Jered Weaver’s 2015 season has gone poorly. His actual and projected performance are both at career-worst levels, partly due to injury and mechanical issues. Most alarming is his large velocity drop; Weaver has lost 2.5 mph off a fastball that was already among the slowest in the majors. Throwing 85 mph is an ominous sign, as few pitchers can succeed at that velocity.

If there’s a silver lining, it’s that diminished velocity is nothing new to Weaver, who has long been able to push through it and dominate. From 2010 – 2014, Weaver lost about 1 mile off his fastball per year, yet posted an ERA- of 78, and a RA9-WAR (FanGraphs WAR based on actual runs allowed) of 25.9. How did the crafty Weaver prevent runs at a higher level than esteemed contemporaries like Cliff Lee, Adam Wainwright and David Price?

While support from one of MLB’s best defenses has helped, the keys for Weaver lie elsewhere. The fly ball pitcher is a fine fit for spacious Angel Stadium and its fly ball-suppressing marine layer. Weaver’s deceptive motion is also crucial; his violent, crossfire delivery allows him to hide the ball and helps his diminished stuff play up.

Those reasons, by themselves, are clear. Less obvious are how they might blend together to provide an additional boost; Weaver is said to be helped by the distinctive, sandy-colored rockpile that sits to the left of the batter’s eye at Angel Stadium. By releasing the ball more than three feet from the center of the rubber, Weaver pitches with the rockpile as the backdrop of his release. This makes the ball tougher for batters to pick up, reducing contrast at all times, but particularly in the daytime when the sun reflects off the rocks.

Jeff Sullivan has shown in several articles that Weaver likely takes advantage of these conditions. After breaking up Weaver’s career stats (through 2014) by time of day, home/road, and batter handedness, we continue to see a relationship emerge.

JERED WEAVER PITCHING SPLITS, 2006-2014 vs. LHB vs. RHB Time Park SO% BB% HR% SO% BB% HR% Day Angel Stadium 27.7% 6.6% 1.1% 25.8% 6.6% 1.7% Night Angel Stadium 20.9% 6.0% 2.1% 20.0% 5.1% 2.6% Day Road 19.0% 8.0% 3.2% 20.6% 6.1% 2.9% Night Road 17.7% 6.5% 3.5% 19.0% 7.7% 2.7%

In the daytime at Angel Stadium, Weaver has been an elite pitcher. Against batters on both sides of the plate, Weaver’s strikeouts spike and his home runs plummet, relative to the three other park/time subsets. The improvements against lefties in home day games are especially stark; compared to road matinees, his strikeout rate increases by 8.7 percent and his home run rate improves by 2.1 percent. A home park advantage vs. left-handed batters carries over to night games too, where his strikeout and home run rates top his road marks by 3.2 percent and 1.4 percent, respectively.

Weaver’s splits align with the rockpile theory. All told, it seems like an ideal match of a slinging pitcher, a sunny SoCal location, and a tan rockpile dreamed up by the Disney company to add flair, house groundskeeping equipment, and provide a napping spot for Troy Percival. But let’s take this theory a step further and go beyond Weaver—does the rockpile at Angel Stadium provide a league-wide advantage to right-handed pitchers with a release point far from the rubber?

Set-Up

This is a question of batters’ pitch recognition, and data will need to be partitioned into numerous subsets. Plate appearance-level stats will constantly present small sample size conundrums, even before any adjustments are made for context. Pitch-level numbers, on the other hand, lend themselvesnicely to studies of pitch recognition, allowing us to hone in on the batter vs. pitcher match-up and expand our sample size. With our two stats of choice—whiff percentage and non-chase percentage—we’ll compare players’ Angel Stadium/away splits in the PITCHf/x era of 2008–2014.

With whiff percentage, we’ll see if the rockpile harms batters’ ability to make contact. The stat is defined here as ((misses + foul tips)/swings)), and is adjusted for projected batter quality. With non-chase percentage, we’ll see if pitchers in front of the rockpile induce more chases on pitches out of the zone. Non-chase percentage is calculated as (1 – (swings on balls/balls)), where pitches landing outside the rule book strike zone are designated as balls. Non-chase percentage is obviously much like O-Swing percentage, but this definition better facilitated the hitter quality adjustments.

Accounting for the rockpile’s off-center location, we’ll examine only pitches thrown by right-handed pitchers to left-handed batters. We can more finely assess potential effects through these match-ups, as it’s lefty hitters who will need to stare into Angel Stadium’s rockpile at the point of certain righty pitchers’ release. More fortunate righty batters, in contrast, appear to view the standard green backdrop. You can see the difference at the right.

