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This week’s question, 2002’s first, comes from Jesse Alson-Milkman:

Is there any pitcher in the history of the game who has had his strikeout
rate fluctuate as wildly as Mariano Rivera has? In 1996, Rivera
pitched 107 2/3 innings, striking out 130 men. By 1998, he’d dropped to a
low of 36 strikeouts in 61 1/3 innings. In 2001, though, he was back to 83
whiffs in 80 2/3 frames. What gives?

Thanks for the question, Jesse.

To put Jesse’s question in rate terms, Rivera fell from 10.9 strikeouts per
nine innings pitched (K/9) to 5.3 K/9, then rebounded to 9.3 K/9 this year.
That’s a drop of 5.6 K/9 followed by a rise of 4.0 K/9. In order to compare
Rivera’s swing to others, we’ll need to decide on a metric to evaluate the
changes.

One way we can do this is to take every pitcher, and look at every
combination of three seasons from his career (they need not be consecutive,
as with Rivera’s 1996, 1998, and 2001). We’ll look at the change in
strikeout rate between years 1 and 2 (10.9 – 5.3 = 5.6 decrease for Rivera),
then between years 2 and 3 (5.3 – 9.3 = 4.0 increase). Of course, we’ll want
to ensure that each comparison moves in the other direction (an increase and
a decrease, rather than 2 increases or 2 decreases).

We could measure the size of the "bounce" by the sum of the
magnitude of both changes (5.6 + 4.0 = 9.6 for Rivera). However, this
doesn’t distinguish between a huge change followed by a small one, and a
bounce that’s more "even" on both sides. For example, a drop from
10 K/9 to 3 K/9 and back to 5 K/9 would be a bounce of size 9 (that is, 7
for the first half + 2 for the second). The rebound is actually quite small.
A drop of 8 K/9 to 3.5 K/9 and back to 8 K/9 is still a bounce of size 9,
but with a change of 4.5 on either side.

I’m going to propose measuring the bounce by the size of the smaller change,
in order to distinguish between these two cases. It’s that both the increase
and decrease were large that caught Jesse’s attention, and prompted him to
ask the question. Thanks to Sean Lahman’s free database of baseball stats
www.baseball1.com) we can look at the biggest
"bounces" in strikeout rate. I’ve limited the search to pitchers
who threw at least 60 innings in each season of the triad (comparable to
Rivera’s 61 1/3 innings in 1998), and who pitched in with the modern
pitching distance of 60 feet, six inches (that is, since 1893). For each
pitcher, I’m using only their largest three-season fluctuation:

 Pitcher Year1 K/9 Year2 K/9 Year3 K/9 Diff12 Diff23 Size John Hiller 1968 5.5 1975 11.2 1979 5.2 5.67 -5.92 5.67 Bill Bailey 1908 3.6 1914 9.2 1921 2.4 5.64 -6.76 5.64 Lee Smith 1981 6.8 1989 12.3 1992 7.2 5.51 -5.11 5.11 Dennis Eckersley 1976 9.0 1983 3.9 1991 10.3 -5.10 6.37 5.10 Mike Scott 1981 3.6 1986 10.0 1990 5.3 6.44 -4.70 4.70 Bill Caudill 1979 10.4 1981 5.7 1982 10.5 -4.70 4.79 4.70 Ken Dayley 1982 4.3 1987 9.3 1989 4.8 4.99 -4.50 4.50 Dick Selma 1967 5.8 1970 10.3 1972 5.3 4.50 -4.95 4.50 Wes Stock 1962 4.7 1964 9.1 1965 4.7 4.44 -4.43 4.43 Gene Garber 1973 3.5 1976 9.0 1984 4.7 5.43 -4.31 4.31 Rich Gossage 1976 5.4 1977 10.2 1985 5.9 4.79 -4.29 4.29 Scott Garrelts 1986 6.5 1987 10.8 1989 5.5 4.28 -5.23 4.28 Dave Burba 1992 6.0 1994 10.2 1998 5.8 4.19 -4.37 4.19 Lindy McDaniel 1957 3.5 1960 8.1 1974 4.0 4.61 -4.16 4.16 Jim Perry 1962 3.4 1964 7.6 1973 2.9 4.16 -4.68 4.16 Jim Maloney 1961 5.4 1963 9.5 1969 5.2 4.09 -4.38 4.09 Curt Schilling 1992 5.9 1997 11.3 2000 7.2 5.45 -4.08 4.08 Wayne Twitchell 1974 5.8 1976 9.9 1978 5.5 4.07 -4.31 4.07 Dave LaRoche 1974 4.8 1975 10.3 1979 6.2 5.51 -4.07 4.07 Mariano Rivera 1995 6.9 1996 10.9 1998 5.3 4.06 -5.61 4.06 Claude Raymond 1965 7.4 1969 3.3 1970 7.4 -4.06 4.02 4.02 Brian Williams 1992 5.1 1995 9.4 1996 5.4 4.32 -4.02 4.02

There are a few things worth noting in the table above beyond the simple
ordering of seasons. First, the vast majority of the pitchers on the list
bounced "up." That is, the middle season is a spike to a much
higher strikeout rate. This is consistent with what we might expect from a
typical career path: increasing levels of performance, followed by a
decline. In fact, Rivera is one of only four pitchers who’s bounce went
"down," whose strikeout rate fell precipitously, then rebounded.
The others were Bill Caudill, Claude Raymond, and Dennis
Eckersley
. Eckersley is the only one of the four for whom any of the
seasons were as a starter.

Only one pre-1950 pitcher appears on the list, Bill Bailey, and
listing him could be considered cheating, as his peak season of 9.2 K/9 in
1914 came in the Federal League. It was also the only above average season
of his career (ERA+ of 109, according to
www.baseball-reference.com).

The increased strikeout levels of the past few decades have made it easier
to post a wider range of rates. Between 1893 and 1950, there were three
seasons of 60 or more innings pitched where a pitcher struck more than one
man per inning: Bailey in 1914, and Bob Feller in 1936 and ’37.
Since 1950, there have been close to 400 such seasons. Mike Scott,
Scott Garrelts, Jim Perry, Jim Maloney, and Curt
Schilling
are the only pitchers on the list who were primarily starters
in at least two of the seasons listed. It’s easier to post a fluky strikeout
rate in a smaller number of innings.

Getting back to Jesse’s original question, we see that Mariano Rivera’s big
fluctuation in strikeout rate isn’t the largest ever, but does rank in the
top 25 such bounces. The all-time champion is John Hiller, who struck
out 87 in 70 2/3 innings in 1975, surrounded by more modest strikeout rates.
Three other pitchers topped a fluctuation of at least 5 K/9 on each side,
including the aforementioned Bill Bailey, and two of the most dominant
closers ever, Lee Smith and Dennis Eckersley. Interestingly,
Smith’s was an up bounce, while Eck’s was down.

While Rivera doesn’t top the list, he does share the distinction of the
smallest interval for all three seasons in the bounce–four years–along
with Garrelts, Caudill, and Wes Stock. Lindy McDaniel has the
longest stretch on the list: 17 seasons, two more than Eckersley.

Keith Woolner is an author of Baseball Prospectus. You can contact him by
clicking here.

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