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In baseball, as in life, weird stuff happens. Sometimes, this stuff has an aptitude-based explanation; sometimes, it comes as the result of random variation; and most of the time, it's the combination of the two. Because most achievements have both factors behind them, we have an integral statistical concept: regression toward the mean.
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While regression to the mean confuses and misleads a lot of people, it's not all that complicated. In a nutshell, it's the idea that a player will tend to approach a certain level of performance. This affects everyone, but the extremes in particular: The really good players will generally play a little worse, while the really bad players will generally play a little better. It doesn't mean that they'll all play at the same level, or that the good and bad players will flip (which the law of averages might suggest). It permeates every aspect of the game, and one can hardly understate its impact.
We'll look at Phil Hughes as a case study. Sabermetrically-inclined folks have written a lot about him this year, and for good reason: Of the 855 batters whom he faced in 2014, he walked 16. The resulting 1.9% BB% led the majors easily (second-place Hisashi Iwakuma sat a comfortable 1.1 percentage points behind) and gave him the best strikeout-to-walk ratio of all time.
Was it a total fluke? Not really — Mike Podhorzer's expected walk rate equation puts it at 0.8%. So why does Steamer predict it'll rise to 4.3% last season? With seemingly little evidence to substantiate it, why should we think that Hughes will depreciate?
To answer that question, I looked to history. Hughes's 1.9% 2014 walk rate translates to a z-score of -2.45, meaning it was two standard deviations below the mean for qualified pitchers. TBF for pitchers goes back to 1916, so I examined the past 99 seasons. In that span, there were 7,354 pitcher seasons that qualified for the ERA title; of those, 82 (including Hughes) featured a walk rate z-score of -2 or lower.
Possessing a suitable list of comparisons for Hughes, I then looked to the following season for each pitcher, to see if he qualified, and if so, what their z-score was. I've put the results in an entirely-sortable table below:
| Name | Season | BB% | z_BB% | Next | nBB% | nz_BB% |
|---|---|---|---|---|---|---|
| Phil Hughes | 2014 | 1.9% | -2.45 | 2015 | N/A | N/A |
| Josh Tomlin | 2011 | 3.2% | -2.26 | 2012 | -- | -- |
| Dan Haren | 2011 | 3.5% | -2.08 | 2012 | 5.1% | -1.04 |
| Brandon McCarthy | 2011 | 3.6% | -2.02 | 2012 | -- | -- |
| Cliff Lee | 2010 | 2.1% | -3.26 | 2011 | 4.6% | -1.43 |
| Roy Halladay | 2010 | 3.0% | -2.72 | 2011 | 3.8% | -1.91 |
| Carl Pavano | 2010 | 4.1% | -2.06 | 2011 | 4.2% | -1.67 |
| Joel Pineiro | 2009 | 3.1% | -2.18 | 2010 | -- | -- |
| Paul Byrd | 2007 | 3.4% | -2.12 | 2008 | 4.5% | -1.37 |
| Greg Maddux | 2007 | 3.0% | -2.34 | 2008 | 3.7% | -1.74 |
| Carlos Silva | 2005 | 1.2% | -2.92 | 2006 | 4.0% | -1.62 |
| David Wells | 2005 | 2.7% | -2.13 | 2006 | -- | -- |
| Brad Radke | 2005 | 2.8% | -2.08 | 2006 | 4.6% | -1.32 |
| Brad Radke | 2004 | 2.9% | -2.14 | 2005 | 2.8% | -2.08 |
| David Wells | 2004 | 2.5% | -2.32 | 2005 | 2.7% | -2.13 |
| Jon Lieber | 2004 | 2.4% | -2.36 | 2005 | 4.5% | -1.19 |
