Beware the player who performs best when either far behind or far ahead.

Someone gave me that advice years ago, and it comes to mind as the season unfolds for New Jersey Devils forward Ilya Kovalchuk.

A high-scoring winger acquired last year, Kovalchuk thrived when his team seemed to be out of contention. Then, with his help, the Devils did what seemed to be impossible — they played themselves back into the playoff picture. But now that things are close, Kovalchuk must prove that he can still score.

It’s not just Kovalchuk. There are a lot of athletes who do just fine when the outcome is clear. Those aren’t the athletes that you want on your team. You want the athletes who thrive when the score is close. The athletes who love to make a difference.

That’s why on big stages — like the NCAA tournament, the World Series, the Stanley Cup playoffs — it’s often the unlikely heroes who emerge. Those players are used to fighting for their lives every night. For them, the stakes are always high and the score is always close.

Ali Farokhmanesh led Northrn Iowa on an unlikely run in last year’s NCAA tournament by hitting shots in the last minute. David Eckstein, who began his college career without a scholarship, wound up being a member of two World Series champions. John Druce emerged from obscurity in 1990 to score 15 playoff goals and lead the Washington Capitals on a long run in the Stanley Cup playoffs.

Those are the kind of players you want. They play in the moment because they don’t look ahead or behind. They can’t afford to. They’re too busy.

Kovalchuk has nine game-winning goals this season, an impressive total. But now that the stakes are high and the race is close, the Devils need him more than ever.

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Mike Tully speaks to sports, business and educational groups. He also works with coaches, athletes and teams to make their practice time more productive and efficient. He and Gary Pritchard are co-authors of “Ten Things Great Coaches Know.” To see Coach Tully and Coach Pritchard discuss “Seven Ways to Prepare for Adversity,” go here.