Disclaimer: Fairly long, not too exciting.
I used to hate running. At one point it was definitely the worst thing I regularly put myself through, but as I got into better shape I found my pace and running gradually became a great escape for me. While on a long run now I don't concentrate on how hard it is or how much longer I must go but instead let my mind wander from thought to thought. It has become a great way to focus for me, if only for forty-five minutes or so at a time, and on one of these recent runs I thought of an idea that I couldn't quite shake for a while afterward.
Players who aren't named Carlos Peguero generally learn at a young age the value of taking a pitch or two in their at bats. At first it is simply because young pitchers can't throw strikes. Around high school, at least for me, players begin to learn that just because a pitch is a strike doesn't mean they have to swing and by letting a tough early pitch go they may get a better pitch later in the at bat. Once players get to the beginnings of pro ball or college their approach is thought to be "advanced" if they can take a few pitches, work walks and generally get deep into at bats. Players with this kind of approach in the minors are usually the ones who develop into good hitters at the Major League level. We've known for ages that patient hitters are generally more valuable than free-swingers because their approach will lead to higher on-base percentages and gives them better odds of getting easier pitches to hit in any given at bat. These are basically the commonly accepted values of being patient but on my run I began to think about something that I hadn't really taken into account for a while.
You always hear analysts say that the team needs to try to work deep counts whenever they face a good pitcher. In fact, if you listened to the pregame show a few days ago you undoubtedly heard Mike Blowers say that the Mariners needed to work deep counts against Justin Verlander because by making him work hard they would be able to get him out of the game faster. This kind of statement is probably said hundreds of times by different analysts every year. Qualitatively, it is easy to understand that by getting the Justin Verlanders or Tim Lincecums out of the game earlier your team has a better chance to win. However, when we evaluate baseball we don't simply allow qualitative analysis to be our basis for argument so I have attempted to find a quantitative value for showing patience at the plate that WAR may miss.
First off, I'd like to say that I will be using Fangraphs WAR to determine value and used their database to determine my statistical values except for where otherwise stated. I also would like to say that, going in, I knew the value of seeing a few extra pitches per plate appearance would most likely be miniscule at best so I may use a few extra decimals in order to make sure I don't lose any data.
Fangraphs batted ball data goes back to 2002 so I limited my stats to the last 10 years. Over this period of time the average WAR of a qualified starting pitcher was 3.1 wins per year. The average starter also made 29.3 starts, threw 2906.9 pitches and pitched 182.8 innings. This means that the average start for qualified pitchers was about 6 1/3 innings and 99 pitches and the average value of these starts was about .103 wins. If we divide this value of wins by the amount of pitches we get a value of .00104 wins per pitch thrown.
Now that we have a rough estimate of what the value of any given pitch from the average starter is we can attempt to analyse the value of a batter who works deeper into counts. At this point I used ESPN's database to find the average pitches per plate appearance for batters in 2011. I used ESPN's instead of Fangraphs' because on Fangraphs it is much harder to see the total pitches seen for each player in the league at the same time. In fact, its still mostly a chore on ESPN as well, which is why I limited the data for average P/PA to this year only. I got a value of 3.814 pitches seen per plate appearance for the average qualified batter.
Since I now had an average value I needed a player to compare it to. This was probably all spawned a few weeks back when Matthew wrote about the Battlin' Luis Rodriguez so I decided to look at him first. He has seen 342 pitches in 87 PA this season for an average of 3.93. This deviates from the average by .117. If we multiply this value by his PA then we get 10.182 extra pitches he's seen this year. This equates to an unsurprisingly miniscule .0106 wins above the average player. Its only 87 plate appearance by a replacement level player, however, so I decided to look at Justin Smoak as well. Smoak sees 4.02 P/PA which equates to .05 wins so far this season and gets to about .13 wins over 600 PA.
This is, again, a tiny value so I decided to look at the Mariners in general. I limited this to only their current starters and regular players, except for Mike Carp and Greg Halman because I figured there'd be SSS issues. I calculated the average P/PA for each team in the last ten years and then treated the 2011 Mariners as if they were a full season. Over a full season the twelve Mariners I looked at gave me an average of 3.89 P/PA and .55 wins above average for the season. The average is brought up by players like Jack Cust and Smoak but is brought down to Earth by just about every other player. The Mariners have an awful offence so I looked at the Yankees. They, too, are dragged down by struggling or impatient players like Derek Jeter and Robinson Cano so they gave about the same result as the much worse Mariners.
In conclusion, I can say that there is most likely some sort of value derived by making a pitcher throw more pitches but at the end of the day, unless you have an offence full of Justin Smoaks or Mark Teixeiras it doesn't make much of a difference over a full season and, let's face it, if you have an offence full of players like those two you probably aren't going to be worrying about another win or two down the stretch anyway.
(Disclaimer II: I have no idea how I would derive the WAR of taking pitches because I don't know how many pitches a replacement level player would take per PA and over the years of data there were only a handful of players with 0 RAR bats. This is why I referred to any calculations as "wins above average" instead of wins above replacement.)