Chris Davis and Normalized Home Run Rates

Chris Davis hit his 51st home run of the season last night. 20 years ago, that would have been a pretty big deal, but the years around the turn of the century reset the bar for newsworthy home run totals. After having only two 60 homer seasons in the first 100+ years of baseball, we saw six such seasons in four years. 50 homer seasons used to be the stepping stone to greatness; now, Davis is still 22 home runs away from the single season record.

As we know, though, the game as its being played today doesn’t look like the game that was being played 15 years ago. The strike zone is bigger, the players are smaller, and both runs and home runs are much harder to come by these days. Chris Davis might not set any real records, but hitting 51 home runs (and counting) in this offensive context is still an accomplishment worth celebrating.

But rather than just leave it at that, we can actually just look at Davis’ home run rate relative to 2013 norms, and then compare that to other 50 HR seasons to see how Davis’ HR rate stacks up throughout recent history. So let’s do just that. In the following table, you’ll see each player who has hit 50 home runs in the 50 years preceding this one, with Davis’ 2013 season inserted into the mix, giving us 28 different 50 HR seasons to look at. I’ve also listed the ratio of plate appearances to home runs, the league average PA/HR ratio for that season, and then an index metric I’ve called HR+, that is simply a player’s PA/HR ratio divided by the league PA/HR ratio. Think of it as wRC+, just without the park adjustments, and for dingers only.

Season Name PA HR PA/HR LgHR HR+
1998 Mark McGwire 681 70 9.7 37.2 382
2001 Barry Bonds 664 73 9.1 34.2 376
1965 Willie Mays 638 52 12.3 45.7 372
1990 Cecil Fielder 673 51 13.2 48.3 366
1998 Sammy Sosa 722 66 10.9 37.2 339
1996 Mark McGwire 548 52 10.5 35.7 338
1999 Mark McGwire 661 65 10.2 34.3 337
1977 George Foster 689 52 13.3 44.3 334
1997 Mark McGwire 657 58 11.3 37.8 334
2013 Chris Davis 625 51 12.3 39.4 321
2010 Jose Bautista 683 54 12.6 40.2 318
2002 Jim Thome 613 52 11.8 36.9 312
2001 Sammy Sosa 711 64 11.1 34.2 308
1995 Albert Belle 631 50 12.6 38.4 304
1999 Sammy Sosa 712 63 11.3 34.3 303
1997 Ken Griffey Jr 704 56 12.6 37.8 300
2007 Alex Rodriguez 708 54 13.1 38.1 290
2002 Alex Rodriguez 725 57 12.7 36.9 290
1998 Ken Griffey Jr 720 56 12.9 37.2 289
2006 Ryan Howard 704 58 12.1 34.9 287
2005 Andruw Jones 672 51 13.2 37.1 281
1998 Greg Vaughn 661 50 13.2 37.2 281
2007 Prince Fielder 681 50 13.6 38.1 279
2006 David Ortiz 686 54 12.7 34.9 274
2001 Luis Gonzalez 728 57 12.8 34.2 268
1996 Brady Anderson 687 50 13.7 35.7 259
2001 Alex Rodriguez 732 52 14.1 34.2 243
2000 Sammy Sosa 705 50 14.1 33.4 237

Not surprisingly, we see Bonds and McGwire at the top, but interestingly, look at how close Willie Mays was in 1965 to Bonds’ record 2001 season. While Bonds ended up with 21 home runs, a large part of that difference was just the league norms at the times in which they played. In fact, even Cecil Fielder‘s somewhat forgotten 51 homer season in 1990 was not very far off the mark of Bonds’ HR rate once you adjust for league averages in that season.

And look where Davis stands. There’s four Mark McGwire seasons ahead of him, plus the Bonds/Mays/Fielder group, plus George Foster‘s 1977 season, but Davis’ 2013 season stands ninth in normalized home run rate, well ahead of seasons with bigger HR totals. There’s no trophy for top 10 HR rate relative to league average over an arbitrary timeframe, but this is still an accomplishment worth noting.

But, while the last 50 years is a convenient timeframe for our leader boards, since they can display up to 50 seasons at one time, this window annoying excludes some of the more famous HR seasons in history. So, let’s see how the players in the previous 50 years to our sample did, giving us a range of 1914 to 1963. Prepare to laugh, or be amazed, or both.

