By Roger Weber

In the 1990s hitting took off. Home run production skyrocketed and teams scored more runs than ever before. The single season home run record was almost reached in 1997 and then was shattered in 1998, only to be broken again in 2001. By the twenty-first century, Barry Bonds was making a run at Hank Aaron's career 755.

This increase was at first treated as exciting. It was attributed much to new smaller ballparks and a more diverse playing field in baseball as well as better fitness regimes by players. But players like Jose Canseco started revealing the biggest reason for the increase, steroids. And later, HGH (Human Growth Hormone).

As more records were broken and totals started getting well beyond the limits most fans had once known the emphasis on steroids grew and the mood toward the huge home run totals soured. There's an idea about baseball fans that they view the game as perfect as it was when they were 12 years old. And for many fans in the mid-1990s that was the age of Mickey Mantle, Roger Maris and Hank Aaron. Any unfair advantage players were getting to help them overcome the older heroes was frowned upon. It didn't help that players like Barry Bonds feuded with the media, causing the media to put a very negative spin on most Bonds stories.

When Roger Maris' record of 61 home runs in a single season fell to sixth all time, behind three National League players from the late 1990s, early 2000s, the idea was made widespread that these players must have broken the record through cheating while Maris' record was clean.

And to a large extent, that is absolutely true. Many fans are certain that Bonds, McGwire and Sosa took steroids (although it has not proven yet just who took steroids and how much) but steroids have very clearly affected the game. It is also unclear just how long players have been taking steroids. From 1961 through 2005 total major league home runs have risen at an average rate of 65 per year, with an especially noticeable spike from about 1996 through 2001.  

The rise in home runs is not new. It has been going on since almost the beginning of baseball. Since 1900, a trend line shows home runs have been rising at an average rate of about 46 per year. These aren't terribly huge increases considering over 5,000 home runs were hit in the majors in 2005, but as late as 1960 only a few over 2,200 balls went out of the park.

Just for fun, here's a look at the single season home run list if we adjust the totals by the differences in their league's total:

Player	Year	Total	Adjusted total
Ruth	1927	60	343
Ruth	1921	59	310
Foxx	1932	58	206
Greenberg	1938	58	168
Maris	1961	61	100
McGwire	1998	70	68
Sosa	1998	66	64
Bonds	2001	73	60

Here are some other things to consider, though. Blacks were not included in baseball until 1947. By 1957 they made up 11.5% of the playing field but Hispanics were still not a major part of the game as they are today. With more capable players, the majors can be filled with a higher quality of talent now. The overall talent field is much stronger today than it was in Ruth's or Maris' years in the majors. Some statisticians venture to say that in the 1920s talent was somewhere between 70 to 85 percent of where it is now. And now players tend to have more rigorous lifestyles and are in better shape.

Relief pitching was almost nonexistent in the 1920s. Today pitchers throw harder because they can be replaced after only a few innings. In the '20s it was common practice for a pitcher not to bring his best stuff until the middle innings. Also lights were not part of the game until 1935, and although few studies have shown that day/night conditions have much effect on stats, many players say it is easier to see the ball during the day.

The size of the actual baseball has been changing. The most noticeable change came in 1930 when a "lively" ball was introduced. There is also rumor that similar changes occurred in 1920. In 1931 in the American League home run production dropped almost in half, presumably due to the new ball. We've seen the effect of a smaller ball at Coors Field in Denver, where the ball can shrink a quarter inch in circumference and become half an ounce lighter. There is about 1.5 times as much scoring there as in an average MLB park.

These different players also played in different ballparks. Yankee Stadium was not terribly friendly to hitters, nor has been Bonds' home park to left handed sluggers. Wrigley Field has been more friendly and old Busch Stadium pretty fair. A player's home ballpark can help him or hurt him significantly on a home run chase, and for many players has.

In 1961 a number of changes occurred in the American League which caused home run production to rise about 50%. The season was lengthened by eight games and the league was expanded by two teams. The National League expanded a year later. Roger Maris almost certainly benefited from these changes. If his home run totals had followed the major league trend, he hit the equivalent to 40.7 home runs in 1961, nowhere near the record.

But most of these players' home runs do not follow the league trend, and the record setting seasons rarely follow the pace of the career. We can figure this out by measuring a player's career (with the record years eliminated) by a parabolic model. We can then find a confidence interval range of home runs the player could hit during a particular season and see if his actual total falls in that range that the rest of his career predicts. If it doesn't, there may be a lurking variable causing the total to have been reached, either fairly or unfairly.

Most fans would assume that Bonds exceeds his range using this method, and he does by about 20 home runs. Surprisingly McGwire and Sosa's great years of 1998 and '99 do not exceed their ranges by more than a couple home runs. Of course we don't know when they started taking steroids, but McGwire was a long-time power hitter who had reached the 40-50 home run mark before and was peaking around the time of his records. Sosa was less of a career power hitter but like McGwire was peaking and 60 home runs were well over the predicted numbers but were not out of the question even though his previous-high in home runs was just 40.

Ruth was a career power hitter so his numbers aren't terribly surprising given the rest of his career but are surprising compared to the leagues he played in. In his 1920-21 seasons he out-homered some teams. Roger Maris, never a huge homer hitter but for one season, exceeded his range by almost as much as Bonds, although there was a great deal of fluctuation throughout Maris' career in his home run totals. The 40 number I mentioned that Maris may have had playing as he did in '61 in 1960 would have fit his pace much better. Luis Gonzalez, the first player ever to hit 57 home runs exactly, had the third biggest overage of the top 20 single season home run hitters.

So it's up to you how much weight to put into the different biases of time. Even Hank Aaron supposedly chewed a substance that improved his play. And we don't know the exact steroid effects on the more current players. But we do know many of the other effects. If all the effects are totaled, which they probably cannot be perfectly, some calculations I have done still have Bonds at the top of the single season home run list with Ruth in second and Maris down in fourth. Players like Ralph Kiner move up significantly on an adjusted list. While some players have benefited with unfair advantages like steroids (which some claim Bonds has taken just to match the overall playing field of baseball), they may have also not received the benefit of many other biases. To asterisk a total because of one bias is not very scientific.