On Tuesday, Albert Pujols hit his 13th home run of June and 24th of the season, continuing a power renaissance that’s reminding us of an era in which the three-time MVP was known for more than being a bad investment. Pujols’s comeback is one of baseball’s best stories in 2015 and the only notable non-Trout silver lining in the Angels’ lackluster lineup. It’s also a parable that perfectly illustrates why we should pay attention to projection systems, particularly when they say something counterintuitive.

For the past two springs, Baseball Prospectus’s projection system, PECOTA, has played Argos to Pujols’s Odysseus, expecting some semblance of the old Machine to return even after he’d been replaced by a barely league-average (by 1B/DH standards) imposter who hobbled to first base. This year, PECOTA projected Pujols to be the 18th-best hitter in baseball, which seemed like a stretch, given that Pujols was 35 and coming off two subpar seasons, the latter of which wasn’t even excused by a stay on the disabled list. Thus far, though, Pujols has actually been the 14th-best hitter in baseball (minimum 200 plate appearances), according to BP’s all-in-one offensive rate stat, True Average. Unburdened by outward appearances and recency bias, the system looked past Pujols’s recent plantar fasciitis and the pedestrian stats and perceived that a player who was so good for so long might still have something left.

Yet PECOTA is as hesitant to crown a superstar as it is reluctant to write one off. Even though Pujols is currently hitting as well as he did during some of his years in St. Louis, PECOTA’s TAv forecast for him has hardly changed since the start of the season. The system saw that some pieces of prime Pujols’s ability survived during his down years, but it also sees some pieces of the slower, frailer Pujols lurking inside the seemingly rejuvenated slugger.

The Pujols lesson is an important one to remember as we approach the season’s halfway point. In July, it’s tempting to stop sounding the “small sample” alarm and buy into every breakout and breakdown. But even at this point, that would be premature. Past research has shown that in the aggregate, in-season projections work well even for outliers: Select any sample of players who’ve most outperformed or underperformed their preseason projections, and from that day forward, those players, as a group, will perform almost exactly as well (or as poorly) as their rest-of-season projections foresee, no matter how credible their altered stance, smoothed-out swing, or other post hoc explanation for success.

True Average is park- and league-adjusted, and it’s scaled to a .260 league average, where .220 is terrible and .300 is excellent. Below, I’ve listed the hitters whose True Averages have most overshot or undershot PECOTA’s preseason projections, along with the system’s updated forecast of how they’ll do between today and October. If you think you’re smarter than a statistical algorithm, play along at home, pick your overs and unders, and check your success rate at the end of the season. For a look at the pitchers, click here.

Note: The stats in this article reflect action through Tuesday’s games.

The Overperformers

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Bryce Harper, Nationals (.294 Projected, .414 Actual): Here’s how good Harper has been: Even if he’d been projected to be the best hitter in baseball — and he wasn’t close after coming off a fairly pedestrian, injury-interrupted 2014 — he’d still be beating his projection by enough to rise almost to the top of this list. Harper is having the best offensive season of the past half-century by anyone not named Barry Bonds. On the other hand, he has actually hit the ball less hard than Cameron Maybin. So no, he’s probably not going to finish the season with Bondsian stats. But given Harper’s health and the many improvements he’s made, I’d take the over on his topping any projection that’s still weighed down by what he did while he was playing through pain — even though it’s possible that he’ll be banged up again before the end of the year. RoS Projection: .310 (Over)

Jimmy Paredes, Orioles (.240 Projected, .319 Actual): Paredes is the archetypical Guy Who’s Gonna Regress. He has the fourth-highest BABIP of any hitter with at least 200 plate appearances, one of the 20 worst walk-to-strikeout ratios (0.18), and little speed. The counterpoint: He’s remodeled himself after Robinson Cano, much like last year’s out-of-nowhere hitter, J.D. Martinez, remodeled himself after Miguel Cabrera. The resemblance is uncanny, leading to the obvious punch line that Paredes has somehow stolen the slumping Cano’s mojo. But peak Cano — who, admittedly, also outperformed the modest expectations that prospect evaluators had for him — had several seasons in Paredes’s current range without an abnormal BABIP. As a utility guy, Paredes looks like another entry on the long list of Dan Duquette’s useful finds, but I’d need to see more before subscribing to his future as an above-average hitter. The projections, however, still see him as something far short of average, which is an easier bar to imagine him exceeding. RoS Projection: .250 (Over)

