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Game Theory: Baker Cooks up a Mess


Game Theory: Baker Cooks up a Mess

There’s an expression in sabermetric circles that sums up a starting pitcher’s erosion in effectiveness the longer he stays in the game:  “A team’s worst pitcher is the one who is facing an opposing team’s lineup for the third time.”  Unlike some adages this one isn’t exactly true.  For one, while he’s a rare exception, Justin Verlander actually does have better results as the game goes on.  Even tossing outliers like Verlander aside, the statement itself is a bit of overkill.  A team’s ace becomes something like a league-average pitcher the third time through the lineup, the second best pitcher is something like a #4 starter, and so on.

However, the premise that a pitcher declines in effectiveness as the game progresses is unmistakable.  Whether it has to do with pitch count or seeing the same batters multiple times is a chicken-or-egg type question but the effect is real as shown below (2012 data):

                                                BA/OBP/SLG             K Rate

Average MLB pitcher             .255/.319/.405             19.8%

3rd Time through Lineup         .272/.330/.444             16.8%

While I suggested the adage at the beginning of this piece is a bit of an overstatement, it’s important to note that there is another factor which actually understates the decline in effectiveness.  In the financial industry, “survivor bias” refers to the fact that the worst performing money managers don’t stay in business long enough to accumulate a five-year track record so those that do appear to beat the market as a whole.  The same thing applies to pitchers facing hitters for a third time, typically in the sixth or seventh innings.  Managers tend to only let their best starters pitch that deeply into a game, so it’s fair to assume the actual drop-off in effectiveness is slightly greater than shown above because many weak pitchers are removed from the game before their drop-offs are recorded.

Let’s stick a pin in that concept and we’ll come back to it in a few paragraphs.

On Monday night, Cincinnati’s Bronson Arroyo was locked in a pitcher’s duel with Cliff Lee of the Phillies.  During the bottom of the 7th inning the Reds scratched out 2 runs giving Arroyo a 2-0 lead entering the top of the 8th.  Before we get to what transpired in the 8th inning, let’s take a look at exactly what kind of pitcher Bronson Arroyo is.  This is important because for a manager to make optimal strategic decisions, he must know the strengths and weaknesses of his personnel.

Let’s start with some trivia:  No Major League pitcher has made more starts since 2004 than Bronson Arroyo.  His 297 starts are 2 more than Mark Buehrle, 7 more than CC Sabathia and Derek Lowe, and so on.  In other words, there are no sample size issues when looking at Arroyo’s career results.

                                                BA/OBP/SLG             K Rate

Arroyo vs. all batters               .264/.320/.436             15.3%

Note that Arroyo, over his entire career, has been slightly worse than the average 2012 pitcher (see above).  Now, he’s played primarily in hitter’s ballparks (Fenway and Great American) and MLB scoring from the period 2004-2012 was notably higher than in 2012.  So it’s a fair assessment to upgrade Arroyo to an average MLB pitcher.  (Make no mistake, that’s not a slap at Arroyo; an average pitcher who eats innings to the tune of 200+ every year has value.)

Arroyo is right-handed.  Here’s the average MLB right-handed pitcher vs. left-handed batters in 2012 and the difference between his results against all batters (shown above):

                                              BA/OBP/SLG             K Rate 

Avg RHP vs. LHB                 .260/.332/.416             19.0%

Difference vs. all batters         +5/+13/+11            -0.8%


Here’s Arroyo splits vs. left-handed batters in his career:

                                               BA/OBP/SLG             K Rate

Arroyo vs. LHB                       .289/.346/.485             11.1%

Difference vs. all batters          +25/+26/+49             -4.2%

This is enormously revealing: Arroyo, an average pitcher overall, is a far below-average pitcher when facing left-handed hitters.  His notably low strikeout rate becomes close to league-worse when facing those lefties.  In other words, while he’s average overall, Arroyo’s off-speed effectiveness as a pitcher works very well against right-handed batters but is awful versus left-handers.  To put that career ineffectiveness against left-handers in context, his .289/.346/.485 splits versus lefties is nearly identical to the 2012 Rockies pitching staff (.290/.357/.470) which gave up 870 runs, by far the most in baseball last year.

Now, turn back to the data that led off this column.  If Arroyo is equivalent to the MLB’s worst staff against all left-handers he’s faced, once he’s deep into a game, it has to be materially worse.

Armed with this knowledge, you’d have to conclude that sending Bronson Arroyo to the mound to protect a 2-run lead in the 8th inning is foolish.  Further, by far the worst situation his team could be in is to have Arroyo facing left-handed batters late in the game.  In fact, working off a modification of the adage at the top of these pages, I think it’s fair to come to this conclusion: The worst pitcher on any team is the equivalent of Bronson Arroyo facing a left-handed hitter late in the game.

