While Niantic has not confirmed anything there's a theory that the location of the egg of which it was acquired influences the outcome. By that I'm assuming that the GPS location of the pokestop is stored and then used to find which pool of mons are appropriate.
It makes sense when you think about it. Pokemons that are common to spawn near certain pokestops are more likely to appear near them when luring.
I had a theory myself that your location when the egg hatches influences the pool of pokemons that you can get but I don't hava data to support that theory.
There are no facts out there though, only theories. I'm leaning towards the theory I linked until proven otherwise. I just found it and I'm going to keep an eye on it.
According to this datamine of the most recent APK, there are a couple mechanical changes to encounters.
Code has appeared fleshing out the CRITICAL CATCH mechanic which first appeared in the previous APK but has not been implemented. The following components now appear:
- CRITICALSHAKE
- CRITICALCLICK
- CATCHSUCCESSCRITICAL
I can not confirm whether these have actually been implemented or not yet, but according to this Silph Road reddit thread, they have been:
Critical catches have been implemented. You know it's a critical catch when the ball immediately drops on the ground after hitting the Pokémon and has 4 rays of light leaving upwards in a zig zag motion.
Additionally, as @Rapitor has mentioned in the comments on the question and as I have personally witnessed already, Pokémon now move in more directions than up to mess up your throws. They can move side-to-side (which unfortunately makes their CP go off-screen if you have AR-mode turned off). From that same datamine, it seems there are other states that they can be in:
It appears the way Pokémon interact during wild encounters has been upgraded. There are now several movement types at play rather than just 'wait', 'jump,' and 'attack':
- JUMPMOVEMENTSTATE
- ELECTRICMOVEMENTSTATE
- PSYCHICMOVEMENTSTATE
- SETUPHOVERMOVEMENTNODES
- SETUPFLYINGMOVEMENTNODES
According to the same Reddit thread as above that confirmed critical captures, it appears that different Pokémon tend to move in different patterns (probably explains the naming conventions chosen):
Pokémon move in new ways during the catch sequence. Ledyba will move in a "V" motion, while Qwilfish will move sideways form left to right, with their catch circles following them. Other users in this same thread also report new movements for gen 1 Pokémon like Venonat or Abra.
Another change worth mentioning is that you are still only able to use a single berry at a time during a Pokémon encounter, as mentioned in the (same) Reddit thread:
You can only use 1 berry at a time on a Pokémon. So no, you can't use a razz + a nanab on a Pokémon. The active berry is used as an icon on the Pokémon. Once the icon disappear, on a failed catch attempt, you can use an another berry.
Best Answer
No. The chance of a Pokemon being shiny to an individual player is specific for each Pokemon, and doesn't change based on what Pokemon you've encountered before. This rate is observed to be about 1 in 450.
In fact, it's very common for people to enter the catch screen to see if it's shiny, then flee when they realise it isn't, and repeat for all the Pokemon in the area.
The factors that seem to increase the chance of a specific Pokemon being shiny or not are:
Most events that introduce Shiny Pokemon don't increase the shiny rate. Catch streaks, unlike in Pokemon Let's Go, also don't increase the shiny rate.