We’ll add a crucial level of complexity to the evaluation—PITCHf/x release point data. Once PITCHf/x biases were quelled though pitch type- and park-individualized corrections (see the appendix for a detailed explanation), I narrowed our focus to a specific window of release points. Horizontally, the window extends from the center of the rubber to four feet out toward third base (just a bit beyond Weaver territory); vertically, it includes pitches released between five and seven feet high. All pitches thrown from the window were placed into discrete six-by-six-inch bins, putting four equivalent bins inside of each square foot.

It’s logical that the rockpile’s effects are toughest in the daytime, but the lack of contrast from ball-to-rocks would figure to hurt batters at night, too. So we’ll compare performance in Angel Stadium day games vs. road day games, and then Angel Stadium night games vs. road night games. This will enable us to check if the magnitude of the rockpile advantage is different in the day than night, accounting for general temperature differences as well as possible variation in biorhythms—since some players will be “day people” and others “night people.”

Day games are defined as starting at 2:15 p.m. or earlier, and night games as 6 p.m. or later. Pitches thrown at exhibition sites and domed stadiums were removed to keep shadows and lighting similar. Also discarded were pitches thrown in retractable-roof stadiums when the roof was closed. Plate appearances of starting pitchers-as-batters were left out as well.

With the extensive framework in place, I used the delta method for all comparisons. Samples were matched up by pitcher, role (starting/relieving), release point bin, season, pitch type category, ball-strike count, and time of day. And then for the given subset, stats registered at Angel Stadium were compared with those accumulated elsewhere. For instance, say Weaver had generated a high whiff percentage on 0-2 off-speed pitches when pitching from a certain release point bin at home in the daytime in 2011. We’ll take that whiff percentage and compare it directly to his 0-2 off-speed whiff percentage netted from that release at other major league parks in 2011 day games. This mix of factors adds essential context into the whiff percentage and non-chase percentage splits.

Heat Map Overview

To compare the effectiveness of each release point bin, we’ll use heat maps. A consistent color spectrum will guide our analysis of all effects.

HEAT MAP REFERENCE Color Description Red Performance was enhanced by pitching at Angel Stadium White Performance was roughly equal at Angel Stadium as compared to other parks Blue Performance was better at MLB’s other parks than at Angel Stadium Gray At or away from Angel Stadium, that bin either A) didn’t contain at least 1 successful trial, or B) had less than 20 total trials The scales for effect size magnitudes are exactly alike across the heat maps—within the (-21%, +21%) range—making lightness/darkness of all colors directly comparable.

Researchers across all fields often deem a measure statistically significant when, with 95 percent confidence, they can reject the null hypothesis that the true estimate is equal to zero. Thus, zero isn’t within the scope of the preset confidence level. Here we won’t hang our hats on that 95 percent level, or even define a desired confidence level at the outset. Each box will assert our level of confidence in the Angel Stadium advantage by providing the highest possible level at which the value would be considered “significant.” So our confidence level for each box can span from ~0 percent to ~100 percent. The scales for effect size magnitudes are exactly alike across the heat maps—within the (-21 percent, +21 percent) range—making lightness/darkness of all colors directly comparable.

From there, how can we determine which pitchers can actually take advantage of the rockpile? Our prior is that pitchers like Weaver benefit, but that still presents ambiguity because we don’t have the coordinates of the rockpile’s position in the given batter’s sight line. So to evaluate the heat maps, we’ll hunt for trends and clusters of effects. If the rockpile effect is real, we should be circling the same group of hot zones on the left side of each heat map (in Weaver territory, from the catcher’s perspective). As we move rightward, examining pitchers with more standard release points and arm angles, we shouldn’t see any trends at all. Expect a combination of randomness and effect sizes hovering around white, ~0 values.

Whiff Percentage

We’ll begin by looking at starters’ daytime whiff percentage splits. Did the rockpile give slinging starters a special bat-missing advantage in Angel Stadium matinees?

The answer is both yes and no, because dark red boxes are found throughout the width of this heat map. Say we cut the hot zones in half with two bands, figuring that the orange loop is the approximate rockpile area and the gray loop is beyond the rocks’ scope. How, then, do the effect sizes compare?