Stephen Vogt, Athletics (.268 Projected, .345 Actual): Vogt says he’s walking so much more this season because he’s stopped trying not to. For most players, posting a near-.400 on-base percentage isn’t as simple as setting one’s mind to it, but Vogt’s plate discipline stats in college and the minors support the idea that he possessed this ability before he displayed it in the big leagues. He has already turned 30, so he’s going to have a short peak, but it’s not farfetched to think he might maintain this production for a few more months. RoS Projection: .280 (Over)

Maikel Franco, Phillies (.254 Projected, .330 Actual): The projections say Franco is an above-average major league hitter at age 22, no small feat for a player who last year hit a modest .257/.299/.428 in Triple-A and struggled mightily in a brief big league call-up. The kind of performance he’s posting right now isn’t out of the question for Franco down the road, but I wouldn’t be surprised to see him experience a gentle, Jorge Soler–like comedown from his early success in the short term, as opposing pitchers probe his weaknesses. Phillies fans aren’t allowed to have nice things so soon. RoS Projection: .268 (Even/Under)

Jason Kipnis, Indians (.269 Projected, .344 Actual): Kipnis’s BABIP rivals that of Paredes, so he’s probably had some luck on his side in leading all non-Harper players in FanGraphs WAR. But he was also a productive player two years ago, and some of his issues last season can be blamed on a bad oblique. Even if he is only back to where he was in 2013 — when he struck out much more often, with no more power than he’s shown this year — he’ll beat his rest-of-season projection. RoS Projection: .279 (Over)

Justin Turner, Dodgers (.274 Projected, .348 Actual): Turner also has an origin story based on becoming more like an older player, although his muse, Marlon Byrd, isn’t as impressive as Cano or Cabrera. Even before the big numbers he’s put up in the past season-plus, Turner had been a league-average hitter and a passable defender at multiple infield positions, which made his $1 million signing by the Dodgers two winters ago (following his release by the Mets) look like a bargain. This year’s line seems less like a mirage than last season’s, but I’m comfortable accepting his less inflated rest-of-season figure. He’s still done enough to earn his new status as an everyday player. RoS Projection: .286 (Even/Under)

Todd Frazier, Reds (.278 Projected, .348 Actual): Frazier credits his career high in homers last season to swinging a (literally) bigger bat. Now he’s a few pokes away from eclipsing his 2014 total. He’s hitting the ball harder, pulling it more often, and doing a better job of making contact with off-speed stuff. His home run tally might drop in the second half of the season, but a .286 rest-of-season True Average should be well within his reach. RoS Projection: .286 (Over)

Brandon Crawford, Giants (.245 Projected, .312 Actual): When Jeff Sullivan wrote about Crawford’s progression at the plate in late May, Crawford was hitting .298/.387/.511, and his batted-ball velocity was “right there with Jose Abreu and Josh Donaldson.” Since then, Crawford has hit .244/.311/.430, and his average batted-ball speed is now a few miles per hour below Abreu’s and Donaldson’s (which remain in the top 20). Clearly, Crawford has tailed off. But even that diminished, since-late-May line is better than any Crawford has recorded over a full season and is enough to help him tie his career high in homers and make him a very valuable player when combined with plus defense at shortstop. The projections still see Crawford as a below-league-average hitter, because he was one for the first few years of his career. His recent stats say otherwise. RoS Projection: .257 (Over)

Joe Panik, Giants (.247 Projected, .312 Actual): Small wonder that the Giants have been better than anticipated: Crawford, Panik, and Matt Duffy give them three of the 20 hitters who’ve most outperformed their projections. Unlike Crawford, Panik has actually hit better since his Sullivan post, and the percentage of his flies that are pulled has almost quadrupled. On the other hand, his average fly-ball distance is exactly the same as it was last season, he’s low on the exit-velocity leaderboard, and he hasn’t sustained an Isolated Power this high at any level above Rookie League. It’s easy to talk ourselves into all of these improvements being sustainable, but history tells us that some of them won’t be. If we have to pick a few players who are over their heads, Panik seems like a stronger candidate than most of the rest of the top 10. RoS Projection: .263 (Even/Under)

