Trading Bases on Twitter (MagicRatSF)


Add to Google


Game Theory: Studying the Bard or Throws by any Other Name . . .


Game Theory:  Shakespeare 101, Studying the Bard or (9 Dozen) Throws by any Other Name are Still Too Many 

 Thanks to stat heavy web sites like and the discussion forums at Sons of Sam Horn (which I believe pre-date the existence of FanGraphs and possibly even Boston Red Sox fans have a well-earned reputation as a knowledgeable, statistical-savvy lot.  (They have some other well-earned reputations as well, but in the aftermath of a gorgeous Patriot Day, let’s stay positive today.)  Yet, I’ll bet those attentive, well-studied fans would struggle filling in the blank in this sentence: 

Prior to his first stint as a starting pitcher a week ago today, Daniel Bard never threw more than ______ pitches in any of the first 192 MLB games he pitched in.

Any guesses Red Sox fans?

On May 13, 2009, in the very first game he appeared in, Daniel Bard threw 38 pitches.  Not only did he never throw that many pitches in a game again, except for a 36-pitch appearance last September – more than two years, and 183 games after his debut – he never threw more than 32 pitches in a single game.

*      *     *

One of the common complaints about baseball in the current day and age is that starting pitchers are treated with kid gloves.  Announcers, writers and former players who witnessed or participated in the game two generations ago regale us with stories of Burt Blyleven, Don Sutton, and Nolan Ryan, pitchers who regularly threw more than 260 (and occasionally more than 300) innings a year in the 1970s.  (Only one pitcher, Roy Halladay in 2003, threw more than 260 innings in one season in the last ten years.)  Implicit (or often explicit) in these stories is the theory that the modern pitcher lacks toughness, intestinal fortitude, etc. and that weakness is enabled by teams afraid to overwork the very arms in which they’ve invested millions of dollars.

There’s a problem with that premise however:  Starting pitchers as a whole get worse results after the fifth inning than average middle relievers. 

As with so many of the most valuable discoveries made by baseball researchers since Bill James gave birth to the sabermetrics-era, this assertion seems to run counter to widely-held assumptions.  It’s no wonder why.  As a fan, it’s always disconcerting to watch an ace pitcher get lifted after six or seven innings of work for a nondescript reliever, but surprisingly, it’s often the right thing to do, even if the ace is engaged in a pitcher’s duel.

I’ve taken a look at two different studies that have addressed this seemingly counterintuitive assertion.  The first, contained in The Book: Playing the Percentages in Baseball, by Tom Tango, et al covered the 1999-2002 seasons and the second, authored by Ken Funck at, updated the data for the 2006-2008 seasons.  What both studies found is that while there is a drop-off in starting pitching performance each successive time through the lineup, it’s particularly severe after the second time through the batting order.  Here’s the 2006-2008 data:

Time Through

     Lineup                      AVG/OBP/SLG

        1st                        .258/.319/.406

        2nd                       .266/.327/.421

        3rd                        .279/.339/.449

        4th                        .288/.352/.447

Avg Hitter 2006-08       .267/.335/.424

Once he faces hitters for the third time in a game, the collective major league starter is a below-average pitcher and by the fourth time through – which at an average of 4+ batters an inning usually occurs before the sixth inning ends – his performance drops to the level of a replacement-level reliever.  To be sure, I’m not saying the drop-off occurs with every pitcher, but before any manager, (or fan) decides that the drop-off couldn’t possibly apply to his staff’s ace, consider this warning from the financial industry.

John Bogle, founder of The Vanguard Group and generally acknowledged as the godfather of “index investing” likes to remind investors and analysts of the concept of “survivor bias”.  Bogle knows that due to the distribution of investor performance around the mean, the Vanguard S&P 500 Index Fund (by definition, the mean) will never finish atop its peer group over a one-, five-, or ten-year time period.  However, he takes pains to point out that over a five- or ten-year period, the Vanguard Fund will actually beat far more of its competitors than the rating agencies state when assigning the Fund a grade.  That’s because some poor performing funds in early years don’t exist for five or ten years, meaning the overall return of funds making it to ten years exclude a lot of poor performing ones, and therefore skew higher than the actual population of investors over that period.  That’s survivor bias.

