As per kahneman in his famous book (which should be renamed "fact-templates one ought to memorise and practice becase they do not typically come as part of our intuition"), one fact template is that sample size matters, and that larger the sample size the closer the result to the base rates.

If you toss 10 coins tou might not get 5 -5  heads tails split, but you will get close to thst with 100 cojns, and real close with one million coins

In appendix A, the conclusion is that the smaller hospital will record more days of greater-than-60%-born=boys than the larger one, as the larger one tends more towards the base rate ,here, 50:50.

Which means, you will win if you bet on the smaller hospital having more days where more than 60% born were boys, than the large hospital

 (and also win if you bet more days of more girl babies too, coz it must swing wilder either way?)

How does this translate to the stocks world? Can you bet that a smaller company's share price will delta more than a larger company's ?

Can you build a speculation system based on this?

Ooh!! greedily licks its lips....

First of all, girl-boy birth thinggy is a natural law, more or less. And given some sort of socio political steady state, the company perdormance is typically a function of its past. This truism we take as foundation of all the hot air we make. Smallco reults can dip on things which dont affect Bigco at all. But bigco wouldnt make moves smallco would.  Smallco has the possibility of doubling in size much more than bigco. So there is something there.

We can look at smallco as a small sample size of all the able bodied souls working the economic machine running the economic race.

Conversely we can look at the small hospital as a small enterprise dedicated to producing  baby boys.

A note on execution. Having decided this game, picking the super popular call option as our candidate , we would need to pick calls on both bigco and smallco, and note their highs. 

Of course ,actually buying and selling them on gtts would record a different set of highs.