There are few things that inhibit enjoying a baseball game more than a pitcher who takes seemingly forever between pitches, batter after batter, inning after inning, game after game to the point where fans cringe when it's his turn in the rotation. It would be even more galling for fans consistently subjected to Human Rain Delays if that slow pace also had a negative on-field affect.
There's an old adage in baseball that pitchers who work quickly keep defenders on their toes, which results in them making more plays when balls are put in play. You've probably heard it a hundred times on a broadcast, or in print like this John Lott article quoting Steve Tolleson in June:
The pitching staff, as a whole, works pretty quick on this team, which is a big benefit as to why the defence has done so well.
Or this Lott piece from September 2013 on Ryan Goins:
That [fast] pace keeps defenders on their toes.
In Mark Buehrle and R.A. Dickey, the Jays have the two fastest working qualified pitchers in MLB the last three years, measured as the average time between pitches by pitchf/x and reported as Pace at Fangraphs (under Pitch/fx plate discipline). In fact, since the advent of pitchf/x data in 2007, Buehrle has been the fastest pitcher every year except 2013 when his Pace jumped by a second compared to 2012 and 2014, and Dickey edged him out (another thing for which J.P. Arencibia can be blamed?).
As it turns out, Buehrle and Dickey are two pitchers who create a substantial amount of "hidden" value that is not readily apparent from looking at stats like strikeouts, walks, home runs, etc that are usually best to evaluate and value pitchers. Both field their position very well, control the running game well (Buehrle especially), and Dickey's knuckleball benefits other pitchers via the "Dickey Effect". So if there is a quantifiable benefit to working quickly, both should be among the highest beneficiaries, and it would be one more bauble in each's already overflowing bag of tricks. On the other hand, it may just be another baseball myth passed down as conventional wisdom over the ages that doesn't withstand factual scrutiny. So let's take a closer look.
As noted above, Pace is generated by pitchf/x which was only rolled out MLB wide in 2008. So we're limited to the last seven seasons in terms of data. At the simplest level, better defensive play should result in fewer errors and less unearned runs, so we'll start with looking at unearned runs and pace of pitchers with at least 500 IP from 2008-14:
Clearly, there's no relationship, just an almost completely random scatterplot. Then again, the error/no error distinction is highly subjective, so it's conceivable that even over 500 innings there's too much noise for a relationship to slow though. Nonetheless, strike 1 against.
A more ideal method would be using advanced defensive metrics like DRS and UZR, but the data isn't available split out by pitcher. The next best tool then is BABIP, since the core goal defensive goal is to convert balls in play into outs, or conversely prevent hits on balls in play. Comparing pitcher BABIP and Pace should indicate if there's a relationship between pitchers working faster and getting better results behind them. Using the same sample as above:
Again, a random cluster...and if anything, the relationship is slightly opposite! This conclusion is reinforced by binning the pitchers into groups according to their Pace:
To the extent there's a change in BABIP from working faster, it's higher.
Again, maybe the analysis isn't sophisticated enough. A pitcher's BABIP being strongly influenced by his batted ball profile (line drive, ground ball, outfield fly ball, and popup rates) as well the overall quality of his defenders and park factors. The former can be controlled for by calculated an expected BABIP (xBABIP) based on his batted balls and league averages for each batted ball. It's far from perfect, but it fine for this purpose. The latter can be controlled for by looking only at players who stayed on the same team, and using the team BABIP.
Starting with seasonal data, I ran a regression to predict BABIP for pitchers from 2010-14 with at least 100 innings in a season with the same team (n=674), based on their xBABIP and team BABIP. Both were highly significant factors (p ~ 0 at 10 significant numbers, F=136). Adding Pace into that model actually reduced the explanatory model of the model (F=91) and Pace was an insignificant variable (p=0.33) with a coefficient that would not make a difference even at the extremes between the slowest and fastest pitchers.
I tried repeating this looking at pitchers who had thrown 250 (n=201) and 500 innings (n=79) for the same team over the 2010-14 timeframe, to the same results. There's no evidence for fast working pitchers having balls turned into outs at a higher rate. Strike 2.
I thought of one last way to try and test for an effect. Fangraphs tracks infield hits and bunt hits. Perhaps if infield defenders were more "on their toes", they'd have a better rate of preventing these. Using the same data set of 500 IP starters as for the other plots:
Again, an almost perfectly random cluster. Strike 3. No matter how the data diced, there's no indication faster working pitchers affect their defender's abilities behind them, positively or otherwise. It turns out professional baseball players are, well, very professional about keeping their heads in the game and not losing focus even when a pitcher works at a glacial pace.