Linear Saves

by Keith Glab,
January 28, 2008

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I have often wondered how to evaluate the relievers of today versus the relievers of the 1970s and early 1980s, who often had to pitch two or more innings to earn their saves and were often used in important non-save situations.  Or among today's closers, how would I reconcile Billy Wagner's dominant ERA with Trevor Hoffman's dominant save totals?  And how can I justly compare a dominant reliever with a short career to a steady but unspectacular reliever?  These questions have just become easier to answer with the invention of Linear Saves.

Similarly to how Linear Weights for batters places coefficients on different batter events, Linear Saves gives a weight to a single event for closers: the blown save.  Like with the Linear Weights used to calculate Batting Runs, I do not arrive at these coefficients arbitrarily.  I weigh each pitcher's blown save by the league's save percentage for that year.  More precisely, Linear Saves are a pitchers saves minus his opportunities multiplied by the league's save percentage:

LSV= SV-(Opps*LgSV%)

The result shows how many saves above or below a league average closer that a particular pitcher recorded in a season.  For example, Kazuhiro Sasaki saved 37 games in 40 chances in the year 2000.  The average major league pitcher with 10 or more saves that year converted 82.9% of their save chances.  So an average pitcher in 2000 would have saved 33.2 games in 40 opportunities, meaning that Sasaki saved 3.8 more games than the average closer would have with the same opportunity.

This doesn't account for differences in save difficulty.  In a given season, one closer might be used to protect predominately three run leads while another appears in more precarious save situations.  Fortunately for Linear Saves, but unfortunately for baseball, modern managers don't get too creative when it comes to closer usage, so the game situation distribution for closers probably isn't as disparate as it could be.

A couple of notes on the methodology.  I use 10 saves as my baseline for what a closer is to weed out the save percentages of middle relievers.  A pitcher who enters a game in the seventh inning and allows one run over two frames can earn a blown save, but not a save.  There is no way anyone can earn a save without pitching the final out of a game.  So if a manager regularly brings in a middle reliever with no intention of letting him finish the game, he can rack up some save opportunities, but he will not pile on the saves.  Adding those pseudo-opportunities would taint my calculation of how effective the average closer is in a given season.   

10 is not a perfect number.  Using that as my baseline, I miss Bobby Jenks' 2005 season, in which both of his blown saves came after he assumed closer duties from the ailing Dustin Hermanson.  I catch Paul Assenmacher's 1990 season, in which most of his 10 blown saves occurred before he assumed closer duties from the flailing Mitch Williams.  No number is going to perfectly filter out all the seasons we don't want to consider while keeping all legitimate closer data.  Only considering double-digit save seasons made it much easier for me to compile data, and 10 is probably as good as any other number in the long run. 

Why do I consider the National and American Leagues together?  Several reasons, the most important being sample size. Generally, only 20-40 players per year amass 10 or more saves.  Were we to cut that number in half, our league save percentages would be artificially volatile.  Also, the differences between leagues from 1969 on aren't extreme for closers, despite the designated hitter rule.  Consider that Trevor Hoffman, a career National Leaguer, has only thrown to 23 pitchers throughout his big league career.  That comes to 0.6% of his total batters faced, and you can bet that most of that 0.6% did not occur in save situations.  Finally, as with my double-digit rule, lumping both leagues together made the data compilation much easier.

So here are the save percentages for every year from 1969, when the save statistic was first officially kept, through the present day.  I've also included the leader in Linear Saves for each season:

Year SV% LSV Leader Year SV% LSV Leader
1969 75.0% Ken Tatum - 4.8 1989 80.4% Mark Davis - 5.4
1970 76.6% Wayne Granger - 5.1 1990 80.2% Dennis Eckersley - 7.9
1971 79.7% Ken Sanders - 3.1 1991 80.8% Lee Smith - 4.2
1972 81.8% Clay Carroll - 4.1 1992 81.6% Dennis Eckersley - 6.9
1973 79.0% John Hiller - 4.8 1993 83.5% Rod Beck - 4.6
1974 68.5% Dale Murray - 3.2 1994 80.4% Rod Beck - 5.5
1975 74.9% Rawly Eastwick - 3.3 1995 82.7% Jose Mesa - 6.3
1976 72.7% Dave LaRoche - 3.6 1996 83.6% John Wetteland - 3.7
1977 75.3% Lerrin LaGrow - 3.9 1997 82.7% Randy Myers - 7.0
1978 74.4% Doug Bair - 3.4 1998 83.7% Trevor Hoffman - 7.8
1979 75.8% Kent Tekulve - 3.0 1999 86.0% Mariano Rivera - 4.8
1980 76.5% Dan Quisenberry - 5.5 2000 82.9% Antonio Alfonseca - 4.4
1981 79.5% Don Aase - 2.3 2001 84.9% Billy Wagner - 4.2
1982 75.0% Lee Smith - 3.5 2002 85.2% John Smoltz - 4.7
1983 75.9% Ron Davis - 5.0 2003 83.7% Eric Gagne - 9.0
1984 77.1% Willie Hernandez - 6.6 2004 86.1% Eric Gagne - 4.5
1985 76.3% Jeff Lahti -  3.7 2005 87.3% Trevor Hoffman - 2.8
1986 75.3% Dave Righetti - 3.8 2006 84.3% Francisco Rodriguez - 4.0
1987 75.6% Steve Bedrosian - 3.7     Joe Nathan - 4.0
1988 79.2% John Franco - 5.7 2007 85.2% J.J. Putz - 4.2

Okay, there's lots of good info here.  First of all, comparing straight save percentage of a modern closer to a 1970's closer illustrates nothing.  You're better off comparing a modern slugging percentage to that of a 1970's player.  This is the very reason we need a metric such as Linear Saves. 

To make complete sense of this table, you must realize that the saves rule from 1969 to 1973 was different than the saves rule in 1974, and both varied from the rule from 1975 to present day.  This is why we see definitive eras for save percentage: 1969-1970, 1971-1973, 1974, 1975-1987, and 1988-2007, with efficiency steadily increasing in that last span.  I know Tony LaRussa, Dave Duncan, and Dennis Eckersley are typically credited with revolutionizing modern one-inning closer usage, but I was astonished to see such a clear cut gap in save percentage between 1987 and 1988.  General suppression of runs scored in '88 versus '87 probably played a big role in that distinction.  I do not have an explanation for the extreme differences between 1969-1970 and 1971-1973.

Only Eckersley, Lee Smith, Rod Beck, Trevor Hoffman, and Eric Gagne have led the majors in Linear Saves more than once, and no pitcher has done so more than twice.  No real point here, I just find that interesting.

Here's something important, however.  There are generally higher totals for the Linear Saves leaders from 1988-2007 than from 1969-1987.  This saddens me, as part of what I was going for was equalization across the eras.  Apparently, the sheer bulk of saves in the modern era does outweigh the lower benchmark for excellence in the earlier era  for the purposes of Linear Saves.  Also, in modern years, I'm catching more pretender closers with my base level of 10 saves than in the earlier eras, artificially lowering the league saves percentage.  Perhaps it would make more sense to only look at seasons of greater than 15 saves from 1988 on.

This does not explain the absence of Hall of Famers Rollie Fingers, Bruce Sutter, and Goose Gossage from this list, however.  If this trio was really dominant in the 70's and early 80's, we should still see them lead the majors once in a while, right?  Well to be fair, Sutter finished tops in the NL in '84 with 4.9 LSV, Fingers led the AL in '82 with a relatively lowly 2.8 LSV, and Gossage topped the AL with the same 2.8 figure in '75, plus finished second in the junior circuit in three consecutive seasons (1979-1981). 

Still, an examination of career totals are in order.  The next page contains the career Linear Saves leaders for all 35 pitchers with over 200 saves, as well as a half dozen additional significant relievers.  Note: I've provided both raw career totals (Raw LSV) and the totals for only seasons with 10 or more saves (LSV10).  I believe LSV10 to be more illustrative - why should Robb Nen benefit from working as a closer for his entire career and Jeff Shaw get penalized for pitching five seasons as a setup man?  

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Disagree with something? Got something to add? Wanna bring up something totally new? Keith resides in Chicago, Illinois and can be reached at