Season Name PA HR PA/HR LgHR HR+
1920 Babe Ruth 615 54 11.4 150.1 1,318
1927 Babe Ruth 691 60 11.5 103.6 899
1921 Babe Ruth 693 59 11.7 101.9 867
1928 Babe Ruth 684 54 12.7 87.4 690
1932 Jimmie Foxx 701 58 12.1 71.1 588
1938 Hank Greenberg 681 58 11.7 64.6 550
1930 Hack Wilson 709 56 12.7 62.1 490
1938 Jimmie Foxx 685 50 13.7 64.6 471
1947 Johnny Mize 664 51 13.0 60.9 467
1947 Ralph Kiner 666 51 13.1 60.9 466
1949 Ralph Kiner 667 54 12.4 56.4 456
1961 Roger Maris 698 61 11.4 40.1 350
1961 Mickey Mantle 646 54 12.0 40.1 335
1956 Mickey Mantle 652 52 12.5 41.5 330
1955 Willie Mays 670 51 13.1 42.7 325

Babe Ruth only hit 50 home runs in a season four times, but three of the four times he did it, the league average PA/HR rate was over 100, meaning that an average player in those years would hit five to seven home runs per year. In 1920, when Ruth hit 54 home runs, that accounted for 8.5% of the entire league’s total. These numbers just destroy what we’ve seen in the last 50 years, because the game was entirely different back then, with only a few players hitting balls out of the ballpark on a regular basis. The home run giants of that era towered over their competition in a way that no one does anymore.

Interestingly, look at where Maris’ HR+ rate lies in comparison to Cecil Fielder‘s 1990 season. While there will always be some who attempt to proclaim Maris the “true HR champ”, since they prefer to invalidate all accomplishments during the “Steroids Era”, that argument is already along the path of adjusting for seasonal context. If we’re going to start down that path, might as well go all the way and acknowledge that Fielder’s 51 HR season was more impressive, given the difference in league average HR rates between 1961 and 1990. But, then, neither Fielder nor Maris can stack up to Ruth’s ridiculous accomplishments, given the norms of his day.

True home run champ? I’ll go with Barry Bonds, chemicals and all, given that he hit more home runs in a season than anyone else ever, and that’s really the answer to the question most people want to know. Most impressive HR hitter, relative to his own time? That’s Ruth, and it will be Ruth forever, barring some kind of weird changes to the rules involving pitchers throwing multiple balls at the hitter simultaneously.

Chris Davis isn’t in either of those conversations. And even with a huge barrage to end the year, he’s not going to end up in them. But, he’s playing in different environment than the one we saw 15 years ago, and what he’s accomplished is pretty remarkable. So kudos to Davis on his 51 homer (and counting) season, a feat that stands up pretty well against most of history’s best HR seasons.

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Dave is a co-founder of and contributes to the Wall Street Journal.

37 Responses to “Chris Davis and Normalized Home Run Rates”

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  1. Cody says:

    Brilliant work Dave! Now I just need to time travel to 1920, invent rotisserie baseball, set myself up with the first overall pick, and have the best rotisserie season of all time.

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  2. Gabriel says:

    I liked the contextualization. I’m not sure what the park factors would be in each case, but some of these parks are clearly more beneficial to home run hitters than others. What was Candlestick like back in 1965?

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  3. RedStalk says:

    So if I’m reading this correctly, that would mean Ruth’s worst season above (1928 in-context) would translate to roughly 119 or 120 HR in today’s environment?

    So Ridiculous…

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    • IZZY2112 says:

      No, it wouldn’t. Lg averages aren’t the best method to use for this study.

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      • RedStalk says:

        Forgive me, I worded that poorly.

        I meant not to say that’s how many Ruth would hit, but rather to see how out of place that season would seem. If you did take my meaning and take issue with the use of league average for this sort of comparison, what would you replace it with?

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  4. Steven says:

    Assuming Chris Davis gets 48 more PA, it looks like he needs 5 HR to catch Foster, 6 to catch Sosa and 12 to be the best in the last 50 years, whereas 0 HR would drop him down below Griffey’s 97.

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  5. Owen says:

    A slightly different way of going about it, but basically the same idea as this:

    Plenty interesting enough to read through twice though!

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  6. Mike Green says:

    Although Ruth did not hit 50 home runs in 1918 and 1919, it would be interesting for historical purposes to have those figures.

    Ruth’s role in the ending of the dead-ball era is an interesting topic. If Ruth’s HR+ in 1918 and 1919 was higher than, say, 500, it provides a piece of evidence that his role was more than as a trailblazer. There were changes to the game that happened independent of him- the death of Ray Chapman and the Black Sox scandal- but if there is a evidence that he was a greater home run hitter in his time prior to these events than anyone before or since, it would suggest that a significant part of it was just him.

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  7. robertobeers says:

    Is there a particular reason to use PA as opposed to AB?

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  8. Krevenoitch says:

    It’s the only way to determine the rate at which a player hits home runs.

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    • robertobeers says:

      I asked because it seems using AB or maybe PA-BB would be more representative of a player’s normalized HR-rate given the more correct HR opportunities.

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      • NeilS says:

        At a minimum, you have to remove IBB from the denominator – which probably pumps Bonds’ numbers up a bit. Bonds also has a bunch of gray-area PAs in there, but eliminating IBBs has gotta be done.

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  9. JayT says:

    For someone to hit 8.5% of the home runs in the league today, that would mean they would have somewhere around 419 home runs. It could happen!

