Adam Dunn is the prototypical Three True Outcomes hitter, someone who earns his keep by getting on base and jacking home runs. His fielding makes Pat Burrell-relegated to DH duty-resemble a Fielding Bible award-winner, and while he may have swiped 19 bags in the 2002 season, few, if any, regard Dunn as a baserunning asset these days. Dunn gets paid to rake, and his astute yard work has resulted in 40 or more home runs in each of the last five seasons. It may initially sound odd, but only five players who debuted in or after the 1954 season have been able to accomplish the same feat: Dunn, Ken Griffey Jr., Alex Rodriguez, Sammy Sosa, and Barry Bonds. That’s four of the greatest home-run hitters of all time, and Dunn, a guy lampooned for the non-hitting aspects of his game to the point that one might think he starred in Dorf Goes Fielding. Sosa and Rodriguez extended their feats all the way into a sixth season. The table below shows pertinent home run data for the group:

Player             Years    HRs   Average   StDev
Adam Dunn         2004-08   206     41.2     2.40
Ken Griffey Jr    1996-00   249     49.8     5.95
Alex Rodriguez    1999-03   239     47.8     6.05
Alex Rodriguez    1998-02   234     46.8     6.49
Sammy Sosa        1998-02   292     58.4     7.34
Sammy Sosa        1999-03   266     53.2     9.11
Barry Bonds       2000-04   258     51.6    10.80

Beyond their homer totals and the per-season average, that final column displays the standard deviations of home runs throughout these five-year spans. Standard deviations measure data dispersion, essentially quantifying consistency in a data set. Lower standard deviations indicate that the data set boasted minimal range, hovering close to the mean. Dunn has run laps around his colleagues, meaning that not only has he launched an abundance of dingers over the last half-decade but the raw totals have come close to being replicated each year. In fact, they are identical for the most part. Dunn smashed 46 homers in the 2004 season, and has hit exactly 40 in each of the last four seasons. He has taken to a new level the scouting assessment of “having 40-homer power.”

How rare is this? Obviously it is incredibly rare for someone to produce so many home runs in a short span, but a standard deviation of zero reeks of rarity. Producing identical home-run season twins is not much of a relative feat, but the highest total for these perpetrating players belongs to the aforementioned Junior Griffey, who hit precisely 56 home runs in both 1997 and 1998. A few steps behind him in line stands Barry Bonds, whose 45 home runs in both 2003 and 2004 ranks second. Following these two greats are Alex Rodriguez at 42 dingers in 1998-99, and Jason Giambi‘s 41 long balls in 2002-03. In total, 279 identical-total seasonal pairs were returned involving at least ten home runs. When we move to triplets, the list of examples with at least ten jimmy-jacks is vastly reduced as just 18 seasonal triumvirates surfaced.

So, when viewing the table below, keep in mind that the repeating of players usually signifies that the stretch extended beyond a third season:

Player             Years   HR/YR
Adam Dunn         2005-07    40
Adam Dunn         2006-08    40
Mike Schmidt      1975-77    38
Dale Murphy       1982-84    36
Ken Boyer         1961-63    24
Ken Boyer         1962-64    24
Fred Lynn         1984-86    23
Fred Lynn         1985-87    23
Lloyd Moseby      1983-85    18

Moving on to quadruplets of seasons with identical homer tallies, our list grows even smaller, with just Dunn, Boyer, and Lynn doing so while surpassing the ten-homer plateau. The next-closest total was a meager five home runs per season off the bat of pinch-hitter extraordinaire John Vander Wal (1993-96). Of all the players who made their major league debut in or after 1954, only Dunn, Boyer, and Lynn have produced a home-run standard deviation of zero over a four-year stretch while hitting a noteworthy number of bombs.

Posting identical raw tallies is incredibly difficult, though, so what happens when we adjust our methodology to investigate the lowest standard deviations across five-year spans? To start, I extracted the sum, average, and standard deviation for every five-year span for every player since 1954; for instance, Hank Aaron from 1956-60, 1957-61, 1958-62, and so forth, repeated for each player. Those with fewer than 50 home runs in the span were deleted. (Sorry, but I do not consider Rey OrdoƱez‘s low standard deviation with one or fewer home runs in five straight years to be interesting in any way, shape, or form.) Plus, most of us are going to be curious about the lowest deviations amongst high-summed stretches, instead of those akin to Eddie Taubensee‘s bouncing around eight to 12 home runs between 1994 and 1998.

