I put together this query for two reasons.

Because it's the off-season and what else are we going to do? It addresses real-life arguments I've been having with friends and family of mine for quite some time.

Reason number one I don't imagine I have to explain to you. It is, after all, a long, hard winter. But reason number two requires a brief backstory. One that begins with the legend of Steve Carlton's infamous 1972 season.

Steve Carlton, 1972

I learned the game of baseball, just as most of us have, from my father. As a consequence, much of the history of the game was passed down to me through his particular perspective. And Dad was always fond of reminding me that "the greatest feat in all of sports history was Steve Carlton winning 27 games on a team that only won 59 all season."

Now, let's first give credit where credit is due. This was a wonderful season for Steve Carlton, one that ranks in the top 55 seasons of all-time according to Fangraphs' ERA-. He led the league in ERA (1.97), strikeouts (310), and Complete Games (30) over the course of an unimaginable 346 innings ... and ultimately won a very well-deserved Cy Young award at the end of that season.

But the greatest feat in sports history?

What happens when you break down the numbers to Carlton's season is that you find his run support wasn't bad -- at least not when Carlton was on the mound. The Phillies offense that year wasn't particularly good, scoring just 3.2 runs per game while the league scored 3.9 per game on average. However, when Carlton was on the mound the Phillies managed to "step it up" and reward him with run support of 3.8 R/G. So, in fact, with Steve Carlton in 1972, all we have a historic season from a pitcher who was actually receiving league-average run support. Not as romantic as Dad maybe thought.

Now, in my eyes, this disparity between run support for Carlton and the rest of the Phillies staff just further illustrates why we don't use Pitcher Wins. One pitcher gets 3.8 R/G, while another from the same team gets significantly less.

But not everyone I've encountered in life feels the same way. In fact, an old friend of mine once wrote me that "there is some intangible factor the pitcher's offers [sic] that riles up the bats (maybe for only certain pitchers)."

This is not the worst theory in the world. Carlton did, after all, provide his team with a highly-inspiring 1.97 ERA, while the rest of the Phillies staff mocked their team's odds with a gruesome 4.21 ERA in an era where the league-average was just 3.45. Perhaps the Phillies felt that if there is a chance at all of winning, it was with their ace on the mound. And, just maybe, their game was at it's best on those days for a reason.

So I decided to run a quick query for my friend.

The Test

I pulled all pitchers from 2008-2011 who pitched at least 150 IP and held their ERA to at least 25% below the league's (in other words, a 75 ERA-). I defined those pitchers as "aces." I then measured the team's offensive wOBA in regular season games when (one of) their ace(s) was on the mound compared to games when their ace was on the bench.

Using 148 pitcher-seasons, I found that the average change in wOBA was actually -.009 (with a weighted average change of .007), meaning that hitters actually performed slightly worse with their ace on the mound.

For kicks, I then ran a second query using only pitchers with at least a 60 ERA-, (though this severely limited the sample to just 13 pitcher-seasons). In that sample, wOBA dropped just -.003 points on average.

I thought this was strange that the change in wOBA remained negative, so I expanded the sample to 2002-2011 hoping to eliminate some statistical noise. Using the 148 pitcher-seasons over that time, I found the average loss in wOBA remained negative, though slightly less so, at -.005 (-.006 weighted).

(For the nine aces with at least a 55 ERA- or less from 2002-2011, the loss in wOBA was -.010 on average.)

Implications

So what does this mean? Well, as you may have expected from the beginning, it's very likely that professional athletes at the major league level do not decide to "step it up" based on which pitcher is on the mound that day.

But, if you are slightly more daring, you may now want to argue that hitters might actually slack off slightly on days when their ace is on the mound. They presume they have to work less knowing that Doc, C.C., or Felix will take care of most of the run differential on their own.

It is more likely, however, that the small wOBA drop is in fact just the effect of aces matching up with other opposing aces, assuming teams try to throw their best pitchers up against the opposition's best on the same day.

This is something we can certainly test for in the near future, if there is a reasonable suspicion amongst BtBS readership that hitter's slacking off is actually a plausible explanation, and that any investigation of the matter is not a waste of our time.

Back to Steve

I tried ending the debate with my friend by pointing to Carlton's subsequent 1973 season. In that year, just one season removed from Carlton's historic uber-inspiring performance, the Phillies gave their pitchers an average of 4 R/G of run support, while the ace was left with just a measly 3.6 R/G for all his good work. Of course, by 1973 Carlton had been reduced to a 103 ERA-, and clearly no longer riled up the Phillies' lineup card. Just a year later it seems the Philadelphia Phillie offense was singing "what have you done for us lately, Steve Carlton?"

Follow @JDGentile on Twitter.