| Roy Halladay | 2003 | 3.0% | -2.12 | 2004 | -- | -- |
| Brad Radke | 2003 | 3.2% | -2.02 | 2004 | 2.9% | -2.14 |
| David Wells | 2003 | 2.3% | -2.46 | 2004 | 2.5% | -2.32 |
| Rick Reed | 2002 | 3.3% | -2.24 | 2003 | -- | -- |
| Curt Schilling | 2002 | 3.2% | -2.29 | 2003 | 4.8% | -1.24 |
| Brad Radke | 2001 | 2.8% | -2.15 | 2002 | -- | -- |
| Greg Maddux | 2001 | 2.9% | -2.10 | 2002 | 5.5% | -1.08 |
| David Wells | 2000 | 3.2% | -2.20 | 2001 | -- | -- |
| Greg Maddux | 1999 | 3.9% | -2.08 | 2000 | 4.2% | -1.78 |
| Shane Reynolds | 1999 | 3.8% | -2.13 | 2000 | -- | -- |
| Gil Heredia | 1999 | 4.0% | -2.04 | 2000 | 7.7% | -0.32 |
| Brian Anderson | 1998 | 2.8% | -2.27 | 1999 | -- | -- |
| Greg Maddux | 1997 | 2.2% | -3.06 | 1998 | 4.6% | -1.44 |
| Rick Reed | 1997 | 3.8% | -2.17 | 1998 | 3.4% | -1.99 |
| John Burkett | 1997 | 3.6% | -2.28 | 1998 | 5.4% | -1.07 |
| Greg Maddux | 1996 | 2.9% | -2.37 | 1997 | 2.2% | -3.06 |
| Kevin Brown | 1996 | 3.6% | -2.05 | 1997 | 6.8% | -0.49 |
| Greg Maddux | 1995 | 2.9% | -2.72 | 1996 | 2.9% | -2.37 |
| Bret Saberhagen | 1994 | 1.9% | -2.53 | 1995 | 5.0% | -1.60 |
| Bob Tewksbury | 1993 | 2.2% | -2.92 | 1994 | 3.3% | -1.96 |
| Bob Tewksbury | 1992 | 2.2% | -2.57 | 1993 | 2.2% | -2.92 |
| Jimmy Key | 1989 | 3.1% | -2.26 | 1990 | -- | -- |
| Bill Long | 1987 | 4.0% | -2.30 | 1988 | 5.9% | -0.77 |
| Dennis Eckersley | 1985 | 2.9% | -2.21 | 1986 | 5.0% | -1.44 |
| La Marr Hoyt | 1985 | 2.4% | -2.45 | 1986 | -- | -- |
| La Marr Hoyt | 1983 | 3.0% | -2.45 | 1984 | 4.4% | -1.78 |
| Rick Honeycutt | 1981 | 3.3% | -2.16 | 1982 | 7.4% | -0.10 |
| Bob Forsch | 1980 | 3.8% | -2.09 | 1981 | 5.8% | -0.92 |
| Scott McGregor | 1979 | 3.3% | -2.30 | 1980 | 5.6% | -1.06 |
| Dave Rozema | 1977 | 3.8% | -2.18 | 1978 | 4.8% | -1.49 |
| Gary Nolan | 1976 | 2.8% | -2.38 | 1977 | -- | -- |
| Jim Kaat | 1976 | 3.5% | -2.02 | 1977 | -- | -- |
| Gary Nolan | 1975 | 3.4% | -2.16 | 1976 | 2.8% | -2.38 |
| Fergie Jenkins | 1974 | 3.5% | -2.21 | 1975 | 5.0% | -1.48 |
| Catfish Hunter | 1974 | 3.7% | -2.11 | 1975 | 6.4% | -0.87 |
| Fritz Peterson | 1970 | 3.8% | -2.05 | 1971 | 3.8% | -1.60 |
| Fritz Peterson | 1969 | 4.0% | -2.16 | 1970 | 3.8% | -2.05 |
| Lew Burdette | 1961 | 2.9% | -2.25 | 1962 | -- | -- |
| Robin Roberts | 1956 | 3.3% | -2.15 | 1957 | 4.2% | -1.61 |
| Robin Roberts | 1954 | 4.2% | -2.01 | 1955 | 4.2% | -1.62 |
| Fred Hutchinson | 1951 | 3.5% | -2.51 | 1952 | -- | -- |
| Ken Raffensberger | 1951 | 3.8% | -2.37 | 1952 | 4.5% | -1.84 |
| Ken Raffensberger | 1950 | 3.9% | -2.33 | 1951 | 3.8% | -2.37 |
| Preacher Roe | 1948 | 4.6% | -2.03 | 1949 | 5.2% | -1.58 |
| Schoolboy Rowe | 1947 | 5.3% | -2.10 | 1948 | -- | -- |
| Tiny Bonham | 1945 | 3.0% | -2.36 | 1946 | -- | -- |
| Ray Prim | 1945 | 3.5% | -2.12 | 1946 | -- | -- |
| Schoolboy Rowe | 1943 | 3.5% | -2.14 | 1944 | -- | -- |
| Tiny Bonham | 1942 | 2.8% | -2.40 | 1943 | 5.8% | -1.08 |
| Ted Lyons | 1942 | 3.6% | -2.06 | 1943 | -- | -- |
| Paul Derringer | 1940 | 4.0% | -2.01 | 1941 | 5.7% | -1.31 |
| Paul Derringer | 1939 | 2.8% | -2.28 | 1940 | 4.0% | -2.01 |
| Paul Derringer | 1936 | 3.5% | -2.09 | 1937 | 5.7% | -1.04 |
| Red Lucas | 1936 | 3.6% | -2.04 | 1937 | -- | -- |
| Red Lucas | 1933 | 2.0% | -2.60 | 1934 | 5.4% | -1.00 |
