Sabermetrics: Acquiring HR Hitters

Have you noticed the Astros' proclivity for acquiring low batting average power hitters? Justin Maxwell, claimed off waivers last year, is the likely starting center fielder. The Astros traded for Chris Carter and signed free agent Carlos Pena. Matt Dominguez and Tyler Greene, possible starters at 3b and shortstop, potentially fit the same profile.

Indeed, the Astros' competition for the DH-LF-1b positions reflects a surplus of big, slow footed power hitters. Pena, Carter, Rule 5 draftee Nate Freiman, waiver claim Brandon Laird, J.D. Martinez, and Brett Wallace all fit the position of power hitter.

The most obvious explanation for this trend is that the Astros are moving to the American League, with its DH and power hitting lineups. However, a recent fangraphs article by Steve Staude on team specific hitter values led me to think about a possible sabermetric linkage to constructing the Astros' offense. Simply stated, these hitters may hold more relative value for the Astros than other teams.

Team Specific Runs Scored

Staude's fangraphs article discusses the use of a mathematical system called "Markov chains" to produce more accurate estimations of the run impacts of each type of hit, walk, K, ground out, etc. Thankfully--for both you and me--this article is not aimed at describing the complexities of Markov or linear weights concepts. (If you want to go to the deep end of the pool, read Staude's three part series at fangraphs.) The high level summary: Staude's Markov estimation of runs scored reflects the interaction of various offensive events based on the specific team. In effect, the resulting run impact simulates a typical game for the team.

When we estimate the runs produced by a hitter using wOBA or wRC, the estimations are based on an average team. But the actual impacts may be different for an offensive team which is substantially above- or below- average. Basically, because of the team synergies, good offenses are more productive at converting hits and walks into runs and bad offensive teams have more difficulty producing runs from the hits and walks.

Now, we can get around to the types of hitters who might help the Astros' offense. High OBP players are relatively more valuable to good offensive teams. HR hitters are relatively more valuable to bad offensive teams. A single or walk has relatively more value to a high OBP team, because these events have a higher probability of driving in and scoring runs. A HR has relatively higher value for the low OBP team because it guarantees run scoring in an environment of scarce runs.

Staude provides a common sense explanation in the first article in his series:

The more runners that are on base, the more value any subsequent hit has, all else equal, as there are more RBI opportunities...

If the team has a very high OBP, it will be able to sustain longer rallies, and will therefore be less dependent on the home run to score runs (i.e., singles, walks, etc. will be more valuable relative to the home run, compared to low OBP teams).

In a low-OBP team, however, while a home run is likely to score fewer runs than it will in an otherwise similar high-OBP team, the value of a home run relative to other hit types will be greater, as the team will be less likely to rally.

Digging even deeper, if a team hits a lot of home runs, the average value of a home run actually drops, due to more runners having been cleared from the bases by previous home runs.

Where do you think the Astros fit on the good or bad offense continuum? The Astros were 28th in OBP. The Astros were next to last in wOBA and wRC+ (only the Cubs were worse). The Astros were dead last in scoring runs--and by a considerable margin: the Astros scored 583 runs compared to the 29th ranked Marlins' 609 runs. Astros' base runners had a very low probability of scoring. In short, the Astros' offense was really bad. Therefore, the low batting average power hitters may be flawed, but they are more attractive to a team that produces as few runs and base runners as the Astros.

That's not to say that a high OBP, high batting average, low strike out, 30 HR hitter wouldn't be more valuable to the Astros. But the last time I looked, Albert Pujols and Miguel Cabrera were under contract with price tags of $240 and $152 million, respectively. But, given their (for the most part) defensive limitations and batting flaws, whether it be batting average, strike outs, or both, the power hitters acquired by the Astros are inexpensive--and they are relatively more valuable to the Astros' offense than to a high octane offensive team.

Chris Carter Example

The fangraphs article provides a helpful spreadsheet for estimating R/G based on Markov. The average difference between actual R/G and Markov R/G estimates is less than 1%, but the average difference using the Runs Created formula is 8%. By that measure at least, the Markov estimation seems to be more accurate.

Let's use Chris Carter to illustrate how Staude's Markov-based spreadsheet can be used. I started out with the 2012 Astros offense R/G (the spreadsheet includes all 2010 - 2012 team offenses).

The following 2012 offensive players, whom are no longer with the Astros, seem like hitters that would be part of the DH-LF-1b triangle if they had remained with the team: Moore, Pearce, Francisco, Buck, Downs. They combined for 601 at bats in 2012. (In a sense, these are actual, rather than theoretical, replacement level players.) I removed those players' offense from the Astros' 2012 batting statistics, and replaced their offense with 601 at bats by Chris Carter. In performing this step, I scaled Carter's offensive output in proportion to the ABs and PAs of the combined replaced players.

For illustration, I use Carter's Steamer projection as the baseline for calculating R/G impact. (Steamer projects Carter with a .247, .333, .471 slash line.) For an optimistic scenario, I scaled up Carter's 2012 offensive performance with the A's. In 2012, his slash line was .239, .350, .514. This is optimistic, given the combination of small sample size and likely favorable platoon situations associated with his actual 2012 performance. But we can be like John Sickels and hope that Carter will have a real break out season as a full time player.

Here are the Astros' Markov R/G estimate changes:

Markov Runs Per Game

Astros 2012: 3.74

w/Carter (Steamer): 3.91

w/Carter (2012 rates): 3.96

I utilized the change in the Astros' 2012 Pythagorean record to project the incremental change in wins and losses. Based on a continuation of Carter's 2012 rates of performance, the Astros gain 4.0 wins. Based on the Steamer projections, the Astros gain 2.6 wins. With some rounding, we get a 3 - 4 win improvement by substituting Carter for the five players who will be replaced. I haven't reflected the impact of Carter's defense, or lack thereof, on the win impact. Possibly that will reduce the added wins (though that's unclear, since most of the "replaced" players were poor defenders), but this article is focusing on the offense for our discussion.

Despite the fact that the Astros traded a good shortstop for Carter and potential starting pitcher Brad Peacock, this exercise may illustrate why Jeff Luhnow said that the trade improved the current Astros' roster, as well as future Astros' teams.