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You might see a player's OBP (on base percentage) lower than their batting average for a game or two but there is virtually no chance that it would happen over an entire season as a player would have to have an incredibly higher number of sacrifice flies than total of (walks + hit by pitch).

To review ...

Batting average is calculated as (hits / at bats).

OBP is calculated as (hits + walks + hit by pitch) / (at bats + walks + hit by pitch + sacrifice flies).

Example 1: A player has played 2 games and has 8 at bats, 2 hits, 0 walks, 0 hit by pitch, and 1 sacrifice fly.

Batting average is .250 (2 / 8).

OBP is .222 (2 + 0 + 0) / (8 + 0 + 0 + 1).

Example 2: A player has played an entire season and has 500 at bats, 150 hits, 50 walks, and 5 hit by pitch.

Batting average is .300 (150 / 500).

For the OBP to be lower than the batting average, the player would need 129 sacrifice flies ...

(150 + 50 + 5) / (500 + 50 + 5 + 129) = .2997.

Q: How can OPB be lower than BA?

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You can prove this just from knowing that the three angles of a triangle add to 180 degrees. Label the ends of the arc A and B, the circle's centre O and the "any other point" P. We want to show that angle APB is half of angle AOB. (This uses the notation where you write three letters XYZ to mean the angle formed between straight lines XY and YZ). Consider the triangle formed by O, B and P. The lengths OB and OP are the same (the radius of the circle). This means that the triangle is isosceles and angles OPB and OBP are the same. Since POB + OPB + OBP = 180 degrees and OPB = OBP we have POB + 2 * OPB = 180 With the same working, the triangle formed by O, A and P gives us POA + 2 * OPA = 180 Subtract these two equations: (POB - POA) + 2 * (OPB - OPA) = 180 - 180 = 0 Rearrange: 2 * (OPB - OPA) = POA - POB If you draw a diagram you will see that OPB - OPA = APB and POA - POB = AOB so we have 2 * APB = AOB as required.

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