It’s been more than two weeks since the Ken Rosenthal and Evan Drellich’s bombshell report at The Athletic, which revealed a massive sign-stealing scandal implemented by the Houston Astros beginning in 2017. Since then, we’ve seen reports that the official investigation launched by Major League Baseball has confirmed the system as described by Mike Fiers in that original report; they are continuing to look into other ways the Astros may have cheated during the 2017 postseason and beyond. Whether the Astros were using a modified method on the road relying on “buzzers,” as some have speculated, has yet to be confirmed.

What we do know is that the Astros broke the rules by using technology to steal signs in real-time. Members of Houston’s front office and coaching staff could face significant penalties, and with Alex Cora and Carlos Beltrán implicated as sign-stealing ringleaders, there could be impacts felt in organizations beyond Houston. It remains to be seen just how severe the punishment will be — though our own Craig Edwards argued last week that they could be quite severe indeed — and if any players are caught up in the fallout.

Last week, I took an initial look at whether or not the on-field value of the Astros sign-stealing scheme could be parsed out in the data. Between the changing roster, the changing ball, and the at times non-linear effect of coaching and player development, there was a lot of noise in the data. At a broad level, it’s hard to make any conclusive statements about the specific effects of the Astros sign-stealing, though as I noted, the fact that the team persisted in the practice suggests they believed they derived an appreciable benefit from it. On Friday, two more attempts to answer that same question were made.

Over at The Ringer, Ben Lindbergh concluded:

“Knowing the next pitch just has to help, right? But no matter how we slice and dice the data, the statistical case is less compelling than it would be if sign-stealing made hitting as simple as it seems like it should. Great as the Astros were at the plate in 2017, the most fascinating aspect of their sign-stealing scandal is that it didn’t make them even better.”

Rob Arthur was a little more confident in his conclusions in a piece for Baseball Prospectus:

“We can tentatively conclude that their sign stealing probably had a major impact on the team’s plate discipline numbers. This was not innocent cheating that barely affected the game; according to the available data, it may have yielded an unprecedented improvement in the Astros’ ability to make contact and lay off outside pitches, helping to turn a talented lineup into one of the best-hitting teams of all time.”

In my previous piece, I landed somewhere in between these two positions: sign-stealing probably had an impact, but it was nearly impossible to determine the exact benefit at a team level due to all the noise. But what happens if we drill down to the per-pitch level, as I did with the run expectancy (RE288) data in my article last week, and this time focus on individual players?

Before we get to the analysis of individual players, I’d like to present some adjusted data from my analysis last week based on the sign-stealing timeframe Arthur proposed in his article. He scanned the TV broadcasts for the telltale audio cues created by banging a trash can and found that the Astros likely began using their sign-stealing system around May 19. With that date in mind, here are the Astros’ adjusted run values against the three major pitch types while at home in 2017. (Note, because we’re working with different sample sizes, I’ve scaled the run values to standardize the values per 100 pitches.)

Astros Pitch Type Run Values At Home Year Fastball Breaking Offspeed Swing Runs 2017 – Pre 5/19 -0.76 -1.34 -2.32 2017 – Post 5/19 -0.65 -0.56 -0.91 Change 0.11 0.78 1.41 Take Runs 2017 – Pre 5/19 1.07 1.26 1.77 2017 – Post 5/19 1.19 1.36 1.54 Change 0.12 0.10 -0.23 SOURCE: Baseball Savant Pitch Values scaled to per 100 pitches.

And here’s a table comparing home performance against away performance after May 19.

Astros Pitch Type Run Values Home/Away Split Year Fastball Breaking Offspeed Swing Runs 2017 – Home -0.65 -0.56 -0.91 2017 – Away 0.37 0.07 -1.11 Difference -1.02 -0.63 0.20 Take Runs 2017 – Home 1.19 1.36 1.54 2017 – Away 1.15 0.87 1.29 Difference 0.04 0.49 0.25 SOURCE: Baseball Savant Pitch Values scaled to per 100 pitches.

