So far during the 2014 season, the following players have a higher batting average than on-base percentage:
But wait! How is this possible? Every time a player gets a base hit, it increases his on-base percentage. How is it possible to lower the on-base percentage? The answer is because of the sacrifice fly. When a hitter hits a sacrifice fly, it does nothing to his batting average, but it lowers his on-base percentage. The formula for the sabermetric on-base percentage is:
(H + BB + HBP) / (AB + BB + HBP + SF)
The article in the link was written in 1973 in the Baseball Research Journal by the Society for American Baseball Research (SABR) and doesn't include the sacrifice fly stat. By the time on-base percentage became an official stat in 1984, the sacrifice fly was included. My best guess as to why they decided to include it is because the hitter isn't willingly giving himself up (as opposed to a sacrifice bunt) and by taking a full swing he is attempting to get on base.
Using Neftali Soto as an example, he has 2 hits in 10 at bats for a batting average of (2/10) .200. He has 0 walks, 0 hit by pitches, and 1 sacrifice fly for an on-base percentage of (2/11) .182.
The exact formula to keep a hitter's batting average equal with his on-base percentage is that sacrifice flies must equal:
(1/AVG - 1) * (walks + hit by pitches)
So say Soto goes crazy and gets 2 walks and 2 hit by pitches in his next game (with nothing else happening). In order for him to keep his batting average above his on-base percentage:
1 / .200 = 5
5 - 1 = 4
4 * (2 + 2) = 16
He'd have to get 16 + 1 consecutive sacrifice flies. Let's test this. (2 + 2 + 2) / (10 + 2 + 2 + 16) = 6/30 = .200. .200 AVG = .200 on-base percentage. Add 1 additional sacrifice fly in order for his average to remain above his on-base percentage.
Now the league leader for most sacrifice flies in a single season is Gil Hodges' 19 in 1954, so a player would have to have a very low number of walks and hit by pitches and a very high number of sacrifice flies in order to keep it up for a full year. With the way the formula works, the higher the batting average, the fewer amount of sacrifice flies are needed to keep the average equal to on-base percentage.
Ernie Bowman has the highest number of at bats (125) to still be able to keep his batting average above his on-base percentage. He had 23 hits for a batting average of .184 and 0 walks, 0 hit by pitches and 2 sacrifice flies for an on-base percentage of .181.
The last time this phenomenon happened to a Tiger player was in 2012. Omir Santos had a .125 batting average and a .111 on-base percentage in 8 at bats. He had 0 walks, 0 hit by pitches and 1 sacrifice fly. Full list of Tiger players is below:
Pretty neat, huh? Math rules!