STARTERS’ DAYTIME WHIFF% SPLIT Bin ANA Swing Total Road Swing Total ANA Whiff% Road Whiff% Difference (ANA – Road) St. Dev Confidence Level Rockpile Loop 1,013 1,629 28.0% 20.1% +7.8% 1.7% 99.992% Gray Loop 889 1520 19.9% 15.5% +4.5% 1.6% 96.6%

In the orange loop, starters register a whiff percentage that’s 7.8 percent higher at Angel Stadium than away from it. With a rather assured confidence level of 99.992 percent, we see that slinging starters did benefit. But the Big A advantage isn’t truly unique to them, as pitchers in the gray loop see their whiff percentage jump by 4.5 percent, also coming with a very strong confidence level.

There is a noteworthy +3.4 percent difference between the loops’ Angel Stadium gains, which is significant at the 68 percent confidence level. So the rockpile pitchers could be gaining an advantage on the non-rockpile pitchers—but the arbitrary definitions of the clusters prevent us from putting much stock in this difference. It’s more apt to say that all righties in the window get a boost by pitching their day games at Angel Stadium, regardless of their arm angle and the position of the rockpile. Totaled, the entire population of pitchers in the window see their whiff percentage jump 4.8 percent (with 99.93 percent confidence).

How do the splits change at night? Let’s take a look:

Again we see a consistent clump of reddish areas on the left, but the difference this time is that they’re partitioned off by both blue and white boxes around the -2 border. In the rightward area of the loop, we obtain more of the randomness we’re pursuing: red boxes mixed in more evenly with cold zones and minuscule values. How do the night-game results for looped-area pitchers compare to non-looped pitchers?

STARTERS’ NIGHTTIME WHIFF% SPLIT Bin ANA Swing Total Road Swing Total ANA Whiff% Road Whiff% Difference (ANA – Road) St. Dev Confidence Level Rockpile Loop 4,852 13,031 20.2% 17.7% +2.5% 0.7% 97.99% Non-Rocks 5,123 12,717 17.9% 18.4% -0.5% 0.6% –

These results follow our prior: the more rockpile-friendly starters net an advantage at night as batters cope with suboptimal contrast from backdrop to ball. In the nighttime, looped starters see their whiff percentage increase by 2.5 percent (with 98 percent confidence) when pitching in Anaheim. This is substantially smaller than the possible daytime whiff percentage rockpile effect, but it makes sense, since glare is eliminated at night.

Moreover, pitches right of the loop show a split of just about zero when considered in totality. If we subtract the -0.5 percent non-loop estimate from the observed +2.5 percent rockpile effect, the confidence level is a strong 97.4 percent.

I’ll test whiff percentage one more way—by combining all data into a generalized effect. That means putting together starters’ day and night stats, and also adding in relievers and their smaller sample sizes. That aggregated heat map is shown below.

Seems like this heat map contains more reddish-hued boxes than we’ve previously seen, right? We’ll keep an eye on that when we total up the results, cutting the rockpile band off at the same points.

GENERALIZED WHIFF% SPLIT Bin ANA Swing Total Road Swing Total ANA Whiff% Road Whiff% Difference (ANA – Road) St. Dev Confidence Level Rockpile Loop 7,659 17,524 21.2% 19.1% +2.1% 0.6% 95% Non-Rocks 7,979 17,945 19.0% 18.9% +0.1% 0.5% – Gray Loop 1,432 2,033 23.0% 19.8% +3.2% 1.4% 87%

The pitchers who threw the ball out of the orange loop improved at Angel Stadium, seeing their whiff percentage increase by 2.1 percent. Upon removal of the fluky blue 99 percent box (and its implausible -20.2 percent effect size), the rockpile effect bumps up to +2.3 percent. Outside the circle, pitchers benefited by only 0.1 percent—so in the aggregate, the cold zones wash out those extra hot zones and produce the anticipated effect size of ~0.

But we can’t ignore the top-right cluster of five hot zones. It’s just not the random mix of effects we expect to see: a 3.2 percent whiff percentage increase (with high confidence) at Angel Stadium.

It would be valid to say that pitchers who threw the ball from Weaver’s neighborhood of release points missed more bats in Anaheim than elsewhere. But only one of the whiff percentage charts showed consistent entropy and ~0 values on the right side of its chart. Without that randomness, it’s hard to say that the rockpile provides that special advantage to pitches coming from Weaver’s release point.

Non-Chase Percentage

Now we’ll move on to non-chase percentage. Keep in mind that it’s better for pitchers to register a lower non-chase percentage, indicating that batters are taking fewer out-of-zone pitches. Starters’ daytime non-chase percentage split is shown in the next heat map.

