SAN ANTONIO — Jarron Collins used to study scouting reports as if his career depended on it. In a league filled with some of the world’s greatest athletes, he was a plodding center with few offensive moves.

“For a player like myself, I had no choice: I had to think the game out there,” said Collins, who lasted 10 seasons in the NBA despite never averaging more than 6.4 points per game. “I didn’t have the level of athleticism that other guys had, but I could execute a game plan and do what my coaches asked me to do.”

This relentless preparation has fueled his rise as an NBA assistant. Less than halfway through his first season overseeing the Warriors’ defense, Collins has gotten a young, unheralded group to care about the principles — positioning, communication, effort — that allowed a late second-round pick from Stanford to make life difficult on the likes of Shaquille O’Neal, Tim Duncan and Kevin Garnett.

After languishing at the bottom of the league’s defensive rankings for more than a month, Golden State is beginning to look respectable. It posted the NBA’s best defensive rating during its recent four-game winning streak.

That’s quite the feat for a team that, without Klay Thompson (left knee surgery), Andre Iguodala (traded to the Grizzlies) and Shaun Livingston (retired) has been low on proven defenders. Draymond Green and Kevon Looney are the Warriors’ only players with much of a pedigree on that side of the ball, and they have combined to miss 34 games this season.

That has forced Collins to get creative with his defensive schemes. After a half-decade of barely changing its switch-heavy system, Golden State has ratcheted up the risk in hopes of stealing some wins.

“We’re not one of the best defenses in the league, but we’re also not among the worst,” Warriors head coach Steve Kerr said. “We’ve sort of become middle-of-the-pack over the last few weeks, and that’s a victory for us. JC deserves a lot of credit for that.”

No game better illustrated the Warriors’ aggressive approach than their Christmas Day upset of Houston, in which they sent double-teams toward James Harden at the top of the key on almost every possession. Facing consistent pressure, Harden seldom attacked the rim, attempting only one foul shot and finishing 15 points below his season average.

After the game, Green lauded Collins for a “f—ing phenomenal” game plan. On a national stage, Collins had out-thought one of the most explosive scorers in NBA history, providing a blueprint for other teams to limit Harden.

This came as no surprise to those who have watched Collins. When Ron Adams told head coach Steve Kerr last summer that he wanted to scale back his responsibilities this season, Kerr knew immediately that Collins would take over as the unofficial defensive coordinator.

Just as he did during a decade-long playing career for the Jazz, Suns, Clippers and Trail Blazers, Collins had built a reputation for meticulous film study. His easy-to-digest scouting reports offer defensive objectives and breakdowns of opponents’ tendencies.

Because Collins knows the Warriors can’t consistently shut down players like Harden, LeBron James and Kawhi Leonard, he sets smaller goals for his team: take away their favorite shot, keep them off the foul line, hold them below their season average.

“I think it’s super beneficial for me as one of my player-development coaches,” forward Marquese Chriss said of working with Collins. “I feel like I have the same kind of mind-set with guys like that, so it’s been helpful for me and helpful for other players on the team.”

Other franchises have taken notice. Over the past two years, Collins has interviewed for head-coaching jobs with the Hawks and Grizzlies. Many in the Warriors’ organization believe that his basketball IQ, experience under respected mentors and ability to relate to players ensure that he’ll soon lead a team of his own.

In the meantime, Kerr is pleased to have Collins on his staff. His easygoing demeanor has helped stabilize an inexperienced team during a transitional season. And last month, when injuries depleted Golden State’s frontcourt depth, Collins even joined a few drills.

Tuesday’s game Who: Warriors (9-25) at Spurs (13-18) When: 4:05 p.m. TV: NBCSBA Radio: 95.7

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“The running joke has always been that, if I led the team in scoring, we were probably going to lose that game,” Collins said with a chuckle. “I’ll stick to game plans.”

Connor Letourneau is a San Francisco Chronicle staff writer. Email: cletourneau@sfchronicle.com Twitter: @Con_Chron