My Eevee leveled up, and got more stat points, just like every other generation so far. However, there is an extra stat point, as shown in the yellow circle. Why is this, and can I influence it? Eevee is my starter, if it matters.
Based on a few articles and guides, the yellow "+1" you are seeing is known as an Awakening Value (AV). In the Let’s Go series, AVs are to replace the normal Effort Values (EVs) from the core series.
Despite the elimination of EVs, Pokemon Let’s GO Pikachu/Eevee uses a new system called AVs, also known as Awakening Values. Awakening Values increase whenever a Pokemon levels up or Candy is consumed, so you could say AVs are the EVs of the Pokemon Let’s GO series.
(emphasis my own)
The purpose of AVs is to increase the overall stats of your Pokémon. Based on information from the sources, each stat can have a maximum of 200 AVs.
Every stat is capped at a 200 AV boost and 1 AV is equivalent to +1 boost on that stat (ex: Pokemon with an HP stat of 300 + 200 AVs would result in an HP stat of 500 for that Pokemon)
According to Serebii, as well as personal experience, the AV that increases after leveling up appears to be random.
A guaranteed way to influence and increase a Pokémon's AVs is to use candy from the Candy Jar in your bag. As the AVs increase, so will the number of candy to further increase the stat.
- Quick Candy: Increases Speed
- Health Candy: Increases HP
- Might Candy: Increases Attack
- Smart Candy: Increases Sp. Attack
- Tough Candy: Increases Defense
- Courage Candy: Increases Sp. Defense
- [Pokemon] Candy: Increases all stats