Revitalizing Batting Average with BA+

Ted Williams once said, “baseball is the only field of endeavor where a man can succeed three times out of ten and be considered a good performer”. Batting Average has long been used as a way to compare production of hitters.  Over the years people have come up with stats like OPS+ and wRC+ which are more accurate measurements of a player’s value. Still, batting average is a stat that many use due to its simplistic nature of calculation (total hits divided by total at-bats).  The problem with using magic numbers like “.300” to signify a good hitter, is that the league average fluctuates greatly over the years.  For example, there were just 14 qualified hitters who hit the .300 mark last season, but 20 years ago, 46 players reached .300.  To make batting average a better tool to use, I introduce Batting Average + (BA+)BA+ shows how a player is doing relative to league average (league average being 100).  

Using BA+, the hitter who batted .300 in 2021 would have a BA+ of 123 (23% better than league average), but a hitter in 2001 would have a BA+ of 114 (14% better than league average).

Looking at every 10th year from 1981-2021 we see on the top chart (BA+) everything remains constant.  When we look at the bottom chart (Batting Average) we notice a great deal of variance.  

*Note: From 1901-1971 there were fewer hitters, due to there being fewer teams in the league.

With this, we can compare batters to league average and sort them into categories.

100: League Average

110: 10% better than average (Likely top 50 in League) 

120: 20% better than average (Likely top 20 in League)

130: 30% better than average (Likely top 5 in League)

140: 40% better than average (Likely League Leader)

150: 50% better than average (Among greatest BA+ seasons ever)

156: Ted Williams 1941 Season

158: Ty Cobb 1911 Season

Looking at BA+ over the last 50 years there are only 16 instances in which a hitter had a BA+ of at least 140.

Note: The 2 instances in 2020 were over the 60 game season, and not a full season.  Of course, there can be an argument that natural regression would have brought both hitters’ BA+ down over a whole season.  Even so, I wanted to keep them in the chart and just make a note that they didn’t play a full regular season.

Since 1901, the highest BA+ was 158, set by Ty Cobb in 1911.  In the last 100 years though, there were only 3 occurrences in while a hitter had an over 150 BA+.  

The most notable instance to baseball fans would be Ted Williams in 1941.  His .406 Batting Average equates to a 156 BA+.  In 1957 he set the 2nd highest BA+ with 150.  The only player not named “Ted Williams” to have a BA+ of 150 in the last 100 years was Rogers Hornsby in 1924…   BA+ of 150 can be like the .400 hitter mark that has eluded all who have tried since Ted Williams.  There have been 13 instances where a batter hit .400 in a season since 1901, and 13 instances a batter had a BA+ of at least 150 in the same amount of time.

*Highlighted in yellow are times a batter hit .400 and had a BA+ of 150 in the same season.

Top 10 Hitters in BA+ from 2021

If a player were to hit .400 in 2021, they would have set the all-time BA+ record of 164!  To reach Ted Williams’ mark, instead of comparing 2 unequal .406 seasons, they would shoot for a BA+ of 156.  This would equate to a .380 batting average in 2021.

In a game that is rich with history and magic numbers for players to chase, and fans to argue about, BA+ can be a tool to compare past seasons more equally.  BA+ is certainly not an end-all stat that will tell you who is the most productive hitter, but it is certainly a more useful statistic than just Batting Average when comparing players of different seasons.

2 thoughts on “Revitalizing Batting Average with BA+

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  1. Interesting article, David, and thanks for the work put into it. I don’t see anyone hitting .400 ever again, and your work demonstrates just how incredibly difficult that would be – the best BA+ ever!

    One detail to touch upon. You say, “*Note: From 1901-1971 there were fewer hitters, due to there being fewer teams in the league.” But there were two expansions in the 1990s that changed the number of teams, affecting your 1981 and 1991 comparisons to later decades.

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