| Herb Pennock | 1930 | 3.0% | -2.29 | 1931 | 3.6% | -1.88 |
| Jack Russell | 1929 | 4.1% | -2.11 | 1930 | 5.2% | -1.12 |
| Herb Pennock | 1929 | 4.0% | -2.16 | 1930 | 3.0% | -2.29 |
| Pete Donohue | 1926 | 3.3% | -2.14 | 1927 | 3.8% | -1.80 |
| Pete Alexander | 1925 | 3.0% | -2.23 | 1926 | 3.8% | -1.89 |
| Pete Alexander | 1923 | 2.4% | -2.68 | 1924 | 3.5% | -1.90 |
| Babe Adams | 1922 | 2.1% | -2.42 | 1923 | -- | -- |
| Babe Adams | 1921 | 2.8% | -2.09 | 1922 | 2.1% | -2.42 |
| Babe Adams | 1920 | 1.7% | -2.63 | 1921 | 2.8% | -2.09 |
| Slim Sallee | 1919 | 2.2% | -2.24 | 1920 | -- | -- |
| Babe Adams | 1919 | 2.3% | -2.19 | 1920 | 1.7% | -2.63 |
| Slim Sallee | 1918 | 2.3% | -2.23 | 1919 | 2.2% | -2.24 |
The first thing to point out, obviously, is the fact that 57 of the 81 didn't qualify for the ERA title in the following year. This only proves the point that Jeff Zimmerman's exhaustive research has made: Pitchers get hurt*.
*On the other hand, the fact that "only" 29.6% of those pitchers broke down (compared to ~40% of the pitchers in the aforementioned study) could support another of Zimmerman's theories: Pitchers with good control generally stay healthier.
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For the 58 who did accrue enough innings, though, something becomes clear: They declined. No one did too horribly — everyone's z-score remained negative — and some of them even stayed elite — 16 posted another -2 standard deviation campaign. But on the whole, their performance dropped off, with the group's average z-score in the follow-up year (1.64) more than a half a standard deviation greater than the original year (-2.28). Further, 49 of them saw their z-score increase after their phenomenal year, so even the ones who sustained their dominance did so to a lesser extent.
Why did this happen? These pitchers didn't necessarily devolve as time went along in a true talent sense, they simply benefited from a little less good fortune. In order to post an all-time walk rate like this, everything has to break just right and things usually don't break perfectly forever, through no fault of anyone in particular. As they continued to throw to the best hitters in the world, they performed worse, and in so doing, their walk rate regressed toward the league average walk rate (z-score of zero) during the next season. In other words, this means you're likely to see something between Hughes' old walk rates and his 2014 mark in 2015 due to this shift toward the overall average that has nothing to do with his ability.
Unless he completely melts down, Hughes won't pitch terribly next year. And for what it's worth, if he had put up a 4.3% walk rate this year, that still would have come in at 1.22 standard deviations below average. But he has little to no chance of a repeat, and he shouldn't take the blame for that. The 2014 mark was amazing and performing worse than amazing isn't a deficiency. The universe works in a funny way sometimes; for Hughes, that might end poorly.
. . .
This article has been revised for clarification.
All data courtesy of FanGraphs and Baseball-Reference.
Ryan Romano is an editor for Beyond the Box Score. He also writes about the Orioles on Birds Watcher and on Camden Chat that one time. Follow him on Twitter at @triple_r_ if you enjoy angry tweets about Maryland sports.