Those shots have produced a team-best nine goals. Three have come on the power play, also tops on the club.
After he was acquired from Dallas in a February trade, Neal struggled to get his offense untracked. He averaged 2.6 shots a game and had just one goal in his first 20 regular-season games with the Penguins.
Friday, he will face his former team for the first time, and the Stars can expect to see a winger who is fulfilling the offensive promise the Penguins were counting on when they acquired him.
Penguins coach Dan Bylsma thinks getting to the puck, or a place where the puck will be, has been the key.
"Speed is a big factor for James' game, whether it's on the forecheck, hunting pucks down, pursuing pucks in the offensive zone -- those things he's done extremely well," Bylsma said. "It's led to more opportunity with the puck for him and his line.
"We've seen him get shots on the rush. He's good at doing that. But I think he's also gotten shots from rebound areas, from five-on-five offensive play. I think he's more of a factor shooting on the power play, both from the net-front and the low area."
Steve Sullivan, the other winger on the line often centered by Evgeni Malkin, said Neal has a great knack of putting himself in places to receive and release the puck.
"He's creating those chances himself. Absolutely," Sullivan said. "He's a smart hockey player. He gets himself open. I'm a pass-first, shoot-second [player], so I'm looking for him -- and he's not hard to find.
"Yeah, I force a few pucks to him, but, on most passes, I'm giving it to him because he's open. He's a player who gets into those soft areas and knows where to go to get the puck."
Passing up a shot in this instance, Neal threw the compliment back. The caliber of talent among his new teammates has helped get the puck on his stick a lot.
"Of course," he said. "When you're putting yourself in places to get the puck on net and you're getting the puck from your linemates, you're going to get a lot of shots."
Neal's launches have not been net-seeking missiles in every case. Some of his goals have come from simply throwing the puck toward the goaltender and having it bounce in off an opponent or post.
But that only happens if a player is launching the puck in the first place. He has done that a lot, 124 times.
He also led the NHL in missed shots, 31, before Wednesday. Opponents have blocked 29, although six times he has had just one or no shots blocked. More than half the time, though, his shots result in a goal or a save by the goaltender.
"That's a big thing, getting it through," Neal said. "Guys like to block shots, especially a [defenseman] when you're coming in on him. When you get shots through, you give yourself a chance to score every time."
Neal, 24, has increased his shot total every season. He had 171 as a rookie 2008-09, then 200 and 212.
"I think five shots would be good every game. If you want to set a goal, it would probably be five shots a game," Neal said.
That would lead to 410 by season's end, which would be enough to have beaten Ovechkin in three of the past five seasons.
It also is more than the 350 that Neal found almost silly.
"You just don't want to pass up shots," Neal said, shrugging. "When things are going good and you're shooting the puck well and scoring goals, you don't want to pass up shots."