When the Yankees play the Angels, it’s like a first contact between members of different species, a ball club traveling to Mars (or California — same difference) and finding something that strongly resembles itself but isn’t quite the same. Both the Angels and the Yankees claim to play baseball, but they don’t go about the job the same way. In fact, the Angels aren’t much like any team in baseball, and haven’t been for some time.

The Angels, as conceived by Mike Scioscia and his hitting coach, Mickey Hatcher, are the heirs to Whitey Herzog’s speedbased teams of the 1980s, which is ironic, since they both were Tommy Lasorda men. The analogy is not literal so much as spiritual: Scioscia’s teams are probably as close to Herzog’s as a team can get under present conditions.

Herzog looked at the conditions under which he was playing, with the turf field and the distant fences, and threw in a dash of what would appeal to his own restless mind: He would have never been content to be a push-button manager like Joe McCarthy in the 1930s, as McCarthy’s only instructions to Lou Gehrig, Joe DiMaggio, et al., were “swing away.” Herzog constructed a team that harked back to the low-scoring deadball era. So successful was he at this that none of his St. Louis teams hit even 100 home runs in a season.

That day is gone — the ball is just too lively now to dispense with the home run as a weapon — but Scioscia’s teams have rarely been near the top of the league in runs scored or any other mark of a healthy offense, including home runs hit or walks drawn. They have led the American League in stolen bases for the last three seasons and stand to do so again this year.

Oddly, the Angels score a lot of runs: They’re one of the teams in the American League dishing out five or more runs per game. But their team slugging percentage of .414 is well below the league average, and even then it is misleadingly high, as the number is driven by batting average, not extra-base hits. They are second to last in home runs with 88, leading only the Royals. Few Angels walk: Vlad Guerrero puts up respectable walk totals by virtue of teams being afraid to pitch to him. Of his 59 walks this year, 25 have been free passes. Reggie Willits — who is the player Scott Podsednik was supposed to be — has walked 56 times and would easily lead the team if given regular playing time.

One would think that with an offense as delicately constructed as that of the Angels, they would have to have every position contributing. But they’ve succeeded in ranking fourth in runs scored despite lacking a regular catcher, a second baseman, or a designated hitter. Catcher Mike Napoli is something of a Mickey Tettleton Jr., a valuable hitter who will never hit for a great batting average, but hits enough home runs and draws enough walks to make up for it — but he’s spent significant time on the disabled list. The same goes for second baseman Howie Kendrick, a natural high-average hitter who could be a force at his position if he could just refrain from breaking his fingers.

The designated hitter position was a self-made fiasco for the Angels, foolishly entrusted to Shea Hillenbrand, a relatively weak hitter even at his best. Since his release, the Angels have largely used the position to get Willits at bats, playing him in the field in place of Guerrero or Garrett Anderson. Anderson is the Angels’ other big problem on offense, and will be a key point of blame if the relentless Mariners are eventually able to knock the Angels out of the division lead. Scioscia is not above the blind devotion to long-time players that has plagued other managers. Anderson fits the syndrome perfectly, having played more games for the Scioscia Angels than any other player. Unfortunately, he can’t hit anymore, and hasn’t been an offensive asset in at least four years. Despite this, and between stints on the disabled list, he goes right back into the lineup.

Anderson’s persistence hints at the essence of the Angels’ offensive style: Don’t walk, don’t strike out, just pick your pitch, and drive it. If you put enough balls in play, something will fall in. When that happens, we’ll steal a base, hit and run, and maybe Vladdie will hit one out. While even the most loyal of managers might have a problem with a left fielder/DH batting .271 AVG/.297 OBA/.412 SLG, Anderson is still able to lay the bat on the ball — but only sometimes.

In Anderson — and in their whole approach — the Angels are the personification of Billy Crystal’s old “Saturday Night Live” catchphrase, “it’s better to look good than to feel good.” In Scioscia-ball, approach counts for as much as results. It’s a triumph of style over substance, and it shouldn’t work. In the years where the Angels haven’t had exemplary pitching, it hasn’t. Scioscia does a lot of things well: His willingness to move players like Chone Figgins and Robb Quinlan all over the field has helped the Angels stave off disaster at multiple positions. He’s won one World Series, but he could have had more, if only he had been willing to construct more of a conventional offense. Herzog’s anachronistic offense was meant to liberate the Cardinals. Scioscia’s has often had the opposite effect.

Mr. Goldman writes the Pinstriped Bible for yesnetwork.com and is the author of “Forging Genius,” a biography of Casey Stengel.