As the Phillies batted Monday night in the top of the 8th inning, the lead-off man was left-handed hitting, Dominic Brown.  He promptly singled.  (Left-handed hitters were now responsible for all five Phillies hits off of Arroyo.)  I think it was a mistake to let him pitch to Brown but, I’ll at least concede it wasn’t a high-leverage at bat.  Once the tying run comes to the plate however, Arroyo cannot be allowed to face a left-handed hitter – and he really has no business facing any hitter at all.  However, Reds manager Dusty Baker didn’t see it that way and Arroyo was left in to pitch to Lance Nix, a left-handed hitter.  As a Phillies fan, I was thrilled but, alas, Nix grounded out.  Arroyo followed that by getting right-handed Erik Kratz to fly out.  With four outs left in the game, Phillies manager Charlie Manuel went to the bench and tabbed the Phillies best hitter, the left-handed hitting Chase Utley to pinch-hit.  Utley wasn’t in the starting lineup for the first time in 2013 getting a day off, but he was now in a position to take the Phillies most important at bat of the game.  Watching, I thought, there is no way Dusty Baker is going to let Arroyo pitch to Utley.  I mean, no way in hell can any manager willingly allow massive strength vs. massive weakness with four outs left in the game.

Baker left him in, Utley promptly crushed a home run to deep right center field and the Reds win probability had dropped more than 30 percentage points from a little over 90% to a little under 60%.  (Because the Phillies had four outs left, and the Reds six, the Reds were still favorites to win the game.)

If Joe Maddon or Tony LaRussa had managed to box an opposing manager into a situation where they had their best hitter facing the other team’s worst pitcher at a crucial late-inning point of the game, we’d all marvel at their strategic acumen.  And rightfully, so.  So what do you say about a manager who willingly lets that situation play out against him?

Wait, I know – we call him a players’ manager. 

That, of course, is hogwash.  There is only one type of manager who should be known as a players’ manager.  The manager who puts his players in the most advantageous position to succeed.

Dusty Baker made such a monumental blunder that his players won the game in spite of their manager.  (The Reds took the lead in the bottom of the 8th after Baker sacrificed Shin-Soo Choo for the purpose of allowing Zack Cozart to take the high-leverage at bat, but that’s a discussion for another day.) It’s a senseless mistake that comes from not understanding the strengths and weaknesses of your personnel. 

Baker supporters will point out that his normal go-to, left-handed, 8th inning reliever Sean Marshall is on the disabled list, but again, that misses the point.  It’s not Chase Utley that has the severe platoon splits, it’s Bronson Arroyo!  Of course, the correct, most-optimal decision is to bring in the nearly unhittable left-hander Aroldis Chapman in that situation, but I’ll concede getting a manager to use his “closer” in the 8th inning of a regular season game is futile.  Throwing aside the best option, the point is ANY option was better than Bronson Arroyo in that situation.  Every single Reds bullpen pitcher, right-handed or left-handed, was a better choice than letting Arroyo face Utley.

Across the American sporting landscape, a football coach would be killed if his defense went with the “dime package” in a goal-line situation or if an offense faced a constantly blitzing defense with an empty backfield and a tight end split-wide. This doesn’t happen because football teams have defensive and offensive coordinators who do nothing but specialize in on-the-field strategy.  I don’t understand why baseball front offices don’t observe the type of in-game errors their managers make and employ the same organizational structure.  Let the “players’ manager” roam the dugout, extol the troops, and keep the mood in the clubhouse light.  But during the game, he has to be in constant contact with his strategic coordinator who would be in the press box reminding him all game to never, ever, ever let Bronson Arroyo face an All-Star, possible Hall-of-Fame, left-handed batter, who represents the tying run, late in the game.


Mop Up Duty:

Joe Peta is the author of Trading Bases, A Story About Wall Street, Gambling, and Baseball*  (*) Not necessarily in that order, a Dutton Books/Penguin (U.S.A.) publication currently available wherever books are sold.  Here are three on-line booksellers you can currently choose from:

He is also the author of Trading Bases, the Newsletter, a companion piece to the book.  If you have been forwarded this issue and would like to be placed on the mailing list, please send an e-mail to

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You can follow me on Twitter here:  @MagicRatSF

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Reader Comments (2)

Great post!

April 17, 2013 | Unregistered CommenterwingSTIR

Excellent insight Joe......on 4/9 I stopped at Zeke's (2 blocks from SF Phone Company Park) for a pre-game beer and watched Bronson Arroyo and Lance Lynn toss 3 perfect innings each to begin their matchup. Lynn's got broken up in the 4th; and I left for the Giants game with Arroyo continuing to mow down Cardinals. Saw later that he'd melted down in the 6th and left the game trailing 4-1. Just checked details in the boxscore and all the hits he gave up were to Cardinals LH hitters. This game was just a week ago, how could Dusty have forgotten so quickly? Currently reading your book and enjoying it immensely.

April 19, 2013 | Unregistered CommenterJimbo

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