Paul Goldschmidt, Diamondbacks (.318 Projected, .380 Actual): Until his 0-for-4 on Tuesday, Alex Rodriguez owned the last spot. Rodriguez’s resurgence after a lengthy absence and career-threatening surgery would be an unqualified feel-good story if not for that pesky PED stuff. Adjusted for era and ballpark, he’s hitting roughly as well as he did during his 2003 MVP season in Texas, and he has a top-15 average batted-ball speed. Rodriguez is one of the best players ever, occupying the same stratosphere as legends like Willie Mays, Hank Aaron, and Frank Robinson (who also hit at A-Rod’s age), but it was still improbable that his bat would come back to the degree that it has after such a long layoff. His next challenge: making it through a full season without wearing down.

As for the actual 10th-place overperformer, Goldschmidt: Just when we think we’re properly appreciating him, he levels up and makes himself underrated again. Goldschmidt was already selective, but he has lowered his chase rate even further this season, to the point that only seven qualified hitters are less likely to offer at a pitch outside the strike zone. The result is a career-best walk-to-strikeout ratio, coupled with his usual hard contact. He has delivered higher than a .324 TAv in each of the past two seasons, so I believe he’ll be better than that for the rest of what’s looking like a classic age-27 peak. Historically speaking, betting against Goldschmidt hasn’t worked out well for anyone. RoS Projection: .325 (Over)

Just Missed: Brett Gardner, Nelson Cruz, Rodriguez, David Murphy, Mike Moustakas, Mitch Moreland, Nolan Arenado, Billy Burns.¹ If we slightly lower the playing-time minimum, Randal Grichuk, owner of the highest batted-ball exit speed among non–Giancarlo Stanton hitters, almost makes the top 10.

The Underperformers

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Carlos Ruiz, Phillies (.275 Projected, .206 Actual): Ruiz ranks 150th among 198 hitters with at least 100 Statcast-measured batted balls, which bodes worse for him than it does for fast players like Burns and Dee Gordon. Inside Edge backs up Statcast, giving Ruiz a lower percentage of hard-hit balls than any hitter other than Ichiro. At age 36, Ruiz is a microcosm of a roster that has grown old and ineffective around him. I’m staying away from the over. RoS Projection: .270 (Under)

Rene Rivera, Rays (.244 Projected, .176 Actual): Ironic, right? The Rays replaced Jose Molina, last season’s worst hitter among players with 200 plate appearances, with a younger catcher whom they hoped would approximate Molina’s receiving skills but bring a better bat. Instead, they got a pretty good framer who’s been — you guessed it — the worst hitter among players with 200 plate appearances. Rivera hasn’t been as useless at the plate as Molina was, and he has a higher offensive upside (see last season), but this wasn’t what the Rays had in mind. RoS Projection: .233 (Even/Over)

Ryan Zimmerman, Nationals (.291 Projected, .228 Actual): Zimmerman is suffering from the same plantar fascia problem that plagued Pujols, so if we don’t trust PECOTA, we run the risk of underrating him, too. The difference is that Pujols has had time to recover, while Zimmerman is still on the disabled list. When Zimmerman has had a winter to heal, PECOTA might see his future more clearly than someone who has watched him struggle all season, but it’s hard to have much faith in a quick recovery when “a brisk walk” on a treadmill is the most Zimmerman can manage. RoS Projection: .287 (Under)

Victor Martinez, Tigers (.292 Projected, .230 Actual): Martinez’s four-year contract was a questionable splurge, given his age and the usual concerns about paying for a player in the aftermath of a career year. Since his return on June 19 from a monthlong absence stemming from inflammation in his just-operated-on knee, Martinez has hit .326/.370/.488, albeit without any increase in batted-ball speed. That line is the most positive sign Detroit has seen so far, but it’s not enough to allay all the concerns about his durability. RoS Projection: .289 (Even/Under)

