What do Andrew McCutchen, Buster Posey, Jay Bruce, and 12 other players have in common? They will all be in their age 27 season for 2014 and so we should expect that as a group their wOBAs will decline by 3 points on average. That may not sound like a lot, but it is the start of what will likely be the slow, steady offensive decline phase of their careers. Some will defy those odds, but which ones, and what might be signs of imminent decline?

To begin to answer these questions, I examined how hitters’ aging trends would be affected if certain skills did not decline with age. For example, how would a hitter age if his BABIP was consistently league average? I used wOBA as the measure of performance. The two age profiles in Figure 1 show this story. The solid line shows how players typically age, peaking at age 26, and declining steadily from there (see below for technical details on how this figure was constructed). The dashed line draws out a hypothetical age curve that assumes players’ BABIP is constant over time. Because players under age 30 tend to have above average BABIP, the dashed line is below the solid line for these young players. Conversely, older players would benefit from having their actual BABIP replaced by an average BABIP. The overall consequence of adjusting for BABIP is an age profile that is flatter—meaning that the effect of aging on wOBA is reduced.

Figure 1. Change in wOBA Age Profile when Adjusting for BABIP

The effect is reduced, but not eliminated. What other skills decline with age and how important are they to the decline in wOBA with age? Although swinging strike percentage, K rate, BB/K, and fly ball percentage all have important relationships with wOBA, these factors have little impact on the aging of wOBA. The wOBA age profile adjusted for these factors in Figure 2 is just slightly flatter than the unadjusted profile. This is because swinging strike percentage and K rate typically peak before age 26 and show little decline with age. To the extent that the adjusted curve in Figure 2 is flatter, trends with age in BB/K are most responsible.

Figure 2. Change in wOBA Age Profile when Adjusting for Swinging Strike Percentage, K%, BB/K, and Fly Ball Percentage

Figure 1 demonstrated that BABIP plays an important role in the aging of wOBA. Adding both BABIP and HR/FB skills to the others from Figure 2 explains the entire decline in wOBA after age 26. Indeed, if a player’s BABIP and HR/FB skills (along with the others I’ve mentioned) remained average throughout his career, he would actually show continuous improvement through at least age 30. Figure 3 shows this result. The flatness of the adjusted line indicates that the full set of statistics used in the adjustment does a very good job of accounting for trends in wOBA with age.

Figure 3. Change in wOBA Age Profile when Adjusting for All of the Above and HR/FB

So what does this mean for McCutchen and the others in our list? We may learn the most about how they will age based on observing trends in their BABIP and HR/FB rates from here on out. Doing so will be challenging because these are also among the least reliable measures of performance in a single season. Even so, a decline in these skills could indicate substantial performance losses to come. Additionally, players whose value derives from high walk or contact rates may age less precipitously than others.

A productive avenue for future analysis might be to assess whether there is a relationship between the amount of improvement in BABIP or HR/FB skills a player experiences before age 26 and the amount of decline in those skills after age 26. If so, then we might be able to better predict how a player’s offensive skills will age. However, we can learn a lot about averages, and our long-run projection for any particular player’s performance might improve, but it will always remain uncertain.

Technical Details

The age profiles adjust for what is often referred to as survivor bias—the fact that not all of the players in the sample at age 20 are also in the sample at age 35. To do this I used a technique commonly used by economists and others called fixed effects regression (see Jonah Rockoff’s work on changes in teachers’ performance with experience for one example). I run a regression that includes individual player fixed effects, ensuring that the relationship between wOBA and age is calculated using within-player variation in wOBA over time, rather than variation in performance across players. Consequently, the results are not affected by changes in the composition of MLB players by age. To calculate the adjusted profiles, I account for the other statistics as additional controls. Doing so means that when I adjust for BABIP, I am also adjusting for skills that are related to BABIP. Therefore my results do not depend on any particular model of how BABIP is related to performance. The above results are based on the 1,346 players who played in the majors for at least two seasons between 2002 and 2013. An alternative sample that is restricted to just the 304 players who played at least eight seasons during this period produces similar results, although the average wOBA levels are higher and the curves are less precisely estimated.

About the Author: Elias Walsh spends too much of his free time working with baseball data and trying to win his fantasy baseball league (or so his lovely wife informs him). His day job is a research economist at Mathematica Policy Research, where he conducts research to inform education policy decisions.

Although the Nationals had a disappointing 2013 season overall, Tanner Roark (RHP) was one of their more pleasant surprises. The Nats brought him up in August, as injuries and performance problems created openings for several pitchers in their minor league system.

While Taylor Jordan also performed well, I think it’s fair to say that Roark had the most impressive and intriguing debut for the big-league team. Roark accumulated excellent “traditional” stats, and he did so at least in part by exploiting an unusual but highly effective talent: making batters not swing at good pitches. This post explores Roark’s story, and opens up the question of how his distinctive forte, zone-swing rate, contributes to effective pitching.

To recap, Roark finished 7-1 with a 1.51 ERA over 53 2/3 innings. He allowed only 1 home run in total, or 0.17 home runs per 9 innings; and the league batted .197 against him (– “batting average against” or “BAA”). The Nationals’ ace, Stephen Strasburg, allowed 0.79 home runs per 9 innings, with a BAA of .205. Roark was comparable in BAA to Strasburg, and much, much better at preventing home runs.

Of course, Strasburg reached his figures in 183 innings of pitching as compared to Roark’s 53 innings of pitching. This is what is sometimes described as a smaller sample. But we should not discount Roark’s performance too quickly. His 53 innings involved five starts and nine relief appearances, and a total of 12 appearances with at least two innings pitched. This is considerably more than, say, one start and no relief appearances. Roark played for the Nationals for the last two months of the season. His stint in the majors last year was substantial enough, I think, to merit serious interest.

Roark’s 2013 performance was surprising in part because of his pedigree. In 2012 Roark was 6-17 as a starter in Triple-A, pitching for the Nationals. His 2012 ERA in Triple-A was 4.39 (although his FIP [Fielding Independent Pitching rating] of 3.85 was better). Providing more background, Adam Kilgore wrote in September 2013 that

Roark has never been regarded as a star or a significant prospect. In 2008, the Rangers drafted him in the 25th round. The Nationals acquired him and another minor league pitcher for Cristian Guzman at the 2010 trade deadline. Last winter, the Nationals left Roark unprotected from the Rule 5 draft for the second straight year. They invited him to major league spring training this year, and shipped him out in the first round of cuts.

(Washington Post, Nationals Journal, 9/17/2013; http://www.washingtonpost.com/blogs/nationals-journal/wp/2013/09/17/tanner-roarks-incredible-start-built-on-command-feel-for-pitching/)

Roark’s 2013 performance was also surprising because, with a fastball averaging 92.6 mph, he had good but not overwhelming velocity.

Going back to FIP and similar topics, another reason why Roark’s 2013 performance was surprising was because of some relationships between his statistics. For instance, although his 2012 Triple-A ERA (4.39) was higher than his 2012 Triple-A FIP (3.85), this relationship reversed itself last year in the majors, with Roark posting a 1.51 ERA and a 2.41 FIP. In addition, his xFIP (“expected Fielding Independent Pitching”) was 3.14, significantly higher than the FIP.

“ERA < FIP < xFIP” spreads of this size are not unheard of, but they are rare, especially when your ERA is less than 2.00. In fact, ERA < FIP < xFIP distributions of this type suggest that you are identical to Clayton Kershaw (1.83 ERA / 2.39 FIP / 2.88 xFIP) and that you have just signed a contract worth 215 million dollars!

These observations about Tanner Roark’s performance and pedigree raise several questions:

How did he perform so well in 2013?

What is going on with his ERA<FIP<xFIP distribution?

What can we say about his future performance?

Taking a quick initial look at the ERA<FIP<xFIP distribution, a “negative” delta between ERA and FIP is often attributable to the pitcher having a low Batting Average on Balls in Play (BABIP). Roark’s BABIP was indeed very low, at .243. (Kershaw’s was .251).

Also, although this might sound odd, Roark’s extremely low HR rate (0.17 per 9 innings) pushed his ERA below his FIP, even though home runs are a fielding-independent matter. Roark was fine (league average or better) on the other FIP elements — walks, K’s, HBP’s. But combining these normal-range statistics with his homer rate produces a compromise number and some information loss.