The hypothesized rockpile area looks dubious. For one thing, the orange loop—our hypothesized definition of the rockpile area—contracted. For another, the effects in the rockpile area are weak; joining three reddish boxes are three whitish boxes that present confidence levels in the teens and below. A fence of blue separates the orange loop from another region hosting red boxes. How do the two areas compare?

STARTERS’ DAYTIME NON-CHASE% SPLIT Bin ANA Ball Count Road Ball Count ANA Non-Chase% Road Non-Chase% Difference (Road – ANA) St. Dev Confidence Level Rockpile Loop 1,025 1,503 67.5% 69.5% +2.0% 1.9% 40% Non-Rocks 2,093 4,134 69.5% 70.1% +0.7% 1.2% 21% Gray Loop 870 1,361 66.0% 71.3% +5.3% 2.0% 97%

In the orange band, pitchers are getting batters to chase an additional 2.0 percent of pitches, but we have little confidence that the benefit is real. In contrast is the gray loop, thought to be outside the rockpile area, which shows an effect size and confidence level that more than double the former values. Include the blue fence and the non-rockpile area does trend closer to zero, but it’s besides the point—if the rockpile provides a real benefit, we shouldn’t be seeing a stronger affirmative effect at the right side of the chart.

Furthermore, this chart tells a similar story to daytime whiff percentage: when totaled, all pitchers in the window get more chases in Angel Stadium day games (+1.1 percent) than road day games. This seems small, but it looks real; because as you’ll see in the upcoming heat map, it’s hard to get batters to chase in Anaheim.

Out in Weaver’s neighborhood, there are just two reddish boxes. It’s actually an improvement to the sea of blue and white on the right. Say we defer to the orange loop as our hypothesized rockpile area, and capture the same boxes as we did for starters’ daytime non-chase percentage split. Even in that slimmed-down band, we’re getting too many cold zones in an area that’s supposed to be a strength for pitchers. That finding is just about identical in the aggregated non-chase percentage chart.

The looped areas for both non-chase percentage charts have an effect size of ~0. Outside the loop, pitchers lose more than 2.5 percent of chases in Anaheim. This is actually part of a greater trend—there’s a chase percentage toll at Angel Stadium. An out-of-sample test shows that in general, right-handed pitchers also get fewer chases from right-handed batters when pitching at the Big A in both the daytime (3.6 percent and nighttime (2.1 percent).

One could argue that these results indirectly align with our Bayesian prior, that pitchers who don’t pitch with the rockpile as the backdrop are worse than those that do. But I think that would miss the point—plenty of rockpile-area boxes that were hot for whiff percentage now range from slightly to very cold. To assess that inconsistency, I correlated each whiff percentage release point bin with its correspondingly timed non-chase percentage bin. Separate correlations were formed for both definitions of the rockpile area: the wider loop from whiff percdentage, and the tighter loop from non-chase percentage.

CORR. OF ROCKPILE-AREA BINS FROM WHIFF% TO NON-CHASE% HEAT MAPS Subset Rockpile Definition #1 Rockpile Definition #2 Starters (Day) .48 .41 Starters (Night) .38 .40 Aggregated .59 .64 Aggregated (no blue 99% outlier) .23 .21

The correlation of rockpile-friendly starters’ daytime whiff percentage to daytime non-chase percentage is low, and it doesn’t matter which defined band is used. The story is the same for starters’ nighttime splits. The correlations for the aggregated heat maps look better at first, but those figures are highly deceptive, as once again the dark blue 99 percent value from the whiff percentage chart skews the results. Remove that and the correlations are reduced by two-thirds. For us to reject the null hypothesis, all of these correlations should be higher.

Concluding Remarks

Two findings from this study were 1) that Angel Stadium, in general, improves pitchers’ whiff percentage and non-chase percentage in the daytime, and 2) it’s otherwise hard to get batters to chase pitches at Angel Stadium. Both of these points are made irrespective of the rockpile, which offered glimpses of a potential specialized effect, but not enough concrete proof. Starters’ nighttime whiff percentage and the couple of leftward red boxes from nighttime and aggregated non-chase percentage only hint at the existence of a rockpile benefit.

It is possible that the rockpile is a non-issue due to survival bias; major leaguers’ exceptional vision may abate the hurdle of minimal ball-to-rocks contrast. But I’m left wondering about the impact of missing data: namely, grades on pitchers’ deception. Like Weaver, John Lackey threw with a high and far release point as a member of the Angels, but these former teammates aren’t directly comparable. Lackey’s delivery is much more conventional, and less deceptive, than that of Weaver. Two pitchers with similar release points can present much different pitch recognition challenges for opposing batters. Thus, a release-point-reliant definition of rockpile-friendly may be incomplete; perhaps a rockpile effect can be gained, but only by deceptive pitchers.

