How much Barry Bonds improved in his late 30s might be unprecedented given how much more he improved than anyone else. To look into this we need to have a yardstick and ages for both the before and after to see how big the improvement was.
The yardstick I used is slugging percentage (SLG) compared to the league average. Bonds improved according to several measures in his late thirties, but using SLG takes into account both the ability to get hits and the ability to hit for power. Even if you get a single, your SLG still rises. A player could make a radical change in his hitting style and try alot harder to hit HRs. His HR frequency (HR%) and his isolated power (ISO) might go up, but he could get even fewer hits, lowering his average. We would detect improvement if we used HR% or ISO, yet the player may actually not be doing any better. ISO is SLG minus AVG, and is simply extra bases divided by ABs (while SLG is TB/AB). But SLG, by essentially being AVG + ISO does not have this defect. It includes both the ability to get a hit and hit for power (theoretically, a player could slug 1.000 by hitting a single every time up (having no power), but that is not likely).
The "Lee Sinins Complete Baseball Encyclopedia" was the source of my data. Instead of using SLG, I could have used a stat like offensive winning percentage (OWP, a Bill James creation) that incorporates the ability to hit for power and get on base. In the "Lee Sinins Complete Baseball Encyclopedia" OWP takes into account the league average and park effects. Doing so is normally desirable, but Bonds had some ridiculously high on-base percentages because he got walked so much. Therefore, he is going to come out looking pretty good imrovement wise using OWP. By looking only at SLG, this walk bias is removed. And, as mentioned already, it will be compared to the league average. This is important since some eras in baseball history were tougher on hitters than others. There is a link at the end of this study to ones where I used OWP, HR% and ISO is examining the question of Bonds' improvement as he aged.
But I end up not taking park effects into account (the Sinins database does not adjust SLG for this). Doing this will actually biases the case against Bonds showing the greatest improvement ever even though AT & T park is a tough park for hitting HRs. From 2000-2005 (the years in which Bonds will be considered "old"), the HR rate at AT & T park was only about 80% of average and it was even lower for lefties. So the improvements reported below are also biased against Bonds having the biggest improvements.
So what ages were "young" and "old" in determining who improved the most? My first look was at ages 36-39 compared to being younger than 36. Those ages cover the great seasons that Bonds had from 2001-04. Since his birthday is after July 1, he is considered 36 for the 2001 season. But I also looked at ages 35-38 comapred to everything younger and ages 37-40 compared to everything younger. I found all players who had at least 4,000 plate appearances (PAs) at the "young" age and had 1,000 or more PAs at the "old" age. Then I compared their "young" SLG (relative to the league average, of course) to their "old" SLG. The first look compared what players did under 36 to what they did from 36-39.
The table below shows the ten best improvements in SLG relative to the league average going from "young" to "old." Bonds is first. Under 36, his SLG was 39% better than average (hence the RATE 139). But when he was "old" Bonds was 87% better than average. The last column called "ratio" is actually the "old" rate divided by the "young' rate. For Bonds, this is 187/139. That works out to 1.345, meaning that Bonds was 34.5% better when he was old than when he was young. This is the highest ever and by a pretty wide margin. Notice that the next best 9 cases are all bunched up pretty closely. Bonds stands pretty far above the pack. The average player has an "old" SLG that is 92.8% of his "young" SLG.
We can also look at simply the difference between the player's SLG and the league avereage SLG and how much that difference increased. Bonds had a .567 SLG under 36 while the league average was .409. So he was .158 better than average (that is the first DIFF column). His "old" SLG was .809 while the league average was .433. So he was .376 better (the second DIFF column). But his "old" DIFF is .218 better than his "young" DIFF. That is repoted in the "gain" column. Bonds is way ahead of everyone else.
I am not really sure which one is the best measure, the ratio or the difference. A case could probably be made for both.
An objection here is that I picked Bonds' four best years when he was "old." So let's use 35 as the cutoff. So "young" is under 35 and "old" is 35-38. Bonds is first here, being about 30% better than average when he was "older." But second place is fairly close. Joost, however, played most of the early part of his career in Cincinnati, which had a tough HR park then, allowing only about 85% of the league average of HRs. Most of his 35-38 playing time was with the A's (in 1951-2) and their park allowed about 20% more HRs than average. Galarraga played 2 of his 3 "old" seasons for the Rockies, which helped make him look good then. So Bonds again is far away from the pack.
The next table uses the differences for the age 35 cutoff. Again, Bonds stands out.
I also used 37 as the cutoff, comparing under 37 performance to 37-40. Bonds is on top, so nothing new. But he was hurt when he was 40 and played very little. So his SLG from 37-39 pretty much makes up his numbers here. So I looked at Bonds from age 37-41, when his SLG was about 68% better than average (.727/.433=1.68). Then 1.68/1.42 = 1.183. That would still put him well above the pack (no other players were adjusted, biasing this against Bonds).
Now using differences for the 37 cutoff.
I also found the top 800 seasons in SLG relative to the league average since 1920. Of the players who had at least 4 seasons on the list, Bonds is the only one to have his 4 best seasons at ages 36, 37, 38, and 39. So the average age of his 4 best seasons is 37.5. The next highest average is 35.25 for Cy Williams. But he played some before 1920, so his true average might be lower. Aaron is next on the list at 35. But he benefited partly from playing in a good HR park in his later years. Next is Tris Speaker at 34.5. But he is in the same boat as Williams. Then we have Stargell and Clemente at 33.5, four years lower than Bonds and they benefited in their later years partly because they started playing in Three Rivers Stadium instead of Forbes Field. At age 39, Bonds' SLG was still 86% better than the league average. His best relative SLG before he turned 36 was his 164 at both ages 27 and 28. So at age 39, he was far better than he was at age 27-28. Probably not many players can say that. His relative SLGs from 36-39 were 196, 189, 174, and 186. Even at age 38, playing in a tough HR park, his relative SLG (174) was a good bit higher than anything he had in what are considered normal prime years for a hitter (164).
The link to my earlier articles.
Other sources: Bill James Handbooks and STATS, INC All-Time Baseball Sourcebook