Robinson Cano, Mariners (.309 Projected, .252 Actual): Cano is one of the season’s most mystifying players. He’s still hitting the ball hard — on the batted-ball speed list, he’s just a hair behind Arenado and J.D. Martinez and ahead of Mookie Betts, all encouraging names — but he’s also hitting the ball on the ground at a career-high rate, which means that much of his bat speed is being wasted on parts of the field that don’t lead to a lot of extra-base hits. He’s also — to his own surprise — simply missing pitches more often, even though he isn’t swinging wildly. The best scapegoat seems to be a change in his swing plane, which in theory should be much more correctable than physical degradation. The Mariners just hired a new hitting coach, whom you’ve probably heard of. Maybe Edgar will be able to find and fix a flaw that Howard Johnson couldn’t. I’d be surprised if Cano didn’t come close to PECOTA’s target the rest of the way. RoS Projection: .305 (Even/Under)

Chase Utley, Phillies (.273 Projected, .218 Actual): In mid-May, Utley looked like a great bounceback candidate, based on the fact that he was hitting the ball much harder than his OPS suggested. What’s happened since is a reminder that the stats don’t always improve to meet the batted-ball speed; sometimes, the batted-ball speed sinks to meet the stats. Utley is now closer to the bottom of the exit-speed leaderboard than he is to the top, and the ongoing ankle issues that sent him to the DL late last month are another cause for concern. RoS Projection: .269 (Even/Under)

Chris Iannetta, Angels (.271 Projected, .216 Actual): Iannetta has had an upside-down season. Formerly an offense-first catcher whose glove was well below average, Iannetta dedicated himself to receiving this spring and quickly climbed the framing runs leaderboard. Concurrently, though, his power has evaporated, and his low BABIP is backed by a career-worst lack of hard contact. If Iannetta has an injury, he isn’t telling reporters, but whatever the cause of his issues, it has cost him some playing time that’s now going to offseason acquisition Carlos Perez, who has hit almost as poorly. The veteran’s plate discipline hasn’t suffered, so unless he’s hiding an injury, a correction should be coming. Maybe Iannetta just takes the Nichols Law of Catcher Defense too seriously. RoS Projection: .268 (Even/Over)

Melky Cabrera, White Sox (.278 Projected, .223 Actual): Cabrera has never been a big home run hitter, but he has posted the sixth-lowest ISO among qualified hitters this season, which is particularly disappointing given that he’s playing in an offense-enhancing park. We knew coming into the year that the White Sox had several sketchy positions, but Cabrera’s signing seemed to fill one hole with a competent player. Instead, it opened up another abyss. Chicago is the only team whose position players have collectively been below replacement level, making the Phillies look respectable by comparison. Cabrera batted .329/.390/.466 over his last 20 games in June, though, so maybe the frustrating funk is behind him. RoS Projection: .274 (Even/Over)

Danny Santana, Twins (.245 Projected, .193 Actual): On the heels of a season when he whiffed 98 times against only 19 walks and saw his production propped up by an MLB-leading .405 BABIP, Santana was one of this year’s slam-dunk decline candidates, and that dropoff has come more swiftly and severely than anyone imagined. Incredibly, Santana’s strikeout and walk rates have moved in the wrong direction, and he’s seen one of the highest rates of pitches inside the strike zone, a consequence of his utter lack of power. It’s almost cruel to take the under on .240, but it’s probably the right call. RoS Projection: .240 (Under)

Jon Jay, Cardinals (.269 Projected, .218 Actual): Jay is one of MLB’s most pronounced ground ball hitters, but the lefty pulls less than half of his grounders, and he hasn’t seen a single full shift. He also hasn’t hit the ball hard, but that’s nothing new, and his walk-to-strikeout ratio is a career high. This looks like a plain old BABIP issue, which is likely to solve itself. Isn’t it about time the Cardinals caught a break? RoS Projection: .267 (Even/Over)

Just Missed: Lonnie Chisenhall, Adrian Beltre, Matt Joyce, Carlos Gonzalez, Mike Zunino, Matt Kemp, Aramis Ramirez, David Ortiz, Mike Napoli

1. Burns’s combination of an MLB-leading 27.5 percent infield fly ball rate and a .361 BABIP makes for one of the sport’s strangest stat lines. You have to be a burner to pop up more than a quarter of the time and still have great success on balls in play.