Turning to xFIP, this calculation substitutes out the pitcher’s own homer rate for the league average homer rate. As we might expect, the league average homer-rate was much higher than Roark’s, and this explains the FIP < xFIP delta, while also contributing to the delta between his ERA and his xFIP.

These observations tend to intimate that some of Roark’s statistics are not likely to repeat themselves. Before turning to the “future performance” question identified above, I want to look more at the first question of trying to understand Roark’s 2013 success. There are aspects of Roark’s pitching last year which suggest that his strong performance numbers were not an accident, and that his apparent prowess is not simply overmagnified by the small prism of his innings total.

The first statistic of interest is that Roark was seriously good at throwing pitches in the strike zone which batters did not swing at. This is the Z-Swing% statistic recorded on FanGraphs and other places. Roark’s Z-Swing rate in 2013 was 54.8% (per Baseball Info Solutions [BIS]), or 55.9% per PITCHf/x. This means that batters only swung at Roark’s pitches in the strike zone about 55% of the time.

(BIS and PITCHf/x converge around 55% for Roark’s Z-Swing%. These systems actually diverge, or report different percentages, for some other stats which are not independent of Z-Swing%. Although this is interesting, the differences do not materially affect our evaluative questions. I will cite the BIS plate discipline statistics throughout and compare them to PITCHf/x at various points below).

The complement of Z-Swing% is what I will call “Z-pass” — the phenomenon of non-swings on pitches in the strike zone. Tanner Roark’s Z-pass rate last year was 45% — batters passed on about 45% of his pitches in the strike zone.

This was a very high Z-pass rate. In fact,

• It was the highest Z-pass rate on the Washington Nationals, by about 5 percentage points, among Nationals pitchers with at least 50 innings.

• It also was more or less the highest Z-pass rate in all of major league baseball, again among pitchers with at least 50 innings. Roark came in first in Z-pass rate according to BIS. According to PITCHf/x, Roark was tied for sixth-best in Z-pass rate, behind Sonny Gray with a 47% Z-pass rate.

A high Z-pass rate is indicative of several good pitching qualities. Z-passes are good because they mean that batters are laying off a higher number of pitches which damage their cause and advance the pitcher’s cause. A high Z-pass rate indicates that the pitcher is accumulating strikes while maintaining an atypically lower risk of allowing a hit. (This is true if the pitcher is hitting the strike zone at a reasonable rate. More on this below). Tactically speaking, the Z-pass is the best outcome on the swing v. strike zone matrix below.

Swings on pitches in the zone and out of the zone can lead to hits, and worse. By contrast, if we assume that non-swings in the zone lead to strikes, the Z-pass simply constitutes a good outcome for the pitcher.

How often did Roark throw strikes? In 2013 Roark hit the strike zone 47.7% (BIS) of the time. This was about 3 percentage points ahead of major league average (44.9%). 3 percentage points comes out to about one standard deviation above average. (PITCHf/x reports a higher league-wide strike-zone rate — 49.4% — and a higher strike-zone rate for Roark as well, at 53.8%. PITCHf/x appears to have a larger strike zone than BIS).

It therefore appears Roark was exploiting his elite Z-pass rate often enough for it to be useful, and indeed for him to have an advantage over hitters. Roark accumulated strikes at a good rate; and, by strongly suppressing swings at pitches in the zone, he lowered the risk of allowing a hit. It appears this dynamic was a main factor in Roark’s success in 2013. That’s part of the answer to our “How did he perform so well” question.

Another factor which stands out from Roark’s strike-zone data is that he threw first-pitch strikes 70.6% of the time. This tied for third in major-league pitchers with at least 50 innings in 2013. Consistently gaining an initial advantage over hitters, and doing so at an elite rate, was another main factor in Roark’s success.

Other discussions of Roark have cited his command, his aggression, and an improved mental approach. Going back to Adam Kilgore, he writes:

Roark’s ascension began last season, when he told himself he would not allow his temper to control him on the mound. He would not the things out of his control – fluky hits, errors, whatever – distract him. He would throw strikes. He would be confident. He would attack, above all else.

“I feel that last year is when I had my, I guess, mental turnaround,” Roark said. “That was the biggest thing for me.”

(Washington Post, Nationals Journal, 9/17/2013; http://www.washingtonpost.com/blogs/nationals-journal/wp/2013/09/17/tanner-roarks-incredible-start-built-on-command-feel-for-pitching/)

We can certainly see command at work in Roark’s low homer rate, and his low walk rate (5.4%). We can see both command and aggression at work in his first-pitch strike rate. Roark’s league-leading Z-pass rate substantiates the command/aggression understanding of his performance, and also adds to this understanding.

A pitcher who suppresses swings on pitches within the zone is presumably hitting unattractive parts of the zone, but he may also be throwing in-zone pitches which do not present to hitters as strikes. This sounds like a pitcher on whom it is difficult to make good contact. This is a third idea, beyond Z-pass rate and first-pitch strike rate. One way, however, to be averse to good contact is to be a high Z-pass pitcher.

Being a high Z-pass pitcher does not entail being a high strikeout pitcher. Roark’s strikeout rate was only one percent below major-league average (again, among pitchers with 50 innings and up). Of course, on other measures, like ERA, Roark was much better than league average. I think that connecting Z-pass rate with suppression of good contact can help us understand why.

Z-passes represent hittable pitches – pitches in the zone – which were not hittable enough to induce a swing. Poetically speaking, Z-passes involve real visual ambiguity: since they end up in the strike zone, they can’t look that bad; but they do not look good enough to induce a swing.

How well does this characterization actually apply to Roark’s pitches? On this question, we have the following from the Atlanta Braves:

“He wasn’t missing with any pitches over the plate, it seemed like,” said Braves catcher Gerald Laird. “When he was going away, he was throwing that little two-seamer back door, when he was coming in he was running that two-seamer in on your hands, and he had that little slider working.

“Tonight it seemed like he was hitting his spots and wasn’t making any mistakes. I know (Freddie Freeman) was saying he was starting it at him and running it back over. When he’s doing that it’s hard to pull the trigger.”

(http://www.washingtontimes.com/blog/nationals-watch/2013/sep/17/tanner-roark-shines-nationals-complete-doubleheade/#ixzz2prxGGOUh)

Of course, these descriptions of visual ambiguity — or of evidence which shifts within a fraction of a second — presumably apply to all or most of a high Z-pass pitcher’s offerings, not just to his pitches in the strike zone which do not elicit a swing. The image that emerges is of a player whose whole volume of pitches is tough to react to in a manner that creates good contact.

Roark was actually pretty good at inhibiting contact of any kind, especially on pitches within the strike zone. However, a look at his contact numbers does not immediately confirm this interesting and important point. As we see in the table below (from BIS by way of FanGraphs, again looking at 50+ IP), many of Roark’s contact rates were actually above league average, sometimes by more than one standard deviation.

Before turning to contact rates, you will have noticed that this table also gives us a look at how Roark’s Z-swing rate compared to the rest of baseball. According to BIS, Roark was 3 standard deviations above average on a positive pitching statistic which is completely independent of fielding. He was two standard deviations (56% Z-Swing%, as opposed to 63% league average) ahead according to PITCHf/x — this is still pretty good for a former 25^th-round pick! Some other observations:

• O-contact. Here Roark was much higher than average, but this may not be a bad thing, since contact outside the zone is less likely to be productive for the hitter.

• Z-contact. Roark again was higher than average. But this somewhat unsettling number should not be digested outside of its relevant context, which is helpfully provided by Roark’s Z-swing rate. Looking at Z-contact multiplied by Z-swing yields the interesting result that Roark allowed contact on 51 percent of his strike zone pitches, as opposed to a league average of 57 percent, with a standard deviation of 3 percent.

(PITCHf/x condenses this gap, in much the same way that it condenses the gap between Roark and MLB on Z-pass. PITCHf/x reports Roark at 52.2% contact on all pitches within the zone, and MLB at 54.6%. Thus, if we switch from BIS to PITCHf/x, Roark’s contact rate goes up, and MLB’s goes down.

However, as noted above, PITCHf/x appears to be working with a larger strike zone than BIS (MLB-average Zone% of 49.3 vs. MLB-average Zone% of 44.9). This point complicates Roark’s apparent movement back towards league average. In brief, the fact that Roark’s swing rates go up — while the MLB average goes down — on larger renditions of the strike zone may be a testament to his effectiveness, rather than a knock against it.

• SwStr (swinging strikes/total pitches). Since Roark did a good job suppressing contact within the zone, Roark’s low swinging-strike number does not seem to be an especially important piece in his overall puzzle.

