throwing the ball: smaller circle vs closer to the center of the circle

Solution 1:

Getting a Throw Bonus will increase your chances of getting a Pokemon, with an Excellent Throw resulting in a rather sharp spike to catch chances.

However, to get the XP bonus (and the catchrate bonus), you actually have to hit inside the shrinking circle. It isn't enough to wait for the circle to become small, you must still hit inside the circle and get the bonus.

You can also take your time throwing: the circle will expand out after hitting its smallest point.

Solution 2:

To catch a Pokémon:

1. When a wild Pokémon is nearby, your device will vibrate, and the Pokémon will appear on the map. Touch the Pokémon to begin your attempt to catch it.
2. The Pokémon will appear in front of you. Note: You may need to orient your device or switch out of camera mode
3. Touch and hold your Poké Ball.
4. A target ring will appear around the Pokémon. The ring’s color indicates the difficulty level of capturing the Pokémon. A green ring indicates the capture is low difficulty, orange indicates intermediate difficulty, and red indicates extreme difficulty
5. You have the greatest chance of capturing the Pokémon while the colored ring is at its smallest diameter. At the opportune moment, fling the Poké Ball toward the Pokémon
6. If you are successful, the Poké Ball will capture the Pokémon. Watch out, though—Pokémon can escape from the Poké Ball. Tip: Drag and rapidly spin the Poké Ball in a circular motion before you release it for a chance to receive a curveball bonus. Source:https://support.pokemongo.nianticlabs.com/hc/en-us/articles/221957648-Finding-and-Catching-wild-Pok%C3%A9mon