Pros/Cons of a 40-pitch scoreless first inning

Beyond The Boxscore and Tom Tango asked the following question.

Would you rather be down 1 run, with your starting pitcher having thrown no more than 10 pitches, or would you rather throw a scoreless inning, but your starting pitcher having thrown at least 40 pitches?

To me it kind of seemed like a no brainer. I would rather keep the run off the board. So I put my simulator to the test to see what it thought. My simulator has an engine that worsens pitcher performance based on the number of pitches thrown. It is a good proxy for times through the batting order. Both have an effect on how a pitcher usually gets worse as the game goes on.

What I did is take a game between the Dodgers and Twins early in the week where Zack Greinke pitched against Kyle Gibson. First off, I simulated the game from the very beginning to set a baseline for how often the Dodgers should win this game and how long and how well Zack Greinke pitches. Next, I set the game state to the top of the second inning with the first batter of the inning up. I tell the simulator that the Dodgers number five hitter leads off the 2nd inning and the Twins number six hitter leads off the bottom half. These settings are then kept constant for the remaining trials.

Results: Dodgers win 62.793%, Greinke pitches an average of 6.598 innings with an average FIP of 3.108

The next simulation is with Greinke having made 10 first inning pitches and the Twins starter 15. The score is 1-0 Twins and then 100K games are simulated. So in this simulation the Dodgers are starting the 2nd inning down one run but Greinke starts the inning only having made 10 first inning pitches.

Results: Twins win 50.161%, Greinke pitches an average of 6.875 innings with an average FIP (2nd inning on) of 3.118

Up next I ran the simulation with Greinke having made 40 pitches in the first inning but not having given up a run. So the score is tied 0-0 in the top of the 2nd. The Dodgers have a pretty good bullpen on paper (projection systems) and some of their long reliever options are not terrible.

Results: Dodgers win 60.047%, Greinke pitches an average of 4.969 innings with an average FIP (2nd inning on) of 3.162

Then for fun I had Greinke throw both an 80 and a 100 pitch first inning with the score tied 0-0 heading in to the second inning. Those results are below. I think the one run hole that the away team is put in is a much much larger hole than a first inning where a starting pitcher throws 40 vs 10 pitches. And of course the difference will be a little bit different for each team based on the differences in talent level of the starting pitcher and the bullpen, namely the long reliever. My study just looks at one game but the nearly two innings lost from the starting pitcher will have an impact on the next couple of games as the bullpen will be tired and perhaps a few of them unavailable to pitch the next game. So you can take my results and adjust for those things I just mentioned but I think it is more than safe to say that for a one time deal, the 40 pitch no run first inning is a much better scenario for the Dodgers.

Remarks	Away	Home	Away Pitcher	Home Pitcher	Fave	Away Runs	Home Runs	Win %	Total Runs	Greinke IP	Greinke FIP
Full 9 innings	LAN	MIN	Zach Greinke	Kyle Gibson	LAN	4.490	3.142	62.793	7.632	6.598	3.108
Greinke 10 pitch 1 run first inning	LAN	MIN	Zach Greinke	Kyle Gibson	MIN	3.933	3.719	50.161	7.652	6.875	3.118
Greinke 40 pitch 0 run first inning	LAN	MIN	Zach Greinke	Kyle Gibson	LAN	3.957	2.941	60.047	6.898	4.969	3.162
Greinke 80 pitch 0 run first inning	LAN	MIN	Zach Greinke	Kyle Gibson	LAN	3.952	3.016	59.175	6.968	2.569	3.236
Greinke 100 pitch 0 run first inning	LAN	MIN	Zach Greinke	Kyle Gibson	LAN	3.948	3.149	57.425	7.097	1.640	3.499