Intriguingly, Adam Dunn’s 2004-08 standard deviation of 2.40 sat fairly distant from the top of the heap. The leaderboard was heavily comprised of player repeats with overlapping spans, so for the sake of producing a table with more than three recycled names I took the lowest deviation for each of the overlaps. Below are the sub-2.00 standard deviation spans amongst those with an average equal to, or greater than, 20 home runs per season:

Player             Years  Average   StDev
Fred Lynn         1983-87   22.8    0.40
Cal Ripken Jr.    1983-87   26.4    0.80
Paul O'Neill      1993-97   20.6    1.02
Reggie Smith      1972-76   20.4    1.74
Lee Stevens       1997-01   22.4    1.85
Kirk Gibson       1984-88   26.6    1.85
Edgar Martinez    1995-99   27.2    1.94
Jose Valentin     2000-04   27.2    1.94

In some ways, Lynn was a model of consistency throughout his career, putting up home-run totals between 1982 and 1988 of 21, 22, 23, 23, 23, 23, and 25. In at least one way, he would have been a projection system’s dream. In contrast, here are the lowest standard deviations for those with an average of 30+ home runs per season:

Player             Years    Average   StDev
Frank Thomas      1993-97     38.8     2.14
Carlos Lee        2003-07     32.6     2.24
Ron Santo         1964-68     30.0     2.28
Mike Schmidt      1982-86     36.2     2.32
Billy Williams    1964-68     30.8     2.32
Adam Dunn         2004-08     41.2     2.40

Thomas mashed 41, 38, 40, 40, and 35 home runs in his good run, barely edging out the 31, 31, 32, 37, 32 of Carlos Lee. Lee got a bit selfish in the 2006 season and hurt his consistency level in the process.

If the average filter is again raised to 40 home runs per season, only two stretches resulted in a standard deviation below 3.00: Dunn’s 2.40 from 2004-08, and Rafael Palmeiro‘s 2.99 from 1998-2002. Making matters even more comical is the fact that Dunn currently has 22 home runs to his name, essentially right on pace for 40 or 41 by the end of the year, meaning that Dunn could very well put up a fifth consecutive season of exactly 40 home runs. Only three players since 1954 have accomplished such a feat, and they-Nellie Fox (1959-63), Dave Hansen (2001-05) and Ed Romero (1980-84)-maxed out at two home runs per season. Adam Dunn may experience fluctuations in a few other areas, but if you want precision, betting on 40 home runs in a season from him is a pretty solid move.

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What a fun article! Well done! When you get a chance, it'd interesting to see how rare Eric Gagne's IP string was. Woody
Gagne is the only person since 1954 to have 3 straight seasons with identical IP tallies, at 82.1.
Shouldn't there be some kind of weighting of the standard deviation? For instance, a standard deviation of 2 for a 20 home run guy is less impressive than a standard deviation of 3 for a 40 home run guy, right? I think I've seen a stat that takes this into account, but I don't know it's formal name. Intuitively, it makes sense -- as you increase the raw numbers, you are likely to get a greater standard deviation because you have increased output.
If this were intended to be hardcore analysis or groundbreaking research, yes, but really the Statman's Notebook is just a column designed to have some fun with numbers. Filtering it to different constraints works for me though your proposal certainly works in a different setting. Like I'm not saying Lynn's SD is more impressive than Thomas's... I treated them as separate.
So this column should be re-titled "Rudimentary-Statman Notebook," is that what you're saying? Not exactly what I pay my money to BP for....
Sheesh. Get over yourself.
your comments are not what I pay for. Go away.
Oh Noes! Eric didn't triple-run a Fildergraad Regression Analysis! I'm jumping ship!
The coefficient of variation, CV, is a common one you may have seen. CV = standard deviation / mean, so a s.d. of 2 on a mean of 20 has a .1 CV, while the s.d. of 3 with a mean of 40 has a CV of .075.
Thanks Mountainhawk. That's what I was thinking about, and it seems entirely appropriate here.
Hmm, that would certainly work. Will plug it in when I get home and see what comes up.
Okay, here we go... of guys with an average of at least 20 HR/season in the five year span, here are the lowest coefficients of variation: 1) Fred Lynn (1983-87): 0.02 2) Cal Ripken Jr (1983-87): 0.03 3) Paul O'Neill (1993-97): 0.05 4) Adam Dunn (2004-08): 0.06 5) Mike Schmidt (1982-86): 0.06 6) Frank Thomas (1993-97): 0.06
Thanks, and sorry for my snark above.
No problem... CV is a really good stat to employ in something like this, I just chose to filter it off to incluide different plateaus.
Cool. A Run, Lola, Run and a Dorf reference in the same bit.
Ryan Howard is on pace for 193 strikeouts after back to back seasons of 199.
If he gets to 199, then we'll talk.
Although Vinny Castilla only had two (exactly) 40-homer seasons back-to-back, in those two seasons he had 40 HR's, .304 BA, and 113 RBI (he slugged .548 in '96 and .547 the next year).

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