If we just focus on 2017 and compare the Astros performance before and after the presumed May 19 start date, we can see that they did indeed see a big boost after implementing their trash can system. They saw better results at home against every pitch type, whether or not they swung. And when we compare their home splits against their road performance, we can see that they performed better at home when taking pitches. Looking at the data this way removes some of the noise that was complicating my previous analysis — we don’t have to worry about the change in talent from 2016 to 2017. It also supports the Arthur’s conclusions; the Astros gained a significant advantage at home after implementing their sign-stealing system. I estimate its total cumulative value at somewhere around five wins.

With that out of the way, let’s turn our attention to a few individual players. I won’t go through the entire Astros lineup. Instead I’ll focus on a couple of key players suspected to have been using the sign-stealing system. In their non-comprehensive video review from 2017 for Effectively Wild, Lindbergh and ESPN’s Sam Miller found at least 10 different hitters using the sign-stealing system, including almost all of those with regular playing time. There has been also video evidence of the scheme posted various places, but no official or confirmed list of the players who participated has yet been released, meaning this list could shift as MLB completes its investigation. With that in mind, let’s take a look at a few of the Astros players who have been identified as possible beneficiaries of Houston’s system:

José Altuve

Jose Altuvé Pitch Type Run Values 2017 José Altuve Fastball Breaking Offspeed Swing Runs Home – Pre 5/19 -1.34 -5.61 -6.5 Home – Post 5/19 -1.23 1.07 4.24 Away – Post 5/19 0.83 2.15 3.5 Take Runs Home – Pre 5/19 0.11 -0.19 1.05 Home – Post 5/19 1.53 0.77 3.16 Away – Post 5/19 2.05 0.94 0.92 SOURCE: Baseball Savant Pitch Values scaled to per 100 pitches.

José Altuve improved across the board when batting in Minute Maid Park after May 19. But when we take into account his performance on the road, one thing really stands out; his results against offspeed pitches. His ability to recognize and either take or punish offspeed pitches really took off at home after May 19. As a result, his expected wOBA against offspeed pitches increased from .274 to .363.

Alex Bregman

Alex Bregman Pitch Type Run Values 2017 Alex Bregman Fastball Breaking Offspeed Swing Runs Home – Pre 5/19 -1.25 -3.77 -6.46 Home – Post 5/19 -1.42 0.48 -3.26 Away – Post 5/19 1.44 -0.12 -3.67 Take Runs Home – Pre 5/19 1.03 0.85 1.31 Home – Post 5/19 1.84 2.39 2.41 Away – Post 5/19 1.13 1.04 1.37 SOURCE: Baseball Savant Pitch Values scaled to per 100 pitches.

Like Altuve, Alex Bregman improved almost across the board after May 19, both home and away. But he saw improvements against all pitch types at home that weren’t necessarily mirrored on the road. He really benefited when taking pitches, particularly those thrown out of the zone. This was Bregman’s first full year in the majors, so it’s possible he was still making adjustments to major league pitching. Prior to May 19, he was running an 18.1% strikeout rate, lower than what he posted in his rookie season in 2016, but much higher than his minor league strikeout rates (though again, the quality of pitching he saw relative to that in the minors presumably also improved). After May 19, his strikeout rate dropped to 14.6%, and his chase rate and swinging strike rate saw similar drops.

Carlos Correa

Carlos Correa Pitch Type Run Values 2017 Carlos Correa Fastball Breaking Offspeed Swing Runs Home – Pre 5/19 2.13 0.46 -3.33 Home – Post 5/19 0.54 0.65 3.27 Away – Post 5/19 2.56 1.23 -2.76 Take Runs Home – Pre 5/19 0.13 1.86 3.20 Home – Post 5/19 1.62 1.39 -0.47 Away – Post 5/19 0.79 0.81 0.92 SOURCE: Baseball Savant Pitch Values scaled to per 100 pitches.

