I used lifetime hitting statistics to look at all players who played MLB from 1871 to 2004 to see how Hank Aaron, Barry Bonds, and all other players stacked up.

The statement sum g ab h hr hrhit hrab yrs startyr endyr is a Stata command that summarizes, in order, games, at bats, hits, home runs, home runs per hit, home runs per at bat, years played, the starting year and ending year of the player’s career or 2004, whichever occurs first.

**. sum g ab h hr hrhit hrab yrs startyr endyr****Variable | Obs Mean Std. Dev. Min Max **

————-+——————————————————–

g | 16208 271.6803 451.0802 1 3562

ab | 16208 777.2142 1592.251 0 14053

h | 16208 203.7318 448.6123 0 4256

hr | 16208 14.22378 47.41726 0 755

hrhit | 12747 .0389471 .0706693 0 1

————-+——————————————————–

hrab | 14733 .0079549 .0163393 0 .5

yrs | 16208 4.627962 5.025919 0 35

startyr | 16208 1946.452 38.18067 1871 2004

endyr | 16208 1951.08 38.8478 1871 2004

. sum g ab h hr hrhit hrab yrs startyr endyr if namelast==”Aaron” & namefirst==”Han

> k”

Variable | Obs Mean Std. Dev. Min Max

————-+——————————————————–

g | 1 3298 . 3298 3298

ab | 1 12364 . 12364 12364

h | 1 3771 . 3771 3771

hr | 1 755 . 755 755

hrhit | 1 .2002122 . .2002122 .2002122

————-+——————————————————–

hrab | 1 .0610644 . .0610644 .0610644

yrs | 1 22 . 22 22

startyr | 1 1954 . 1954 1954

endyr | 1 1976 . 1976 1976

. sum g ab h hr hrhit hrab yrs startyr endyr if namelast==”Bonds” & namefirst==”Bar

> ry”

Variable | Obs Mean Std. Dev. Min Max

————-+——————————————————–

g | 1 2716 . 2716 2716

ab | 1 9098 . 9098 9098

h | 1 2730 . 2730 2730

hr | 1 703 . 703 703

hrhit | 1 .2575092 . .2575092 .2575092

————-+——————————————————–

hrab | 1 .0772697 . .0772697 .0772697

yrs | 1 18 . 18 18

startyr | 1 1986 . 1986 1986

endyr | 1 2004 . 2004 2004

The average number of games played is 271 for all players. Aaron played 3298 and Bonds 2714 (through 2004). Both are far above the MLB average. They are 4 or 5 standard deviations above the mean (nothing is normal with exceptional talent).

Aaron played 22 years, Bonds was in MLB 18 years in 2004 and will have played 21 years at the end of this season. The average for all players is just 4.6. Again, Aaron and Bonds are way above the average, in fact they are so far above that they are 6 to 7 standard deviations above the mean. But, you should know by now that nothing is normal here (the normal distribution would say this is an impossible feat).

The average player (there is no such player, this is just a phrase that leads to poor thinking) had 777 at bats, Aaron had 12364 and Bonds 9098, somewhat behind Aaron and both are far beyond the mean.

Hits, home runs, and the other statistics can be read from the tables. Aaron had about 1000 more hit than Bonds. They are both 9 or more standard deviations above the mean for all players. Nothing Normal once again.

14 career home runs is average, but Hammerin’ Hank got his famous 755 and Bonds had 703 in 2004 and has since gone to 756 last I heard.( I have been out riding and have not kept up.) This means Aaron is 15.75 standard deviations above the mean of all players. Bonds is 14.65 std above the mean at 703 and 15.78 std above the mean at his record 756. They are both so far above the mean that their achievements would not be matched in millions of years of baseball if home run hitting were a normal feat. They are impossible, but they exist. So, get over any thinking about norms of home run hitting.

Bonds’ home runs per at bat are only a little higher than Aaron’s being 0.077 versus 0.061. The mean for all players is 0.0079. Barry is almost 10 times more likely to hit a home run in an at bat as the average for all players. Hank is almost 8 times.

Home runs per hit is a good measure of power: Barry hits 0.257 home runs per hit. Hank hits 0.200. The mean for all players is 0.039. On average a player hits 4 home runs in every 100 hits. Hank hits 20 and Barry hits 26. In his record year, McGwire hit 52 home runs in every 100 hits. Many others have exceeded Barry’s career stats for home runs per hit in individual seasons. In his record year, Barry hit 46.7 home runs per 100 hits. Kilibrew, Maris, Mantle, Kingman, Schmidt, Jackson, Stargell, Fielder, Buhner and Williams all exceeded 30 home runs per 100 hits. If you compare that to the MLB average of 4 home runs per 100 hits you see how different the leading home run hitters are.