The standard contact rates reported by BIS and PITCHf/x do not do a good job of communicating how well a pitcher actually prevents contact, because these contact rates only look at swings. Since you can suppress contact by suppressing swings, multiplying the contact rate by the swing rate provides a better view of how a pitcher is actually doing along this dimension. Despite a “zone-contact” rate which was higher than league average, Roark was very good to excellent at suppressing contact within the strike zone.

We are exploring a clue provided by Roark’s excellent Z-pass rate that Roark was good at inhibiting solid contact. This clue was supported by our look at Roark’s contact rates, which indicate that he was pretty good at suppressing contact flat out. The idea that Roark’s pitches were visually ambiguous enough to limit good contact receives further confirmation from his batted-ball statistics. In addition, looking at these statistics (2013, 50+ IP) will bring us around nicely to the question of how well Roark might sustain his performance in future seasons.

Roark’s ground-ball, fly-ball, and infield-fly rates combine to indicate a strong bias against good contact. Roark had a somewhat high line drive rate, and, admittedly, line drives are a form of good contact. For instance, I suspect it’s unusual to have a somewhat high line-drive rate and a markedly low BABIP. Roark’s line-drive rate provides one specific indication that his BABIP is due to increase. However, a low line-drive rate is not entirely at odds with the idea that a pitcher is suppressing good contact — especially if we are thinking about home runs. Since most line drives are not home runs, a slight tendency towards line drives is a small but genuine homer-prevention measure.

In this way, Roark’s line drive rate coheres with his ground-ball, fly-ball, and infield-fly rate statistics. All of these rates, and especially their combination, suggest a low-homer pitcher. Why didn’t Roark give up a lot of home runs? Well, he got a lot of grounders and infield flies, while limiting his fly balls overall, and he gave up a somewhat high proportion of line drives. It is very plausible to suppose that Roark’s extremely low HR/FB rate overshoots the anti-homer bias suggested by his other batted-ball rates. Equally, however, the other rates tell a clear enough story that a low homer rate is not at all a surprise. Roark was very good at inhibiting good contact.

How will he do in the future? A nice way to frame this question is in terms of Roark’s ERA, FIP, and xFIP numbers mentioned earlier. And, leading up to that, I think it’s helpful to assess the respective importance of two things: (1): the overall coherence of Roark’s 2013 statistics; and (2) the sample sizes in which they were achieved.

In terms of coherence, Roark’s statistics tell a consistent story:

• Looking at Z-pass, Roark was very good at limiting swings on good pitches

• Looking at Z-swing * Zone%, Roark was very good at limiting contact within the zone

• Looking at his batted ball rates, Roark was very good at limiting good contact

I could be wrong about this, but I do not see relationships among Roark’s 2013 statistics which point to trouble looking ahead. These statistics tell a consistent story of effectiveness. You can focus on his low swinging-strike rate if you like, but this rate was consistent with Roark being at least one standard deviation (two sd’s according to BIS) better than average on limiting contact within the zone.

In addition, there are pockets within Roark’s portfolio where some stats are very good and others are even better, like the HR/FB rate relative to Roarks other batted-ball statistics. However, this type of overshooting is a good problem to have. To the extent that the non-harmonic components of Roark’s statistical portfolio are extremely good statistics, this relates to the issue of our expectations for future years. A version of Tanner Roark based on 2013, but without the extra anti-homer overshooting, would still be above MLB-average.

As noted above, Roark only pitched 53 innings, and that’s a much lower total than what a starting pitcher would typically accumulate over a full year. Although we intuitively regard this as a small sample, it does not follow that Roark’s performance is without predictive value. As is often pointed out on the pages of FanGraphs, statistics stabilize, or acquire predictive value, at different thresholds (http://www.fangraphs.com/library/principles/sample-size/). Generally speaking, fielding-independent stats stabilize more quickly for pitchers than fielding dependent stats; this is a helpful point in assessing the forward relevance of Roark’s 53 innings.

Some of Roark’s relevant statistics are above their stabilization thresholds. Roark allowed 153 balls in play (BIP), which puts him above the stabilization points for groundball rate and flyball rate:

70 BIP: GB rate

70 BIP: FB rate

Roark faced 204 batters, which is above the stabilization points for walks and strikeouts:

70 BF: Strikeout rate

170 BF: Walk rate

However, Roark was league-average in K’s and was “only” one standard deviation above average in walks; these numbers are not as good as Roark’s plate discipline statistics like Z-pass and suppression of contact within the zone. So it’s not clear whether Roark reached the stabilization points for key parts of his performance.

But this is more or less where I will have to leave it. Figuring out the stabilization point for Z-pass is beyond the scope of the present study. Indeed, my post has probably pushed us to near overload regarding things that we ever wanted to know about Tanner Roark! By the same token, it’s not clear that learning more about Roark’s statistical profile would shift our opinion much about his prospects for future performance. This is what I think we have to consider:

In an intuitively small sample size, Roark put up a consistent portfolio of excellent fielding-independent stats: on limiting zone-swings, limiting contact in the zone, and limiting good contact. Very broadly, the size of a sample has to be balanced with the consistency of the evidence within it. Just imagine watching a one-round boxing match in which one competitor knocks the other one down three times. This is a small sample which tells a very compelling story about the respective abilities of the boxers. Roark’s sample size is larger, of course, and his performance was not as dominant. Nonetheless, his limited 2013 season is packed with a lot of positive indicators.

Here are a few final comments about what Roark might do in the future, framed in terms of his ERA, FIP, and xFIP:

As we discussed above, the delta between Roark’s ERA and FIP is primarily a matter of his low BABIP and his very low homer rate. Although Roark’s BABIP will probably go up, there are signs he may be better than average at suppressing hits: he showed a tendency to induce ground balls and infield flies; the latter especially inhibit BABIP.

Roark’s very low homer rate pulls down both his ERA and his FIP. Although his .17 homers per 9 innings will almost certainly go up, there are signs he may be better than average at suppressing home runs…signs which are distinct, that is, from his one homer allowed in 53 2/3 major league innings!! Roark’s tendencies toward ground balls, infield flies, and line drives are all anti-homer measures. These tendencies flow, by hypothesis, from his ability to inhibit good contact by throwing visually ambiguous pitches.

The most eligible view by far is that Roark will regress towards league average in future years. But accepting this view should not deprive us of optimism. Roark could go back at least one standard deviation on each of the ERA-like measures and still be at league average or better than league average. That’s a good position for any pitcher. It’s a great position, albeit a paradoxical one, for a pitcher who is currently slated to compete for no better than the 5th spot in the Washington Nationals’ 2014 starting rotation!! Suffice to say I think that Roark ought to receive full consideration for the opportunities available to him.

Earlier today, I was looking at trends and projections for some Cubs prospects and looked up Starlin Castro.  A trend immediately struck me: his 2010 batted ball statistics are nearly identical to his 2013 peripherals.

Stat:      ISO         LD%        GB%       FB%      IFFB%

2010:   .108      19.5%      51.3%     29.2%     7.0%

2013:   .102      19.9%      50.7%     29.4%     7.6%

These two seasons are closer than any of his other seasons in batted ball numbers.  A key difference?  2010 BABIP was .346, 2013 BABIP was .290.  His career BABIP is .323.  So is it we assume some good luck in 2010 and bad luck in 2013?

It should be noted that his BB% in 2013 was his career low, and his K% was his career high mark.  So can we expect some regression in those numbers as well?

I think the answer is yes to both questions.  In 2012, his BABIP was .315.  Even if Castro could return to that level (right around his career average), he looks much better than the .245 hitter we saw in 2013.

Additionally, his K% in 2013 was 3.8% higher than his previous career high, so I tend to expect a slightly lower rate in 2014 (though his contact rate in 2013 was also the lowest in his career, so if that is a trend, it is possible the K% could stay).

I’m still a firm believer in the idea that the past management, while trying to teach Castro to be selective and patient, actually taught him to take pitches for the sake of, well, taking pitches.  This could also potentially explain the low contact rate.  The numbers indicate that he didn’t learn to distinguish balls from strikes any better, and that maybe for him, the best approach is to swing at whatever looks good.

Given the striking similarities between his rookie season in which he hit .300 and garnered national attention as an upcoming star and 2013, it’s easy to dream about a bounceback 2014 season.  Only time will tell if that’s a reality, but I believe that Cubs fans have reason to be optimistic.