Carlos Correa’s results weren’t nearly as straightforward as Altuve’s or Bregman’s. He saw some improvement in some aspects of his game, but also developed struggles in others. The two aspects that really stand out are his swings against offspeed pitches and his fastball takes. When swinging at offspeed pitches, Correa scuffled prior to May 19 and on the road, but he crushed offspeed pitches at home. He posted a .452 expected wOBA on contact against offspeed pitches after the sign-stealing system was implemented, a 73 point improvement over what he had posted before then.

Evan Gattis

Evan Gattis Pitch Type Run Values 2017 Evan Gattis Fastball Breaking Offspeed Swing Runs Home – Pre 5/19 -0.51 3.54 -6.50 Home – Post 5/19 -1.36 -0.33 -2.50 Away – Post 5/19 3.83 -1.31 -7.91 Take Runs Home – Pre 5/19 1.51 -0.81 1.90 Home – Post 5/19 1.07 0.64 1.25 Away – Post 5/19 0.75 0.86 -2.37 SOURCE: Baseball Savant Pitch Values scaled to per 100 pitches.

Like Correa, Evan Gattis‘ results are a little all over the place, though he did enjoy the same big improvements when swinging at offspeed pitches. He may have also benefited when watching breaking balls and offspeed pitches go by.

Carlos Beltrán

Evan Gattis Pitch Type Run Values 2017 Carlos Beltrán Fastball Breaking Offspeed Swing Runs Home – Pre 5/19 -1.76 -6.25 5.16 Home – Post 5/19 -1.78 -3.08 -2.79 Away – Post 5/19 -1.68 -1.82 -1.79 Take Runs Home – Pre 5/19 1.19 1.10 0.73 Home – Post 5/19 1.28 0.53 0.68 Away – Post 5/19 1.07 0.34 1.71 SOURCE: Baseball Savant Pitch Values scaled to per 100 pitches.

Despite being named as one of the instigators of the sign-stealing scheme, Beltrán’s results don’t really point to him having derived any benefit from the system. He got a little better at taking fastballs but no other parts of his approach at the plate really stand out. He was in the final season of his long career, so it’s possible no amount of forewarning of the pitch type could have helped combat the effects of aging.

Based on this second look at the data, we can probably determine the true benefit gained by the Astros on a team level. But when we begin digging into how individual players benefited, each player seems to have responded differently. Some improved across the board, while others improved against certain pitch types. And then there were players like Gattis and Beltrán who didn’t seem to improve in any one area. That’s to be expected. Not every batter will be well equipped to put the knowledge of which pitch is coming into action. Lindbergh touched on this idea towards the end of his article:

“Major league hitters don’t have superhuman reflexes. What they have is learned perceptual skills, honed through picking up patterns over thousands and thousands of pitches. Simply telling them which pitch is coming, instead of making their brains work for it, sounds like it would simply allow them to skip a step and be even better. But disrupting their regular process might make them worse.”

Once Major League Baseball concludes its investigation, we may have a more complete (and accurate) list of the players involved, though Rob Manfred may choose to keep that information private. Until the official investigation is closed, the best we can do is make educated guesses about which of these players benefited from the sign-stealing system, and by how much. This glimpse at the individual results gives a better idea of which players might have benefited from sign-stealing and which ones seem to have been unable to utilize it to the fullest extent. Beyond Bregman’s comprehensive improvement — which may have been him simply adjusting to major league pitching — most of the gains we see above aren’t as significant as we might expect, though their aggregate effect is notable. As Jeff Sullivan pointed out back in 2017, the Astros were projected to have a good lineup before the season even started. Some of the benefits of the sign-stealing system were bound to be marginal because of that baseline talent level. But when you have an organizational culture that values the cumulative effects of many marginal improvements, implementing a sign-stealing system to help your batters gain an edge, even a small one, might be just what you’re looking for.