It is also intriguing to look at how small positive variations, say an increase in home runs per hit or just more hits with the same power combined with more at bats, can drive a player’s performance to new highs. The variability of all these measures is so high, that slumps and outstanding years are largely due to chance.

I have to conclude that anyone who posits some kind of norm for home run hitting, whether in a year or a career, doesn’t know what he is talking about. In truth, all these results follow from De Vany’s Law of Home Runs. Season home runs follows an infinite variance stable distribution. Career home runs is so variable that it does not even have a mean (technically the probabiiities are so diffuse and heavy far out on the upper tail that the first moment of the distribution does not converge — its value is infinite which is to say that the mean does not exist).

I used lifetime hitting statistics to look at all players who played MLB from 1871 to 2004 to see how Hank Aaron, Barry Bonds, and all other players stacked up.

The statement sum g ab h hr hrhit hrab yrs startyr endyr is a Stata command that summarizes, in order, games, at bats, hits, home runs, home runs per hit, home runs per at bat, years played, the starting year and ending year of the player’s career or 2004, whichever occurs first.

The average number of games played is 271 for all players. Aaron played 3298 and Bonds 2714 (through 2004). Both are far above the MLB average. They are 4 or 5 standard deviations above the mean (nothing is normal with exceptional talent).

Aaron played 22 years, Bonds was in MLB 18 years in 2004 and will have played 21 years at the end of this season. The average for all players is just 4.6. Again, Aaron and Bonds are way above the average, in fact they are so far above that they are 6 to 7 standard deviations above the mean. But, you should know by now that nothing is normal here (the normal distribution would say this is an impossible feat).

The average player (there is no such player, this is just a phrase that leads to poor thinking) had 777 at bats, Aaron had 12364 and Bonds 9098, somewhat behind Aaron and both are far beyond the mean.

Hits, home runs, and the other statistics can be read from the tables. Aaron had about 1000 more hit than Bonds. They are both 9 or more standard deviations above the mean for all players. Nothing Normal once again.

14 career home runs is average, but Hammerin’ Hank got his famous 755 and Bonds had 703 in 2004 and has since gone to 756 last I heard.( I have been out riding and have not kept up.) This means Aaron is 15.75 standard deviations above the mean of all players. Bonds is 14.65 std above the mean at 703 and 15.78 std above the mean at his record 756. They are both so far above the mean that their achievements would not be matched in millions of years of baseball if home run hitting were a normal feat. They are impossible, but they exist. So, get over any thinking about norms of home run hitting.

Bonds’ home runs per at bat are only a little higher than Aaron’s being 0.077 versus 0.061. The mean for all players is 0.0079. Barry is almost 10 times more likely to hit a home run in an at bat as the average for all players. Hank is almost 8 times.

Home runs per hit is a good measure of power: Barry hits 0.257 home runs per hit. Hank hits 0.200. The mean for all players is 0.039. On average a player hits 4 home runs in every 100 hits. Hank hits 20 and Barry hits 26. In his record year, McGwire hit 52 home runs in every 100 hits. Many others have exceeded Barry’s career stats for home runs per hit in individual seasons. In his record year, Barry hit 46.7 home runs per 100 hits. Kilibrew, Maris, Mantle, Kingman, Schmidt, Jackson, Stargell, Fielder, Buhner and Williams all exceeded 30 home runs per 100 hits. If you compare that to the MLB average of 4 home runs per 100 hits you see how different the leading home run hitters are.

It is also intriguing to look at how small positive variations, say an increase in home runs per hit or just more hits with the same power combined with more at bats, can drive a player’s performance to new highs. The variability of all these measures is so high, that slumps and outstanding years are largely due to chance.

I have to conclude that anyone who posits some kind of norm for home run hitting, whether in a year or a career, doesn’t know what he is talking about. In truth, all these results follow from De Vany’s Law of Home Runs. Season home runs follows an infinite variance stable distribution. Career home runs is so variable that it does not even have a mean (technically the probabiiities are so diffuse and heavy far out on the upper tail that the first moment of the distribution does not converge — its value is infinite which is to say that the mean does not exist).