A scant few right-handed starting pitchers could fit that criteria of rockpile-friendly. A Weaver-like cross-body motion often leads pitchers to the bullpen, as few could maintain their balance through that delivery and pitch with command. Weaver’s gaudy pitch recognition splits illustrate how he may capture an advantage quite unlike his more standard peers.

WEAVER’S PITCH RECOGNITION SPLITS Subset ANA Trials Road Trials Angel Stadium Gain St. Dev Confidence Whiff% Day 486 479 +11.5% 2.9% 99.97% Whiff% Night 2,098 1,603 +4.0% 1.3% 97.4% Non-Chase% Day 689 732 -0.9% 2.5% — Non-Chase% Night 2,909 2,180 +1.6% 1.4% 35%

In home day games, Weaver’s whiff percentage climbs massively, much larger than the bump enjoyed by the pitchers in that chart’s gray or even orange loop. His night whiff percentage is higher than the general cases as well. And, he’s managed to rise above the Angel Stadium penalty when it comes to chases. Keep in mind that his numbers were included in all previous heat maps—if we left him out of those, he’d stand even taller above his peers.

The possibility that deception is the key to a rockpile benefit is potential good news in what has been a challenging year for Weaver. It won’t be easy to navigate the season with his depleted arsenal, and that additional help at home could be important in the next year-plus.

References and Resources

Appendix: Release Point Corrections

In constructing a study that’s dependent on reliable release point data, it’s important to discuss and address the errors that are ingrained into the PITCHf/x measurements. The “release point” reported by PITCHf/x is actually the initial point at which the system picks up the ball in its flight: when it’s at a distance of 50 feet from the back point of home plate. A pitcher’s true release point distance out of the hand is better approximated, generally, at 55 feet. This five-foot difference can create issues across pitch types; for instance, a big breaking curveball thrown for a strike can easily have its release height overstated, incorrectly logging a higher release than a fastball. Plus, PITCHf/x is more accurate at measuring events at home plate rather than at the mound, leading to possible release point errors of two-plus inches. And lastly, the PITCHf/x cameras are calibrated differently across parks, and so measurement errors vary depending on the locale.

To refine the data, I employed a multi-pronged algorithm. First, all pitch data was shifted backward to reflect release at 55 feet rather than 50 feet. Then, with MLBAM’s classifications, I placed pitch types into bins. This allows us to guard against classification errors and still make corrections that are tailored to certain families of pitches. This matters because differences in hand position on the ball, depending on the pitch type, lead to slight differences in release point. The pitch bins are itemized in the following table, with MLBAM pitch type abbreviations displayed in parentheses.

PITCH TYPE CATEGORY Hard Off-speed Breaking 4-seam fastball (FF) Changeup (CH) Curveball (CB) 2-seam fastball (FT) Splitter (FS) Knucklecurve (KC) Sinker (SI) Forkball (FO)* Slider (SL) Cutter (FC) General fastball (FA) *Most forkballs are misclassified changeups and splitters – http://www.baseballprospectus.com/article.php?articleid=26281

*Most forkballs are misclassified changeups and splitters.

Here’s where my process got rather gory: for each of the three pitch categories, in each park-year, I took a rolling 15-game average of pitchers’ horizontal and vertical release points. Then I calculated the difference at that park from the weighted “baseline,” which is the release data for those very same pitchers at all other parks in that same rolling average sequence.

This process appears similar to that which is built into Brooks Baseball’s player cards, with some exceptions. I corrected data strictly for match-ups of right-handed pitchers vs. left-handed batters, as pitch location influences release point; this is effectively a control for how left-handed batters are approached differently by opposite-handed pitchers. I also discarded player-year-pitch types with large outlying standard deviations in release point. In the population are some pitchers who vary their arm angle in the midst of appearances, whether it’s deliberate and strategic or due to inconsistency. Mid-year mechanical alterations and changes in position on the rubber can also create issues. These cases, while small (just ~3.5 percent of x0 data and ~2 percent of z0 data) could potentially have distorted the corrections.

Once adjusted, I had more tightly-clustered release point data with which to work. Across the three pitch bins, the standard deviation of each pitcher’s vertical release was reduced by ~19.5 percent; for horizontal release, the standard deviation came down by ~9.5 percent.