At the beginning of this season, Major League Baseball instituted a new set of rules to make the games go faster. The idea was to limit how often batters can step out of the box during at-bats, thereby shortening the delay between pitches. The Red Sox’s David Ortiz was not happy about these rules and suggested that the changes could harm his performance. As indicated by his temporary benching two months into the 2015 season, Ortiz may have been right.

Thus far, the much-discussed batter’s box rule changes have had at most only a minor effect on the overall time of games. For individual batters, however, the impact of the rule has been anywhere from negligible to remarkable. Some hitters already had quick routines and didn’t need to make any alterations. Others liked to step off the plate after every pitch, a habit that the new rules outlaw.

The older veterans have been the most affected by the rule change. I’ve shown before that older batters are the players most likely to dawdle, the 39-year-old Ortiz included. From last year to this year, Ortiz has decreased his time between pitches by almost two full seconds, according to Fangraphs. Given Ortiz’s rather vocal opposition to the idea of cutting any time from his routine, it seems reasonable to believe that this was a change the new rules forced upon Big Papi.

Whatever his struggles with the clock, Ortiz has endured a disappointing season so far at the plate. Big Papi is currently earning a .289 weighted On-Base Average (wOBA), 20 percent worse than an average hitter in this overall measure of offensive production. This mark is far off his projected performance (.365 wOBA, according to the Steamer projection system) and the worst he’s put up since 1999, when he played in only 10 games.

Ortiz isn’t the only veteran slugger suddenly looking helpless with the bat. Tigers designated hitter Victor Martinez has gone from tearing the cover off the ball (a .411 wOBA last year) to rarely getting it out of the infield this year (.246 wOBA). Aramis Ramirez has fallen apart in a similar fashion, dropping from .334 to .274. Some of these hitters’ underperformance can be blamed on injuries, small sample size and bad luck, but some of it likely comes down to decreased skill. Hitters over 35 who have racked up at least 100 plate appearances (PAs) have been an underwhelming lot this year, collectively falling .016 shy of their projections by wOBA (on average). To put that in perspective, that’s roughly the difference between the offensive performances of Mike Trout and Brandon Belt this year.

Older hitters are always risky and come with the chance of sudden collapse, but last year hitters over 35 with at least 300 PAs hit only 3 points worse than their projected outcomes.

It’s tougher to figure out whether it’s the rule changes that are causing older hitters to do poorly, though. For all hitters, no correlation is obvious between being forced to speed up and doing worse than expected. The lack of a relationship implies that pace may not be the driving factor.

When you look at it with regard to specific hitters, however, pace begins to seem much more important. Every pitch that’s thrown in the majors has a run value attached to it. If a 1-1 pitch is a strike, it increases the probability of a strikeout happening, and an average 1-2 count is going to lead to .0748 fewer runs than the 1-1 count. If we take those expected run values of each pitch, we can see whether a long delay before the pitch changes the number of runs that come from it.

For all hitters in 2014, pitches that were preceded by more than a 30-second delay were worth about .0028 runs per pitch. Pitches that followed less than a 30-second delay were worse (at -.0052 runs per pitch), but only by a small margin. So there was a very slight advantage to the batter to stepping out of the box or otherwise postponing the pitch.

Ortiz, on the other hand, gains an inordinate amount of value from delaying the pitch.

For Ortiz in 2014, pitches thrown after 30 seconds gained .0289 runs, whereas pitches under 30 seconds were worth only .0014 runs. The difference a few seconds makes to Ortiz is about three times the value for the average batter. This isn’t a fluke just for 2014: Four of the past five years have seen Ortiz reap great benefits from delaying the time between pitches by 30 seconds or more.

Ramirez’s numbers tell a similar story. Since 2011, Ramirez has been building his value from delays that last more than 30 seconds. In 2014, Ramirez added .0556 runs per pitch when time between pitches was long, but he lost .0013 runs per pitch when it was short.

We can also contrast Ortiz and Ramirez with younger sluggers. The Marlins’ Giancarlo Stanton, for example, is every bit as powerful and patient as Ortiz (if not more so). But Stanton delivers his hits about equally whether the time between pitches is long or short (.0183 for long and .0224 for short). If anything, Stanton does slightly better when there’s less time.

We can’t say for sure that the delay between pitches causes Ortiz or Ramirez to do better. But consider that these players are on the older side and are potentially losing the physical skills that made them threats in their younger years. In the absence of the muscles needed to adjust to pitches in the air, these more seasoned sluggers might make up for it with experience. By taking their time to anticipate what pitch is coming next, Ortiz and others like him may be able to guess where a pitch will go before it leaves the pitcher’s hand. In this way, experience can compensate for deteriorating bat speed.

That process of educated guessing takes time, Ortiz says. If Big Papi feels hurried or distracted by the umpire (even if he isn’t actually taking any less time between pitches), it could contribute to a reduced ability to predict the next pitch. In turn, that could change hard-hit fly balls to weakly struck grounders, as Ortiz estimates the wrong location of an oncoming pitch.

It’s hard to ever count Ortiz out. Many commentators incorrectly predicted his demise in 2009, but Ortiz came roaring back to post a couple of his best seasons in the last five years. Still, Ortiz is facing a new and difficult task: adjusting to his declining physical skills, potentially without having the time to use his most valuable mental skill (experience). Thanks to the new emphasis on pace of play, it’s a dilemma common to many of the elder statesmen of baseball.