(I posted this earlier at the-billy-goat.mlblogs.com.  For more Cubs news and analysis, feel free to check out the blog.)

Is positional versatility underutilized? What does it cost for a player to transition from one position to another? MLB rules state that players currently in the game may switch positions at any dead ball, so why don’t teams shift their stronger fielders around the diamond based on batted ball profiles? Would it be worth it, in terms of runs, to try to have players play multiple positions and shift around the diamond? These are the questions that the following research attempts to answer.

I. The cost of transitioning between positions

The first thing that must be evaluated is what a player gains or loses when moving from one position to another. To do this, I looked at a player’s Total Zone and Defensive Runs Saved numbers, on a per inning basis, for each position they played at least 500 innings at. I did this for every player that met this minimum during the years from 2003-2013 (2003 was chosen as the cutoff because that is the first year DRS numbers are available). After data collection, for each position I took the total per inning number, subtracted from the position they were moving to, multiplied by 1200 innings for roughly a full season. I did this for every position, but I will only list the important positions for the purposes of this research. Since teams would most likely be shifting based on handedness and pull rates (though they theoretically could shift based on other things like GB/FB ratio if they had an outfielder who played a fantastic infield position or vice versa), this makes the important transitions ones shifting between the right and left side of the diamond. Those transitions are as follows:

(Note that due to how this was calculated, the inverse transitions, like 2B-SS, are the same number, but negative. This data was all gathered from Baseball Reference.)

SS-2B: 2.32 TZ runs for a season

SS-2B: 1.82 DRS

3B-1B: 4.68 TZ

3B-1B: 4.41 DRS

LF-RF:  -1.03 TZ

LF-RF: -2.05 DRS

(Personally, I had thought left field was more difficult, though maybe that is a result of mostly watching games in PNC park. It is also worth mentioning that on an individual basis, LF and RF are where Total Zone and Defensive Runs Saved had the largest disagreements)

So, as most people would expect, shortstop came out to be the most difficult position on the field, followed by second base and center field, third base and right field, left field, and first base. So, now that we’ve established that baseline for players transitioning between positions, we can move on to how many runs they would gain or lose in the process.

II. Estimating the number of fielding opportunities

Initially, I could not find detailed batted ball information broken down by handedness. So I attempted several methods of quantifying the impact, using the Cubs fielders as an example, and continually came up with the Cubs gaining 3-6 runs over the course of a season while shifting 20-30% of the time. However, those methods will not be discussed here. This is because Tony Blengino posted this wonderful article yesterday, complete with a batted ball breakdown for left and right handed hitters. So, it was revision time.

Step one was to take the number of fielding opportunities (also from Baseball Reference) for each of the examined positions, so I could get TZ/Fld and DRS/Fld numbers. This was also done with the transitions applied, to get TZ/Fld and DRS/Fld numbers for when they were playing the alternative position. Then, Blengino’s breakdown was combined with the average GB%, FB%, LD%, and IFFB% for left and right handed hitters. This gave a more specific batted ball breakdown for each area of the field. This breakdown is as follows:

With this information, I could get to work on estimating the number of fielding opportunities for each position. The first thing to do was to find the number of balls put in play against the Cubs for their 6149 PAs. For right handed batters I took the 6149 PAs * 58% (percentage of RHH) * 68.77% (percentage of balls put in play by RHH). For left handed hitters it was 6149 * 42% * 67.76%.

Unfortunately, this is where I ran into a small problem. I don’t know which balls hit in an area are attributed to which fielding position. For example, I don’t know what proportion of line drives to right field are caught by the first baseman, and what proportion is considered a ball the right fielder should field. This information is likely available, but I do not have it, and could not find it. If someone does find it, I would love to be able to do this more accurately. As it stands, I made educated guesses. The estimated fielding opportunities for each position, broken down by handedness, are as follows for Cubs fielders:

(Percent chance a ball in play was hit into that position’s area, and actual total number of fielding opportunities from last season in parenthesis)

1B: 93.88R (3.83%), 244.35L (13.96%)

1B Total:  338.23 (333 actual)

2B: 223.67R (9.12%), 273.44L (15.63%)

2B Total: 497.11 (496 actual)

3B: 351.59R (14.34%), 69.12L (3.95%)

3B Total: 420.71 (424 actual)

SS: 415.05R (16.92%), 170.37 (9.74%)

SS Total: 585.42 (584 actual)

LF: 459.42R (18.73%), 217.04L (12.40%)

LF Total: 676.46 (676 actual)

RF: 280.80R (11.45%), 331.27 (18.93%)

RF Total: 612.07 (662 actual)

(Estimations attempted to keep close to the actual number and proportion of fielding opportunities. I could not get it to happen properly for RF. It will have to be ironed out at a later date.)

III. Estimating the number of fielding opportunities and runs when shifting

The first thing worth mentioning is the total number of additional runs saved depends entirely on how often a team chooses to run this particular shift. When estimating for the Cubs, I chose to run this shift 25% of the time against all batters (Normally, one might only shift against left handed hitters, but the data suggests that Darwin Barney may be better off playing shortstop than Starlin Castro, so the Cubs will be shifting 25% of the time against all hitters). The first thing to do is to find out a position’s number of fielding opportunities when it is shifting to cover someone else 25% of the time, and when it is covered 25% of the time.

When covering, this is done by taking the number of fielding opportunities when the ball is more likely to be hit at them (like when a 1B is facing a LHH) + 25% of the position being switched to (3B against RHH) + 75% of opportunities when the ball is less likely to be hit at them (1B against RHH). So, a 1B would be playing 1B against every LHH, 3B against 25% of RHH, and 1B against the other 75% of RHH. For being covered, it is the opposite. All fielding opportunities when it is less likely to be hit at them (1B against RHH) + 25% of the alternative position (3B against LHH) + 75% of their original opportunities (1B against LHH). The new total number of estimated fielding opportunities for covering and being covered is as follows:

1B

Original: 338.23

Covering: 402.66

Covered: 294.42

2B

Original: 497.11

Covering: 544.95

Covered: 471.34

3B

Original: 420.71

Covering: 464:52

Covered: 356.28

SS

Original: 585.42

Covering: 611.19

Covered: 537.58

LF

Original: 676.46

Covering: 705.02

Covered: 631.80

RF

Original: 612.07

Covering: 656.72

Covered: 583.51

Essentially, this would get your strongest fielders more fielding opportunities, provided they are still strong after making the transition. Converting the previous formula to runs is simple, since we took both the regular and alternative position’s TZ and DRS runs per fielding opportunity. So for covering this becomes the more likely side * TZ(or DRS)/Fld + 25% of the alternative position’s strong side * AltTZ(or AltDRS)/Fld + 75% of the original weaker side * TZ/Fld. For being covered, the runs per fielding opportunity are added into that previous formula in the same way. That gives us the total number of runs for covering and being covered as follows:

When optimizing the lineup, since one of each pairing (1B-3B, 2B-SS, LF-RF) must be covered, both Total Zone and Defensive Runs Saved agree that 1B should cover for 3B (due to a love of Rizzo’s defense. TZ would disagree if Valbuena had played the whole year) and 2B should cover for SS (both metrics love Barney and dislike Castro). They disagree on RF and LF, where TZ thinks LF should cover, and DRS thinks RF should cover.

If optimized for Total Zone runs, shifting 1B-3B, 2B-SS, and LF-RF 25% of the time results in a total TZ runs for these positions of 7.81, which is a 2.81 run improvement over the original lineup.

If optimized for Defensive Runs Saved, shifting 1B-3B, 2B-SS, and RF-LF 25% of the time results in a total DRS of 22.31, which is a 2.31 run improvement over the original lineup.

IV. Conclusions

Running this shift for the Cubs 25% of the time resulted in a gain of 2-3 runs over the course of the season. This is not an insignificant amount of runs, but there are some things that need to be mentioned.

1. This shift is run 25% of the time against the average for left and right handed hitters. If a team is really going to shift 25% of the time in this method, they will do it against the 25% most extreme pull hitters for each handedness. I do not know the batted ball profiles of the most extreme pull hitters, but it would result in more fielding opportunities when covering, and fewer when being covered. This would likely increase the total number of optimal runs gained significantly. Since I do not have those profiles, I am unsure by what specific margin, but I would love to be able to know.

2. This enables you to somewhat “hide” a poor fielder, particularly at first base. The greatest difference in the odds of a ball being hit at them is between first and third base. If one fielder was particularly poor, you could make sure the odds of a ball being hit to him were always low. The greater the difference between the positions being switched, the greater the overall runs gained are for the season.