Let’s apply that concept to starting pitchers.  Elite pitchers are much better than the average starter and the results above include all starting pitchers for the first trip through the batting order.  The second time through the line up excludes those pitchers who got knocked out in the first or second inning, or before the tenth batter was even faced.  That’s a group of pitchers that truly had an awful start, but it’s a small sample – only about 60 out of 10,000+ starters didn’t make it to the tenth batter over the three-year period.  However, by the time you get to the fourth time through the lineup – 28 batters into the game – only the best pitchers typically remain in the game.  Just over one-third of total starts resulted in a fourth trip through the batting order, and those starts are made by the most accomplished pitchers.  Again, that’s survivor bias.  So given that elite pitchers are even better than the average pitcher the first or second time through the lineup and that they make up almost the entire population of pitchers who get to face hitters for the fourth time in a game, the drop-off is even greater than the above table appears.

*      *     *

Through six innings yesterday, the Boston Red Sox and the Tampa Bay Rays were locked in a 0-0 contest.  In holding the Rays scoreless, Red Sox starter Daniel Bard, a converted reliever making just his second career start, had thrown 87 pitches and faced 24 batters, meaning he was two-thirds of the way through Tampa’s batting order for the third time.  In his previous 2012 start, in a much cooler weather environment incidentally, Bard had thrown 96 pitches and couldn’t get through the sixth inning.  Boston’s manager Bobby Valentine, aware of this and the fact that Bard had already walked four batters and hit another through six innings of work should have thanked Bard for a shutout performance, told him to get in the clubhouse and enjoy some Popeye’s and a Sam Adams, and turned to his bullpen the rest of the way.

Instead, Valentine sent Bard out to pitch the seventh.  For two batters, Valentine looked smart as Bard quickly got two outs – but the manager has to be aware that he is playing with fire at an extremely crucial point of the game.  Therefore, after Bard walked Sean Rodriguez with two outs brining Desmond Jennings up to the plate – to start Bard’s fourth trip through the Rays’ line up – Valentine has to go to the bullpen.  Instead, he allowed Bard in the game and Jennings singled.

This brought left-handed Carlos Pena to the plate to face the right-handed Bard, for the fourth time.  This piece is long enough so I won’t trot out more numbers but trust me, Pena is far better against right handed pitchers than lefties, let alone righties he is seeing for the fourth time in a game.  Valentine had two lefties in his bullpen, Justin Thomas and Franklin Morales, and Thomas was warming up.  To top it all, Bard had thrown 103 pitches at this point!  Inexplicably, Bobby V. left Bard in game and Bard, clearly laboring at this point, walked Pena on four pitches.

As I wrote on Twitter, “Grady Little just muttered to the TV screen, even I would have lifted Bard.”

At this point Bard now has to face the Rays best hitter, Evan Longoria, for the fourth time in the game, with the bases loaded of a scoreless game, having thrown 107 pitches on an unseasonably hot April afternoon.  Honestly, at this point, even though it never gets done anymore, Valentine should probably bring in his closer, but once again he did nothing.  Pitches 108-111 were balls, the Rays scored the only run of the game and Valentine, not Bard, should be the one credited with the loss.

Postscript:  After watching Bard throw balls on his last eight pitches and after squandering the platoon advantage against Pena, Valentine finally brought in left-handed Thomas who promptly retired Luke Scott to end the inning.  Red Sox fans and commentators have every right to question the competence of Bobby Valentine after his decision-making yesterday.

Mop Up Duty:

Joe Peta is the author of Trading Bases, the Newsletter, a companion piece to Trading Bases, A Story about Wall Street, Gambling, and Baseball*  (*) Not necessarily in that order, a Dutton Books/Penguin (U.S.A.) February, 2013 release.

If you have been forwarded this issue and would like to be placed on the mailing list, please send an e-mail to

All newsletter archives are located at

You can follow me on Twitter here:  @MagicRatSF

I will be updating progress on the path to publication on Facebook as well where I can be found here:!/profile.php?id=1761681056

If you want to be taken off the e-mail list, please let me know at

PrintView Printer Friendly Version

EmailEmail Article to Friend

Reader Comments

There are no comments for this journal entry. To create a new comment, use the form below.

PostPost a New Comment

Enter your information below to add a new comment.

My response is on my own website »
Author Email (optional):
Author URL (optional):
Some HTML allowed: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <code> <em> <i> <strike> <strong>
« Game Theory: Lee vs. Cain - For Fans, a San Francisco Treat | Main | Game Theory: WWJD, or What Was Joe (Girardi) Doing? »