S06E17 How did Sam come up with the number "50,000" extra survivors from un-sinking the Titanic
In S06E17 "My Heart Will Go On", in the modified reality, Sam and Dean have never heard of the Titanic, they don't know it's meant to sink, they don't know how many people would have died, but then as soon as Balthazar said he saved the ship, and they realize someone is killing the descendants of the survivors, it takes about two seconds for Sam to figure out an estimation number and say: "That's maybe like 50,000 people."
Where did that number 50,000 come from?
Is that really about 50,000 extra survivors and descendants if the Titanic didn't sink?
Sounds like a Fermi Problem again, so let's do a Fermi Estimation.
First, how many people actually died on the Titanic?
The official number is about 2200 passengers on board; approximately 1500 people died. Among them, the majority (more than 1300) were men, especially from crew and third class, who can be presumed to be all young, strong, healthy males who would have been likely to have started a new family.
Assuming 80% of the survivors would have a family, that makes about 1000 extra families.
Then, how many descendants would those families create?
From 1912 to the S06 timeline (2011), almost exactly 100 years. Assuming roughly 20-25 years per generation, that's about 4-5 generations.
Between 1912 and 2012, each generation's time era is roughly: 1930s, 1950s, 1975s, 2000s.
The birth rate and family size for immigrants (those who would travel to the new land in the early 20th century) changed a lot during those times. From open source information, we can get that:
During the 1930s, the Great Depression: roughly 2 children per family
1950s Baby Boom: Almost 3-4 children per family
1970s and later: Generally 2-3 children per family
For a simplified model, say average 3 children per family, and each child will form a new family, and a total of 4 generations. That makes 3*3*3*3=81 descendants after 100 years.
Considering the average age of about 75 years old in the 20th century, and wars and diseases, say half of those people stay alive in 2012, then it's about 40 descendants per survivor.
But if assuming at least three-fourths of those people would stay alive, then it makes about 60 descendants per survivor.
Which makes it roughly 1000*40=40k to 60k extra people.
So it's quite reasonable to say it's about 50k people's lives being affected, and it's 50k souls for Cas's war machine.
It's actually a little impressive to see Sam figure out that estimation number in like 2 seconds in the middle of a conversation, arguing with Balthazar.