3. The Cubs were a terrible team to choose. I initially thought of this idea as I was speaking with a member of their front office, so I did this work on their team specifically. The reason the Cubs are a poor team to choose is because the disparity between the positions being switched is relatively small, except for 2B-SS which has a smaller impact. As mentioned above, this results in a smaller amount of runs gained. A team with a large disparity between first and third would see a far greater impact, particularly with a very good third baseman and poor first baseman due to the transition between positions. I will likely do this with additional teams in the future.

4. As mentioned, this was only run 25% of the time. The more often it is run, the more total runs will be gained.

5. This could be done far more accurately. I do not have all the information I would like available to me right now. I know that an entity like Baseball Info Solutions already records batted ball data to a large number of vectors on the field, as that is how DRS is calculated. That information could be used to come up with far more accurate results in terms of the exact likelihood a batted ball will be fielded by a specific position.

6. The transitions between various positions vary widely on an individual basis. I used the average numbers over a very large sample, so it should be a decent approximation, but every player is different. For every player that went from a very poor shortstop to an excellent second baseman, there is one who performed worse in the same transition. However, due to the transition values roughly lining up well with the positions that are generally known as being difficult, I have no issue with using them.

7. I did not look into whether shifting defensive positions could come with a reduction offensively. Theoretically, a player may slide a bit if he has to focus more attention on fielding multiple positions. I have not yet looked into this. If such a reduction exists, it could possibly be neutralized by an organizational philosophy embracing positional flexibility as players develop.

Overall, the Cubs could likely gain around 3 runs by shifting 25% of the time. If a team has a greater difference between fielders, and shifts with greater frequency, I don’t think it’s unreasonable to expect that team to improve by 1-2 wins over the course of the season. Shifting has grown far more popular lately, and it has been demonstrated to improve overall defense. I believe this is an extension of shifting. It makes sense to shift your fielders to where the other team hits the ball most. It also makes sense to shift players in this manner, and give your better fielders more opportunities to field the ball while giving your poorer fielders fewer opportunities. If you’re going to put a fielder where they hit the ball most, you might as well make it the fielder that is most likely to make a play.

V. A more extreme example

When I wrote this article a few days ago (but hadn’t decided to post it yet) I mentioned that the Cubs were not the greatest choice of team. So, I ran it on a more extreme example, and with greater frequency. As far as frequency is concerned, I upped it from 25% of the time to 50% of the time. For the team, I needed a team with an excellent third baseman, and below average first baseman. The first team that I thought of was the Orioles, so that is the team I used. Considering this is just a quick example to demonstrate the top end of the spectrum rather than the bottom, and the process was not changed, I will not walk through the process in detail again and will just provide the total runs.

If optimized for Total Zone runs, shifting 3B-1B, 2B-SS, and RF-LF 50% of the time results in a total TZ runs for these positions of 49.34, which is a 15.34 run improvement over the original lineup.

If optimized for Defensive Runs Saved, shifting 3B-1B, SS-2B, and LF-RF 50% of the time results in a total DRS of 44.65, which is a 14.65 run improvement over the original lineup.

(For reference, the Orioles when run 25% of the time were approximately an 8-9 run improvement)

With the same potential improvements and diminishments as mentioned in the first example, this is more of an idea of the top end of the spectrum. The Orioles, already a strong defensive team, could potentially gain about 1.5 wins by shifting in this manner 50% of the time. There are definite caveats to consider and improvements to make, but shifting like this could have an extreme defensive impact.

Welcome to the 3^rd annual forecast competition, where each forecaster who submits projections to bbprojectionproject.com is evaluated based on RMSE and model R^2 relative to actuals (see last year’s results here).  Categories evaluated for hitters are: AVG, Runs, HR, RBI, and SB, and for pitchers are: Wins, ERA, WHIP, and Strikeouts. RMSE is a popular metric to evaluate forecast accuracy, but I actually prefer R^2.  This metric removes average bias (see here) and effectively evaluates forecasted player-by-player variation, making it more useful when attempting to rank players (i.e. for fantasy baseball purposes).

Here are the winners for 2014 for R^2 (more detailed tables are below):

Place

Forecast System

Hitters

Pitchers

Average

1st

Dan Rosenheck

2.80

2.50

2.65

2nd

Steamer

1.60

6.00

3.80

3rd

FanGraphs Fans

5.80

2.75

4.28

4th

Will Larson

6.60

3.00

4.80

5th

AggPro

6.40

4.25

5.33

6th

CBS Sportsline

5.40

8.00

6.70

7th

ESPN

6.60

7.50

7.05

8th

John Grenci

8.00

8.00

9th

ZiPS

9.80

7.25

8.53

10th

Razzball

6.80

10.25

8.53

11th

Rotochamp

8.60

9.00

8.80

12th

Sports Illustrated

8.80

12.00

10.40

13th

Guru

10.60

12.00

11.30

14th

Marcel

11.20

12.50

11.85

And here are the winners for the RMSE portion of the competition:

Place

Forecast System

Hitters

Pitchers

Average

1st

Dan Rosenheck

2.60

2.00

2.30

2nd

Will Larson

3.60

2.50

3.05

3rd

Steamer

1.80

5.00

3.40

4th

AggPro

4.00

3.00

3.50

5th

ZIPS

6.00

5.75

5.88

6th

Guru

4.80

7.25

6.03

7th

Marcel

6.20

8.50

7.35

8th

John Grenci

7.50

7.50

9th

Rotochamp

9.40

9.00

9.20

10th

ESPN

9.20

10.50

9.85

11th

Fangraphs Fans

11.80

8.75

10.28

12th

Razzball

9.40

11.25

10.33

13th

Sports Illustrated

10.60

11.75

11.18

14th

CBS Sportsline

11.60

12.25

11.93

I’m beginning to notice some trends in the results across years.  First, systems that include averaging do particularly well.  This is pretty well established by now, but it’s always useful to reflect upon.  It’s been asked in the past to perform evaluations separating forecasts computed by averaging with those that do not include information from others’ forecasts (more “structural” forecasts). I decided not to do this because the nature of the baseball forecasting “season” makes it impossible to be sure forecasts are created without taking into account information from others’ forecasts. This can include direct influence (forecasting as a weighted average of others’ forecasts), but can also occur in more subtle ways, such as model selection based on forecasts that others have put forward.  Second, FanGraphs Fans are always fascinating to me, and how they can be so biased, but yet contain some of the best unique and relevant information for forecasting player variation. The takeaway from the Fans forecast set is that crowdsourced-averaging works, as long as you can remove the bias in some way, or ignore it by instead focusing on ordinal ranks.

Some additional notes: it would be interesting to decompose these aggregate stats in to rates multiplied by playing time, but it’s difficult to gather all of this for each projection system. Therefore, I focus on top-line output metrics.  Also, absolute rankings are presented, but many of these are likely statistically indistinguishable from each other.  If someone wants to run Diebold-Mariano tests, you can download the data used in this comparison from bbprojectionproject.com

Thanks for reading, and please submit your projections for next year! Also, as always, I welcome any comments, and I’ll do my best to respond.

