Linear Saves

by Keith Glab,
January 28, 2007

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Before I delve into the significance of relievers as compared to other position players, let me re-visit the question of Billy Wagner versus Trevor Hoffman.

A reliever has ended a season with 5.0 or more Linear Saves only 14 times in the past 40 years.  Billy Wagner is four years younger than Trevor Hoffman.  To eclipse the all-time saves leader in LSV10, Wagner will need to match Hoffman until he retires, then average more than 3.6 LSV10 for the extraneous four seasons.  To match him in Raw LSV, Wagner will need to match Hoffman, then average over 5.2 Raw LSV for those extra four seasons.  Looking at Raw LSV makes some sense for these two, as Wagner's historically bad mark of -6.4 LSV in the year 2000 was not the result of middle relief usage; Wagner was the Astros' closer and blew nine of 15 save opportunities due in part to an injury.  It doesn't make sense to throw that season away when analyzing Wagner's effectiveness as a closer.

Which is more likely, for Wagner to approach Hoffman in either of those Linear Saves categories or for Wagner to suffer a decline in his later years, causing his ERA+ to approach Hoffman's?  I had always contended that before I put Trevor Hoffman on my Top 200 List, he would need to clearly separate himself from Wagner.  Hoffman's complete dominance in all-time save efficiency may give him that separation.  Yes, Hoffman has rarely been asked to retire more than three batters to get a save, but no less frequently than Wagner has.  

If an active player does surpass Hoffman, it will likely be Eric Gagne, who turned 32 this month.  Gagne has the highest single-season LSV total (9.0), the highest two-year total (13.5), and the highest three-year total (17.8), amassing that final figure over three consecutive seasons, 2002-2004.  I understand that Gagne was chemically enhanced those seasons and has been punished with the durability of a pixie stick in the years since.  I noticed his disastrous stint with the Red Sox last year.  I'm not saying I would bet on Gagne.  But no relief pitcher in the history of the game has the upside that Gagne has, and the Brewers did well to risk $10-$11 million to see whether Gagne could be that guy once again.

Oh that Keith, he's over-valuing relievers again, isn't he?  Well, think about it.  Remember, each positive Linear Save represents one save that a league-average closer would not have been able to nail down in the same number of opportunities.  So each Linear Save is worth roughly one win to a team.

I say roughly because not every blown save is a guaranteed loss for the team.  Particularly in the case of old school relievers, when they might blow a save before the ninth, then pitch two scoreless innings to lead their team back to a victory.  As a counterbalance, the entire worth of a closer is not measured in how he performs in save opportunities.  What a reliever does when he enters a tie game or with his team down by one is worth at least as much as a save with a two-run lead.  Again, old school relievers have more value outside their save totals, which again provides an equalizing counterbalance.  I would venture to say that every reliever is worth slightly more "wins" than his Linear Saves totals, with pre-1988 relievers worth moderately more than those totals.                             

Here are those 14 seasons of at least 5.0 Linear Saves, along with that year's leader in Batting Wins and Pitcher Wins, as derived from Batting Runs and Pitching Runs:

Year LSV >5 BW Leader PW Leader
1970 Wayne Granger 5.1 Carl Yaztremski 6.8 Bob Gibson 4.5
1980 Dan Quisenberry 5.5 George Brett 6.3 Steve Carlton 5.2
1983 Ron Davis 5.1 Boggs/Murray 4.6 Jesse Orosco 5.2
1984 Willie Hernandez 6.6 Eddie Murray 4.9 Bruce Sutter 4.3
1988 John Franco 5.7 Wade Boggs 6.4 Frank Viola 4.7
1989 Mark Davis 5.4 Kevin Mitchell 6.7 Brett Saberhagen 5.3
1990 Dennis Eckersley 7.9 Rickey Henderson 6.1 Roger Clemens 6.2
1992 Dennis Eckersley 6.9 Barry Bonds 7.6 Greg Maddux 6.0
1994 Rod Beck 5.5 Frank Thomas 6.6 Maddux 6.8
1995 Jose Mesa 6.3 Edgar Martinez 6.7 Maddux 6.4
1997 Randy Myers 7.0 Larry Walker 6.6 Clemens 7.9
1998 Hoffman 7.8 Tom Gordon 6.7 Mark McGwire 8.9 Maddux 6.4
2003 Eric Gagne 9.0 Barry Bonds 8.3 Esteban Loaiza 5.6

Again, none of these measures is a perfect measure of win value, but it's pretty evident that the best reliever seasons of all time do match up well with the top starter and hitting performances during the same year.  At the very least, I feel better about the Willie Hernandez and Dennis Eckersley MVP selections than I did before developing this metric. (When Eckersley won the 1992 AL MVP, Frank Thomas led the AL with 6.5 Batting Wins and Clemens led hurlers with 5.3 Pitcher Wins).  A dominant performance from a closer can boost a team as much as anything else can.

This doesn't mean that individual closer seasons are always evaluated correctly.  Poor Cy Young Award choices include Mike Marshall 1974 (-1.6), Sparky Lyle 1977 (0.4), Bruce Sutter 1979 (1.4), and Rollie Fingers 1981 (1.0).  Dennis Eckersley's 1990 season and Trevor Hoffman's 1998 season at the very least merited more consideration for the Cy Young Award than the 5th place finish they each received.

In examining career totals, closers do not fare nearly so well.  Trevor Hoffman's total of 32.1 LSV10 would just miss ranking in the top 100 of Batting Wins seasons and ranks 35th among Pitcher Wins.  Lee Smith's second place total of 24.4 would rank 65th among pitchers, were both metrics a completely accurate assessment of win value.  Indeed, it is extremely rare for a closer to sustain success over an entire career.  While the Yankees and Padres should be applauded for their retention of Mariano Rivera and Trevor Hoffman, I scratch my head at the fact that Lee Arthur Smith toiled for eight different franchises in his big league career.

Relievers are a double-edged sword.  It's relatively common for one to dominate in a given season, but quite rare to find one that can perform consistently over an extended period.  Therefore, even though individual closer seasons have made more of an impact on Major League Baseball than any one closer's career has, the scarcity of a consistent relief performer makes him far more valuable than a flash-in-the-pan closer.

As far as Linear Saves go, they are far from a perfect statistic, but work much better in conjunction with ERA+ and longevity to determine a reliever's worth than saves or save percentage alone do.  I'd like to think that there's a way to incorporate innings per relief appearance that would treat multi-inning closers a little more fairly, but haven't brainstormed anything as of yet.

I hope this is only the beginning.  I plan to sift through game logs from 1957-1968 to expand my database of Linear Saves.  Feel free to download the Excel spreadsheet and play around with it yourself.  Want to use a baseline of 15 saves to identify a closer rather than 10?  Think I should use three-year save percentage averages rather than a single year in determining yearly LSV?  Want to compare relievers not to the average closer, but to some concept of a replacement level reliever? Go for it, and please send any interesting research and findings to the email address below.  I'm particularly interested in hearing from those who knew who Ron Davis was before reading this article, because there's a good chance that you're more knowledgeable about baseball than I am.       

Special thanks to Baseball Musings, The Hardball Times,, The 2005 ESPN Baseball Encyclopedia, and for assistance in compiling the data used in this article.

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