That's why the proposed £40 million transfer sending Costa to the Blues, per Daily Mail reporter Neil Ashton, represents a perfect match.
Since moving from a roving wide role this summer, Costa has thrived as the focal point of the Atletico forward line. He has hit 32 goals this season in a lone match-winner role who adds a flourish to Madrid's plethora of workmanlike grafters.
Costa fits so smoothly into the Atletico framework because he matches his teammates for effort. That quality will certainly appeal to Chelsea boss Jose Mourinho, who has always placed a premium on attackers who combine toil with talent.
None of the three strikers Mourinho has trusted this season offers that same invaluable fusion. Veteran Samuel Eto'o hasn't lost his assurance in front of goal, but he lacks the energy to harass defensive lines the way Costa does.
Almost forgotten £50-million flop Fernando Torres has displayed his quality as a link player but has long since waved goodbye to his A-grade finishing ability.
Finally, Demba Ba can still come alive in the box, but he is not technically gifted enough to be the fulcrum of any attack.
Chelsea's sputtering trio has condemned the team to poor results more than once this season. The problem has been most obvious away from home. A recent 1-0 defeat to Aston Villa was the latest evidence of how Chelsea misfire away from Stamford Bridge.
But the Blues also shot blanks in a stale home draw with West Ham United in January. If they don't win this season's EPL title, Chelsea won't have to look past their ailing forward line for the reason why, as one stat from Squawka vividly illustrates:
What Mourinho needs is a legitimate match-winner. That is exactly what Costa has become.
Costa is now every bit as dynamic as the man he replaced at the heart of Atletico's attack, Radamel Falcao, according to AtleticoFans.com writer Martin Rosenow:
Mourinho needs that kind of presence at the tip of this Chelsea team. He wouldn't even have to alter the way Chelsea build their attacks to suit Costa.
Since selling Juan Mata, Chelsea lack a prolific creator in the middle. But so do Atletico, who rely instead on the toughness and savvy of the underrated Gabi Fernandez.
Costa flourishes thanks to the supply of able wide players like Arda Turan and Koke. The latter is joint-second on the La Liga assists table, with 11, per ESPN FC.
Like Madrid, Chelsea also count on wide players for their creative output. Fleet-footed wing ace Eden Hazard is the most generous provider for the Blues, with seven assists, per more figures from ESPN FC.
Costa perfectly fits how Chelsea construct scoring chances, but Mourinho must move fast for the recently called-up Spain international.
Goal.com reporter Wayne Veysey confirms Chelsea want to complete a deal for the 25-year-old before that happens:
Chelsea won't want a bidding war for Costa, even if he is guaranteed to boost their firepower.