R^2 Detailed Tables

system

r

rank

hr

rank

rbi

rank

avg

rank

sb

rank

AVG

AggPro

0.250

6

0.42

9

0.308

8

0.32

1

0.538

8

6.4

Dan Rosenheck

0.296

3

0.45

1

0.340

3

0.3

3

0.568

4

2.8

Steamer

0.376

1

0.45

2

0.393

1

0.31

2

0.572

2

1.6

Will Larson

0.336

2

0.43

6

0.345

2

0.21

13

0.509

10

6.6

Marcel

0.146

12

0.36

12

0.236

12

0.27

8

0.477

12

11.2

ZIPS

0.118

13

0.42

8

0.230

13

0.3

4

0.504

11

9.8

CBS Sportsline

0.278

4

0.44

3

0.320

4

0.25

10

0.542

6

5.4

ESPN

0.241

7

0.43

5

0.317

5

0.29

7

0.532

9

6.6

Razzball

0.239

8

0.43

4

0.314

6

0.24

11

0.553

5

6.8

Rotochamp

0.234

9

0.41

10

0.287

9

0.23

12

0.569

3

8.6

Fangraphs Fans

0.268

5

0.42

7

0.272

10

0.3

6

0.574

1

5.8

Guru

0.186

11

0.33

13

0.263

11

0.3

5

0.476

13

10.6

Sports Illustrated

0.221

10

0.4

11

0.314

7

0.27

9

0.541

7

8.8

system

W

rank

ERA

rank

WHIP

rank

SO

rank

AVG rank

AggPro

0.13

3

0.15

4

0.25

4

0.402

6

4.25

Dan Rosenheck

0.17

1

0.19

2

0.27

2

0.406

5

2.5

Steamer

0.09

6

0.15

3

0.26

3

0.341

12

6

Will Larson

0.16

2

0.19

1

0.24

5

0.413

4

3

Marcel

0.05

14

0.02

13

0.17

9

0.293

14

12.5

ZIPS

0.09

7

0.07

9

0.21

6

0.375

7

7.25

CBS Sportsline

0.1

5

0.08

7

0.15

10

0.359

10

8

ESPN

0.08

10

0.05

11

0.2

7

0.43

2

7.5

Razzball

0.06

13

0.07

8

0.14

12

0.374

8

10.3

Rotochamp

0.08

9

0.06

10

0.17

8

0.359

9

9

Fangraphs Fans

0.11

4

0.08

5

0.28

1

0.435

1

2.75

Guru

0.07

11

0.05

12

0.11

14

0.343

11

12

Sports Illustrated

0.09

8

0.02

14

0.14

13

0.338

13

12

RMSE Detailed Tables

system

r

rank

hr

rank

rbi

rank

avg

rank

sb

rank

AVG

AggPro

22.495

4

7.34

4

23.217

4

0.03

4

7.096

4

4

Dan Rosenheck

20.792

3

6.91

1

21.867

2

0.03

5

6.467

2

2.6

Steamer

20.355

2

7.02

2

21.817

1

0.03

3

6.258

1

1.8

Will Larson

20.091

1

7.2

3

22.234

3

0.03

8

6.864

3

3.6

Marcel

23.473

6

7.51

6

23.831

6

0.03

7

7.334

6

6.2

ZIPS

25.380

7

7.43

5

25.662

7

0.03

1

8.048

10

6

CBS Sportsline

25.866

10

8.63

13

26.837

10

0.03

12

8.527

13

11.6

ESPN

25.698

8

8.37

12

26.418

9

0.03

6

8.120

11

9.2

Razzball

25.831

9

8.01

9

27.842

12

0.03

9

7.920

8

9.4

Rotochamp

26.199

11

8

8

25.995

8

0.04

13

7.686

7

9.4

Fangraphs Fans

26.854

13

8.12

10

30.804

13

0.03

11

8.289

12

11.8

Guru

23.187

5

7.58

7

23.608

5

0.03

2

7.198

5

4.8

Sports Illustrated

26.609

12

8.24

11

27.173

11

0.03

10

8.009

9

10.6

system

W

rank

ERA

rank

WHIP

rank

SO

rank

AVG rank

AggPro

4.4

3

1.031

4

0.17

4

47.01

1

3

Dan Rosenheck

4.25

1

1.014

1

0.17

1

47.9

5

2

Steamer

5.02

8

1.030

3

0.17

2

49.45

7

5

Will Larson

4.34

2

1.017

2

0.17

3

47.44

3

2.5

Marcel

4.62

5

1.158

13

0.18

8

50.84

8

8.5

ZIPS

4.78

7

1.101

7

0.17

5

47.85

4

5.75

CBS Sportsline

5.56

13

1.134

11

0.19

11

57.14

14

12.3

ESPN

5.81

14

1.126

10

0.18

7

53.54

11

10.5

Razzball

5.39

12

1.115

8

0.19

12

55.55

13

11.3

Rotochamp

4.71

6

1.138

12

0.18

9

51.81

9

9

Fangraphs Fans

5.29

10

1.123

9

0.17

6

52.57

10

8.75

Guru

4.51

4

1.093

6

0.19

13

48.79

6

7.25

Sports Illustrated

5.33

11

1.176

14

0.18

10

55.32

12

11.8

John Grenci

5.14

9

1.080

5

0.19

14

47.26

2

7.5

Last week I looked at the 2014 free agent class and how some of the big contracts of the offseason stacked up against our idea of fair market value. Afterwards, I tried to use this model to predict contracts for Ubaldo Jimenez and Ervin Santana, but came across the problem of factoring in the draft pick compensation, which I left out of my initial article simply because of its complexity. Draft pick value is highly variable, and it gets more difficult to assign costs when a team surrenders multiple draft picks. Regardless, I wanted to take a closer look  because of the impact it will have on the top remaining free agents.

Let’s assume that each team places a dollar value on their first unprotected draft pick ($X). In a vacuum, if a team evaluates a player’s performance as being worth a certain amount of money ($Y) over Z number of years without any draft pick compensation, then they should only be willing to pay $(X-Y) if they will be forced to surrender a draft pick. For example, if the Orioles think that Ubaldo Jimenez would be worth $60M over 4 years, but value their first round pick at $10M, then they should only be willing to pay him $50M for those same four years. Of course this isn’t really fair to the player, but those are the rules.

So, how much do teams value their draft picks at? There’s no way to know for sure, but some research has already been done on the matter. Andrew Ball at Beyond the Box Score explored this question last summer, assigning a dollar value to certain tiers of draft picks. For our purposes, the important ones are the 8-15 draft picks (worth an average of $15.2M of net value) and 16-30 (worth $7.17M). This sounds like it’s in the right ballpark, but seemed a little bit low to me. Sky Andrecheck calculated average WAR by draft pick back in 2009, and found that the 10th overall pick was worth an average of 6.2 WAR, while the 30th pick was worth 3.6 WAR, numbers slightly higher than the more recent study. We also have to account for the fact that a team will pay around 30-35% of a player’s market value while under team control, and that they have to pay an average of $2M to sign a player drafted in the mid-to-late first round.

Taking all of this into account, I’d estimate that the net value of an unprotected first round draft pick can range anywhere from $10-25 Million dollars. This may sound a little bit high, but with the cost of a win at $6-7M, even a player who produces only 0.5WAR per season and costs a total of $10M for those six years of team control can provide $10M of savings. Since the teams signing high-priced free agents are usually pretty good and therefore have a lower draft pick, we’re probably looking at $10-15M in most cases. (Early second round picks might be closer to $8M.)

While this is great in theory, how have the attached draft picks affected the signings so far this offseason? In the table below, I included a more standard model — $6.5M per win with 5% inflation and standard aging (from Jeff Zimmerman’s contract calculator) — along with a modified version of my previous model. I didn’t want to mess with the aging curves so I used the same as Zimmerman (-.5 WAR/year until age-32 season, -.7 WAR/year after), I bumped inflation up to 6%, and I didn’t want to push a win past $7M so instead I gave a slight boost to the players’ WAR projections (just 0.2 WAR). I think it’s fair to assume that the team with the highest bid also expects the player to perform slightly better than projected.

The first two columns show the player and their total salary (assuming no options are vested or picked up by the team). The next three columns represent the “Standard” projection, followed by my “Modified” projection. The top six players were extended qualifying offers, so the signing team had to surrender a draft pick. The bottom eight players had no such compensation attached.

Regardless of which model you use, the conclusion is the same: so far this offseason, players who have cost the signing teams a draft pick have actually made more than the models predict. Much more. On average, these six players have been overpaid by about $9 million, while players with no draft pick compensation attached have actually been underpaid by an average of $7 million. This is the complete opposite of what we would expect if teams are acting rationally when it comes to the cost of their draft picks. When forced to pay what is essentially a $10M fee, these teams not only didn’t penalize the player, but actually paid them more. This could mean one of a few things:

Teams are willing to pay a premium for “elite” talent. The six players with free agent compensation attached include the only four free agents projected to be worth at least 3 WAR in 2014, along with the two next-best available outfielders. While Dave Cameron has long espoused the idea that the cost of a win is linear and there is no “bonus” for elite players, the fact that these six players haven’t been penalized for the attached draft pick tells us that teams may be willing to pay more to land the big guns. This could have to do with elite players (and their agents) being unwilling to take a discount because of the attached draft pick and there being at least one team who will cave and give the big contract, essentially ignoring the additional cost. This brings us to the second possibility:

Teams are not acting rationally with their draft picks. No prospect is a sure thing, so it could be easy for a team to talk itself into giving up a hypothetical player who may never make the majors in order to get a stud on their roster for the upcoming season. There are a lot of other factors here, notably the fact that signing team is usually at a high-leverage spot in the win curve and doesn’t know where they will be when the draftee they are giving up would be ready to contribute. Texas, for example, has a few players locked up long term, but also has some key pieces (Darvish and Beltre) who could be gone in a few years. Positional needs also certainly play a role here, but even when a team is willing to spend big money to improve in the short term, it’s tough to argue that they couldn’t have allocated their money better by upgrading at several other positions for the same cost (as Dave Cameron argued earlier this week). The Rangers, for example, could have kept David Murphy (2 years, $12M), signed Chris Young (1/$7M) for outfield depth, improved behind the plate with Jarrod Saltalamacchia (3/$21M), and bolstered their rotation with Matt Garza (4/$50M) instead of signing Choo, saving $40M and a first-round draft pick. The last possibility is that…

Something is wrong with the model. The other difference between the six players with a draft pick attached and the remaining eight is the length of the contract (an average of 6 years vs 3.5 years). If the teams signing these contracts expect the cost of a win to increase faster than the 5-6% inflation rate we project, then the middle and later years of this contract look a little bit better, but not by much. The only way to make the draft-pick contracts look better is if the players age much more gracefully than the average player, a pretty big risk to take on a $100 Million investment. The model also doesn’t account for any impact the signings may have on ticket sales. Five of the six big contracts came from big-market teams with lucrative TV deals, and teams may be willing to pay a premium to invigorate their fanbase with the addition of an elite player that might not be accomplished by signing a few mid-tier free agents who might add the same total value to the team. While I can’t speak to the economics, we all know that at the end of the day, the most important thing for the fans is to win.

While this is an interesting phenomenon, it doesn’t help us predict the kind of contracts the remaining free agents will get. As we saw with Kyle Lohse last year, while teams may be willing to look past the loss of a draft pick for an elite player, they might not if player in question is closer to league-average. While the free agents with a draft pick attached have actually signed for significantly more than market value, I wouldn’t expect to see this trend continue this offseason. With most of the contenders’ rosters pretty much ready for the season, they’ll only sign that extra piece if the price is right, including the loss of the draft pick. When it comes to players like Nelson Cruz and Kendrys Morales who may only generate $20M of value (2-3 WAR) over the next two years, the $10+ Million valuation of a draft pick explains why the market for them has been so slow. While things worked out fine last year for all of the free agents who turned down their qualifying offer, we could see a couple players really suffer this year, which may make agents — and teams — think twice about the qualifying offer next offseason.

Jeff Sullivan recently suggested that despite his reputation Tom Glavine did not pitch to a significantly more generous strike zone. Sullivan points out Glavine did not get significantly more called strikes than other pitchers, even during the peak of his career. Sullivan’s analysis piqued my interest and made me wonder if Glavine’s reputation for getting a wider strike zone helped him succeed in ways beyond called strikes.

Glavine’s reputation alone likely influenced a batter’s behavior at the plate, encouraging batters who were behind the count to swing at questionable pitches. Batters believed if they did not swing these pitches would be called strikes for Glavine (when a batter swings at a pitch out of the zone when the batter is ahead of the count that has more to do with a pitchers stuff than the batter giving the pitcher an expanded zone). So, what would we expect from a pitcher who is getting batters to expand the strike zone? You would expect batters to make poor contact, yielding a lower BABIP. The batter would most likely swing at pitches outside the zone when the batter is behind the count.

Based on this reasoning, I hypothesize that Tom Glavine will see a greater reduction in quality of contact when he gets ahead of the count than a league-average pitcher. I’m going to look at the time span from 1991 to 2002 because that was the time span Jeff looked at and because I like palindromes.

To measure quality of contact I will be looking at BACON (batting average on contact). BACON is slightly different than BABIP because BACON includes home runs. If batters are expanding the strike zone when Glavine is ahead in the count we should see the quality of contact decrease. To measure the decrease in quality of contact, I will look at the ratio of BACON when Glavine is ahead to BACON to when Glavine is behind (the lower the number the greater improvement the pitcher experiences by getting ahead in the count). I will refer to this measure as EXP (a lower EXP shows a greater decrease in quality of contact, an EXP above 100 shows an increase in quality of contact).  The graph below compares Glavine’s EXP to the league average EXP for each season during the 11-year span.

 The league-average EXP is consistent year to year, hovering around 91, which suggests batters expand the strike zone for most pitchers when batters are behind in the count. Glavine’s EXP is not always better than the league-average EXP. In ‘94 and ‘96 Glavine was actually worse when ahead in the count than when he was behind.  This is to be expected because BACON takes a while to stabilize. Looking at Glavine’s data for a single season is subject to a fair amount of random noise because you have a relatively small sample of data. One season for Glavine gives us about 170 fair balls with Glavine ahead and 280 fair balls with Glavine behind. However, over a larger sample BACON stabilizes. At around 2,000 fair balls (more than in a single season for Glavine) BACON stabilizes. For example, when looking at the league-average EXP for a full year BACON is stable — with 3,500 fair balls with the pitcher ahead of the count and 4,600 fair balls with pitcher behind the count.

To make sure we are not just attributing skill to some random variation we need to look at a larger sample for Glavine. Over the 11 year span form 1991-2002 Glavine induced weaker contact (lower BACON) than the league average both when he was ahead of the count and behind the count. This is not surprising as we would expect a good pitcher to be better than average ahead and behind the count.  What’s interesting is Glavine has better than league-average EXP  (87 vs. 92) which suggests Glavine is better at expanding the strike zone than league-average pitchers. This comes with the caveat that while we have 3,056 fair balls when Glavine is behind the count, we only have 1,853 fair balls when Glavine is ahead — just shy of the 2000 at which the measure should stabilize.  Even so, the difference between Glavine’s EXP and the league-average EXP is very convincing.

To stabilize BACON, I increased the sample by looking at all the balls put in play. I compared balls put in play when the pitcher had two strikes to balls put in play when the pitcher had fewer than two strikes, which led to EXP2: the ratio of BACON when a pitcher has two strikes, to when he has fewer than two strikes. The table bellow shows a comparison of the quality of contact in two strike counts to non-two strike counts.

Even with this larger sample size Glavine’s BACON is still lower than the league average in respective counts. More importantly, his EXP2 is still better than league average (although higher than his EXP).  Pitchers in general try to induce weaker contact when they are ahead of the count, but the data shows Glavine is doing something special to induce even weaker contact.

Is Glavine getting batters to give him a wider strike zone? We cannot definitively say what is causing this pattern in the data, but we are seeing the type of numbers we would expect to see if the batter was giving him a wider strike zone.

All splits number are from Baseball-Reference.

As we look for candidates to regress in 2014, a popular choice is Houston catcher Jason Castro for it seems the Astros backstop has two targets on his back: a high strikeout rate last year of 26.5% and a high BABIP of .351. Steamer and Oliver both project a steep drop in BABIP that will drag his batting average from a solid .276 to the .250s. As Brett Talley wrote, Castro screams regression.

Or does he?

Talley points to Castro’s strikeout rate that has been topped only 61 times in the past decade, and only four times the player matched or bettered a batting average of .276. But that measure may miss the mark. No one is suggesting Castro’s strikeout rate will worsen. When it comes to batting average, the critical question, then, is whether he can come close to maintaining a high BABIP.

On that question the evidence is more promising. In the last decade, only 38 of 1,509 batters have had an infield-fly rate lower than Castro’s 1.8%. Only 47 had a line-drive rate higher than Castro’s 25.2%. Taken together, those two select groups actually have 10 matches — players who managed both a lower infield-fly rate and higher line-drive rate. Here they are along with their BABIP, batting average and strikeout rate:

Player, year, BABIP, Avg., K-rate

Joe Mauer, 2013, .383, .324, 17.5%

Joey Votto, 2011, .349, .309, 12.9%

Howie Kendrick, 2011, .349, .297, 17.3%

Matt Carpenter, 2013, .359, .318, 13.7%

Michael Young, 2007, .366, .315, 15.5%

Joey Votto, 2013, .360, .305, 19%

Adam Kennedy, 2006, .313, .273, 14.3%

Bobby Abreu, 2006, .366, .297, 20.1%

Michael Young, 2011, .367, .338, 11.3%

Chris Johnson, 2012, .354, .281, 25%

What might we gather from this evidence?

(1) All but one of the players topped .276.

(2) The skills involved seem somewhat repeatable: Votto and Young each appear twice and as a group they generally in their careers combined a high LD rate, low IFFB rate and a high BABIP.

