How do Hawkgirl and Hawkman reincarnate?

Question

Reading @Thunderforge's answer to this question, I percieved an assumption he had taken on how Hawkgirl and Hawkman reincarnate (which he confirmed in this comment) and that I originally shared:

"a new child from new parents"

Further contemplation however made me realise that if that were true, than we would run into a huge timeline problem:

It is stated (both in the Arrow/Flash crossover and on Legends of Tomorrow) that

• the cycle of reincarnations started 4000 years ago
• they have - so far - been killed 206 times (or 205 if we exclude the first death, when they were already adults).

That would mean that - on average - they would henceforce have to be killed every 19.5 years (or, if their souls jump into genetically identical (!!!) babies the moment they die, at the age of 19.5 years).

We know Savage tracks them when they, or rather especially when Hawkgirl "emerges", in order to kill them. We also know that they had

a child, the late Professor Boardman, who was 10 when they were killed,

forcing them to be in their mid-20s, at least, at the time of their deaths.

For that to happen, Savage would have had to kill them as children numerous times, which would however not leave them with enough time to grow up, "emerge" and meet in the first place. But they have to "emerge", before Savage can salvage their "lifeforce" (or whatever it is he sucks out of their faces) and/or detect them.

So:

• Is our assumption on how reincarnation takes place wrong, in that maybe they reincarnate into an already adult body (if they magically inhabit a genetically identical baby they can just as easily inhabit a genetically identical adult), and the fact that they remember a childhood is just part of the magic but never actually happened?
• Or did the writers really not think that one through, and should rather have said 106 or 156 instead of 206 reincarnations?

Answers on how this works in the comics are also welcome, if there is nothing provided by the showrunners.

Answer 1

The numbers actually fit, depending on how generous you are with the variance.

Assumptions:

1. Hawkgirl and Hawkman have been doing this reincarnating thing for exactly 4000 years.
2. They have been reborn 205 times.
3. Their lifespan follows a normal distribution (think bell curve).

Based on these assumptions, the average lifespan is 4000/205=19.51 years, as you noted. We can randomly generate data under a normal distribution if we know sample size (205), mean (19.51), and standard deviation. Since the deviation is unknown, we can take some liberties, so I went ahead and picked a standard deviation of 4. This means their lifespan is pretty variable- their lives can range from pretty short to somewhat long- which fits the known data.

I used the statstical programming software, R to simulate data under this model. Running the following will simulate 205 lifespans:

x <- rnorm (205, 19.51, 4)

max (x) ###displays longest lifespan in simulation 
min(x) ###displays shortest lifespan in simulation

I ran the simulation a few times and typically got a minimum lifespan of about 8 years and a maximum somewhere around 31 years. In fact, the probability that Hawkgirl will live longer than 30 years under this model is about 0.5%. Across 205 lives, it's not unreasonable to expect she will live to 30 at least once, long enough to have a 10 year old child.