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  10. AK7007 says:

    Awesome. I love these kind of analyses, and wish that more of the unwashed masses would start using normalized and contextual numbers. I don’t really care about the numbers unless I understand how they compare to other numbers. Baseball is amazing that you can do just this for so much of the game.

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  11. Ruki Motomiya says:

    I love how it’s almost comical how many HRs Ruth hit compared to his peers. How must it have been to see him when he first started mashing?

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  12. Patrick says:

    Interesting article but I wholeheartedly disagree with your conclusion.

    True homerun champ: Babe Ruth — and it is not even close.

    All of your data indicates this is true.

    Bonds best season? 6 guys bested it and Ruth did it four times. Of those four times Ruth’s worst was almost twice as good as Bonds’ best.

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    • Mister says:

      Why does Babe Ruth deserve credit for the fact that the other hitters in his era did not hit for power? It would be one thing if somehow we knew that the lack of HRs in that time was due to extremely good pitching, but we don’t know that. It seems much more likely to me that the other hitters surrounding Ruth in that time were a bunch of slap, contact hitters.

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      • rotowizard says:

        For the same reasons that some people consider Jim Brown to have the best statistical season ever at running back.

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        • Baltar says:

          Boy, I sure hate to say this, since I normally ridicule the “eye test,” but I have never seen anybody break tackles like Jim Brown, not even close.
          I am pleasantly surprised to read in your comment that statistical studies support my opinion that he was the best running back of all time.

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        • Mister says:

          I just think it’s really flawed to simplify it down to “whoever hits most home runs compared to his era is the best home run hitter.” We really don’t know that. When home runs are down, it could be due to the hitters, the pitchers, the umpires, the ballparks, or maybe some mix of all those things. But if it’s due in large part to the hitters, then that just means that Babe Ruth happened to play alongside a bunch of sucky HR hitters. I’m not saying that’s the case, necessarily, I’m just saying that we don’t know, and therefore shouldn’t confidently say that Ruth is the best HR hitter of all time.

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      • Patrick says:

        There are a number of reasons that homeruns are increased in the modern era.

        1) They are more consistent in the production of baseballs–ie they wind them tighter with more regularity. It has been documented that tighter balls travel further.
        This also goes for bats.

        2) Presumed lack of steroids in the 1920s. Bonds definitely juiced. Babe? Not likely.

        These are accounted for in Dave’s calculation of HR+ and I believe they are significant. I just can not account for his conclusion that is contrary to his statistics.

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        • Mister says:

          You know that tighter balls and more steroids likely increase home runs, but we have no way of knowing by how much. It’s impossible to do a controlled experiment here and only change one variable. I am certain that Chris Davis is facing better pitching today than Babe Ruth did, but it’s impossible to quantify the difference. So we shouldn’t just assume that “best relative to era” equals “best.”

          Personally, my opinion is that athletes in all fields have gotten much better over the last 100 years and will continue to do so. I’m not sure if Babe Ruth would crack a starting roster nowadays, and think someone like Davis might hit 80 home runs back in 1925. It’s impossible to prove either of those assertions, however.

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  13. Johnston says:

    Chris Davis deserves a lot of respect for hitting 50 honestly.

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  14. rotowizard says:

    Willie Mays is my hero

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  15. rotowizard says:

    Am I alone in thinking it’s funny that Andruw Jones once hit 51 HRs.

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  16. Drew says:

    I wonder if there were some better under-50 homer HR+ seasons in the 60s or 80s.

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    • MDL says:

      I was thinking of Mark McGwire’s 49-HR season in ’87 while reading the article. Mike Schmidt hit 48 in ’80. It would be interesting to see how these stack up.

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  17. Baltar says:

    I am surprised that Hank Aaron, my favorite player in my youth, does not appear anywhere in these lists. I know that his accomplishments were based partly on a long, consistently good playing career, but I would have thought his best season would appear somewhere.

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  18. DavidKB says:

    I like the idea here, but I don’t think it quite adjusts for the steroid thing (not that it overtly claims to do so completely!). Presumably some relatively small proportion of batters’ home runs were inflated chemically, but that would have a small effect on the league average and a large effect on those batters’ numbers.

    The underlying issue here is the comparison to the league average, which is an attractive but misleading benchmark. If the statistical distribution of home runs changes from year to year, the average will mean a completely different thing year to year. What you would have to do in order to get a consistent benchmark is to model a statistical distribution and determine how statistically rare a particular batter is compared to that distribution, not just to the average. By using the league average you are essentially taking this distribution, chopping at an arbitrary point (i.e. the threshold to the majors) and taking the average of what remains. The error introduced by that method, especially when the distribution is a sharp one (as it certainly is with home runs) will be huge. Of course this method would be a looooot more work, but as you say, if you want to go part of the way toward benchmarking, you may as well contemplate what a full solution would look like.

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  19. d_i says:

    So from 1920 (150.1 HR/PA) to 1921 (101.9 HR/PA) the HR rate increased by nearly a full third. That’s pretty drastic. Wonder why.

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