(3) We wouldn’t expect a player who whiffs a quarter of the time to have a batting average as high as someone who strikes out half as much while putting up similar LD and IFFB rates. Castro is unlikely to approach the median average of this group of .307.

(4) Castro doesn’t need to approach the median average to avoid significant regression. He is more likely to hit closer to last year’s mark than he is to hit in the .250s.

I recently wrote about teams no longer paying a premium to land closers with 9^th inning experience, instead choosing to spend less and acquire very good relievers with little 9^th inning experience.  It seems teams have moved away from the conventional thinking that a closer must have experience or a special mentality in order to succeed as a closer. This made me wonder whether the view that a closer must have to throw hard was still alive. It is important to note that throwing harder certainly gives the pitcher an advantage, but it is also very possible to succeed without being among the hardest throwers. In order to look at this, I looked at all Relief Pitchers with at least 10 saves from 2010-2013 and separated them into two groups based on their average fastball velocity (aFV), based on P/Fx. The aFV for the entire group of 93 pitchers was 93.0. I chose 93 as the divider between High Velocity (HVelo) closers and Low Velocity (LVelo) closers.

Looking at the breakdown of the two groups, the HVelo group included 53 relief pitchers and the LVelo group included 40 relief pitchers. The difference of 13 pitchers between the groups should not affect the results too much, as the sample is big enough to negate this discrepancy. However, the difference does say something about closers during this period, as there were many more hard-throwing closers than low-velocity closers. Looking into the numbers between these two groups for this four-year period, it is clear that the HVelo pitchers were more effective. They averaged 15 more saves over that period and outperformed the LVelo pitchers in every statistic, except BB/9 and BABIP. LVelo pitchers walking fewer batters per nine innings is not surprising, as they usually have better command in order to compensate for fewer strikeouts. HVelo closers were also better at fulfilling their role, as they had a 81.7% conversion rate, while LVelo closers converted just 77.5% of their opportunities. If you look at this four-year window it is clear that the harder-throwing closers have been more successful and there have also been many more hard throwers used in the 9^th inning than LVelo relievers.

However, if we take a look at just the final year of this four-year period, we see something different. Looking only at 2013 and relief pitchers that had at least 10 saves, I broke the pitchers into two groups using the same criteria as before: HVelo is all pitchers with aFV higher than 93 mph and LVelo is all pitchers with aFV below 93 mph. This is the same cutoff as for the four-year period because the mean is relatively unchanged, at 92.8. Unlike from 2010-2013, these two groups were essentially even: of the 37 qualified pitchers, 19 were in the HVelo group and 18 were in the LVelo group. This alone shows that teams are more comfortable using effective relievers in the 9^th inning, even if they do not light up the radar gun.

Just using more LVelo pitchers does not actually prove they are as effective or better than HVelo relievers, but it does show teams may be moving away from the conventional belief that closers must throw hard. When I looked at the numbers of these two groups, I saw evidence that the LVelo group was certainly as effective, if not more effective, than the HVelo group. The HVelo group saved just one game more on average; however, their save percentage was 87%, compared to the 88.7% of the LVelo group. Just as before, the LVelo outperformed the HVelo group in BB/9 and BABIP, but they also had a better average ERA than the HVelo group. While the HVelo pitchers had a much higher K/9 (10.7 vs. 8.4) and a better HR/9, the LVelo group did a better job at preventing runs and also a slightly better job at converting their save opportunities.

Certainly, looking at just one season is not a very large sample, but I believe last season was the beginning of a trend. The role of the closer has evolved quite a bit in recent years and many long-held beliefs are being dispelled. I believe teams have realized that a pitcher does not have to be the hardest thrower in the bullpen, instead he just needs to be the most effective. In 2013, both teams that reached the World Series turned to closers without previous experience and who were both among the LVelo group. The Cardinals chose to give Edward Mujica the closer’s role, instead of turning to young flamethrower, Trevor Rosenthal. Mujica turned in a fantastic season with 37 saves and a 2.78 ERA. The Red Sox also entrusted their 9^th inning duties to a member of the LVelo group, Koji Uehara. Uehara took over as closer after both of the Red Sox’s other options suffered season-ending injuries, but Uehara still totaled 21 saves and a 1.09 ERA. Both these closers overcame common beliefs that closers need experience in the 9^th inning to succeed and must also throw hard.

* I would have liked to look at a larger sample than 2010-2013, but I did not feel comfortable using Pitchf/x data older than 2010. Since its inception in 2006, Pitchf/x has vastly improved and become much more accurate.  

* This post has also been posted on my personal blog, baseballstooges.com.

This post is going to examine the value of the opt-out clause in both the Clayton Kershaw and Masahiro Tanaka contracts. I think this is interesting because the Yankees gave Tanaka an opt-out one year earlier, and gave that option to a commodity with a much more uncertain value.  As we will see, the opt-out clause for Tanaka is going to be a lot more costly to the Yankees than the clause was for Kershaw and the Dodgers.

Let’s start with the projections for each player. ZIPS and STEAMER don’t have anything for Tanaka, but we can make a guess based on the contract he was given that he’s at least expected to be worth a lot of wins over the next several years.  Since he’s the same age, it seems approximately fair to start with 5 wins, and reduce in the same pattern that Kershaw got.  I’ll use the values from Dave Cameron’s excellent article the other day for Clayton Kershaw, and I’ll also take the $/WAR from his projected inflation.  Excess value is the value of that player’s WAR, minus salary.

The key here is not going to be the expected value — it’s going to be the possible variation. Kershaw is expected to get 5.5 wins next year because of the ever-present risk of injury — there are probably Dodgers fans going nuts over that projection because they know that a healthy Kershaw, pitching like he can, is going to be worth closer to 7 wins.  There are certainly scenarios where he manages that, but also scenarios where he tears his rotator cuff and is worthless.  While there is a continuum of possibilities, let’s break the world into two scenarios for each pitcher, an up and a down. The only requirement is that the weighted average of each scenario has to average out to their projections.  I’ve made up some basic numbers here, and you might think they’re reasonable, you might think they’re not, but the point of this article is to illustrate how one extra year and some extra volatility can affect the value of an opt-out clause.

In each scenario, I make the downside a mirror image of the upside. For Tanaka, because he is an unproven commodity, I’ve added 2 WAR to the upside, and subtracted 2 for the downside. For Kershaw, I’ve just added/subtracted 1 for each. I gave each scenario a 50-50 chance of happening.

Let’s think about what happens in each scenario when it comes time to exercise the opt-out clause.  Shockingly, GOOD Kershaw and GOOD Tanaka each exercise the clause. We can see this reflected in the positive “excess value” column of each chart — age 29 for Tanaka and age 30 for Kershaw. They could get more on the free market, so they will. BAD Kershaw and BAD Tanaka both stick with their contracts, because they’re being paid more than market value.  Let’s re-do the charts from the teams’ perspectives, reflecting the opt-out clauses now:

Now let’s take the expected value of these two scenarios, which is in this case a simple average:

We can see that in both cases, the post-option years of the contract become negative propositions for the teams — in fact, they would have to be, by how we’ve implicitly stated the conditions under which the players opt out: if the player were expected to provide positive value to his team, he would opt out.

So how much is the option worth? Ignoring the $20 million posting fee, the Tanaka contract, sans opt-out, was expected to produce $63.9M in excess value for the Yankees. With the option, the expected excess value drops down to $26.1M.  That’s a drop of $37.8M. This could be thought of as the extra money Tanaka puts into his pocket from years 5 onward, if he comes into the league and becomes Justin Verlander.  Kershaw, on the other hand, would be expected to generate $32.3M for the Dodgers, without the opt-out. Now his contract is only worth $19.1M to them. That’s a reduction in value, but because we’ve made him less uncertain, and because the option occurs after year 5, not year 4, the reduction is only $13.2M.  So the extra year and the double variability make Tanaka’s option worth $24.6M more than Kershaw’s.

Again, this depends largely on the choices I’ve made for the range of possible outcomes, and I’ve kind of picked Tanaka’s projection out of thin air (since the excess value of the contract with the opt-out is only $6.1M, considering the $20M posting fee, I would argue that I’m not that far off). I could have made more possible outcomes, or maybe even defined a probability distribution function and integrated over that, if I knew how to do that sort of thing. The only lesson we’re going to be able to take from this is how one year and some extra variability affect the value of the opt-out clause.