T = t) = 1 - bS(t | D) is decreasing between b = 0 and b = 1 if 0 < t < infinity. This means that within the domain 0 < b < 1 inclusive, the minimum value of P(D’ | T = t) is at b = 1.
b is likely much closer to 1 than it is to 0, as statistically more romantic relationships are doomed than not overall. Treating P(D’ | T = t) = 1 - b*S(t | D) with b = 1 gives us the minimum value of P(D’ | T = t), or the minimum value of the probability that a romantic relationship is successful given T = t.
So if we assume b = 1, we get an estimate of the probability that a romantic relationship is successful given T = t, which is slightly lower than the actual value of P(D’ | T = t). If b = 1, then P(D’ | T = t) = 1 - S(t | D)
Substituting S(t | D), we get P(D’ | T = t) = 1 - S(t | D) = 1 - e^(-t/36).
So in layman’s terms, if you plug in a value for** t, time in months**, into P(D’ | T = t) = 1 - e^(-t/36), you will get the minimum probability that a romantic relationship is successful having lasted that long.
So, at 3 years or 36 months, your romantic relationship has a minimum probability of approximately 0.6321 of being successful, plugging 36 in for t. This can be interpreted as, “If your romantic relationship has lasted 3 years, there’s at least a 63.21% chance that he or she is ‘the one’.”
You don’t just need E [F] but also a variable to express how many relationships the individual had before.
Right. I meant F was the number of first dates a given individual will go on in their whole life to find one life-partner. E[F] is the average number of first dates a person goes on in their whole life to find one life-partner. So if we were evaluating a current person’s situation, then to find the expected number of additional first dates they must go on from now on, we would subtract out the number of past ones from the general expected value.
Sorry, should have made that clearer.
If you mean that how many relationships a person would also effect the probability of a romantic relationship being successful, then yeah, that’s probably true. However, I wasn’t accounting for that above. I was just finding a function to represent the general probability of a romantic relationship being successful given its time length. But yeah, if we wanted to, we could throw in more “given’s” or conditions in there (i.e. number of past relationships, number of times cheating, living distance, etc).
I apologize for any grammatical errors in my last major post. I didn’t fully proof-read it.
I used to like math until I started reading stuff like this.
You think the folks responding to your internet poll on this MB are a representative sample of… anything?
Yeah I realize, that it’s probably not completely accurate as it does assume that the folks responding to the internet poll on this message board are representative of the entire population.
But I decided to do it just for fun. Really, the only thing that would affect the function is the mean time at which a doomed romantic relationship ends. This poll spitted out 36 months.
The general form of the function representing the minimum probability a romantic relationship is successful, given T = t, is given by P(D’ | T = t) = 1 - e^(-t/λ) where λ is that mean. That’s always going to be true. You can throw anything in for λ (between 0 and infinity). As λ increases, P(D’ | T = t) increases as well.
So you can think about whether you think 36 months is higher or lower than the actual mean for time it takes for a doomed romantic relationship to end (it may seem very high at face value but consider all the marriages that end after many years), and based on what you think, you can interpret the P(D’ | T = t) value as higher or lower than the actual.
I think I read on another article that the actual mean was 33 months (2 years, 9 months), and its accuracy is also questionable, but I think 36 is not too far off from the actual value for λ.
I meant to say, “As λ increases, P(D’ | T = t) decreases.” I’m sorry.
I wish I could edit.
“Unfortunately, b is currently unknown. b can essentially be interpreted as the probability that a first date with someone will lead to a ‘successful romantic relationship’ with them.”
I said this in the major post with the math. b is rather essentially the probability that a first date with someone will not lead to a “successful romantic relationship” with them.
3 months
then…
30 years.
Currently 48. I guess the first experience made me realize what I really wanted.