There is no correlation between Duration and Hero Damage. Some has higher Duration, some has higher Hero Damage. Objects are grouped into clusters (marked with different colors) based on close values of Duration and Hero Damage.
Duration Hero Damage
Abaddon 2372 578.51
Ancient Apparition 2535 525.87
Anti-Mage 2423 589.48
Bane 2434 400.56
Bounty Hunter 2388 473.49
Brewmaster 2389 513.05
Centaur Warrunner 2447 575.40
Clockwerk 2457 579.04
Crystal Maiden 2437 444.92
Dark Seer 2447 620.82
Dark Willow 2487 556.03
Dazzle 2399 281.68
Disruptor 2435 352.44
Doom 2434 552.99
Dragon Knight 2442 559.67
Earth Spirit 2391 466.56
Earthshaker 2486 613.49
Elder Titan 2493 589.15
Enchantress 2447 541.59
Enigma 2465 537.11
Faceless Void 2478 582.94
Grimstroke 2450 431.15
Gyrocopter 2462 664.21
Hoodwink 2483 548.93
Invoker 2469 666.54
Jakiro 2459 535.71
Keeper of the Light 2433 473.48
Kunkka 2481 656.06
Lich 2462 475.30
Lina 2470 579.98
Lion 2468 339.97
Magnus 2391 511.39
Marci 2372 529.96
Mars 2430 528.04
Mirana 2442 447.88
Nature's Prophet 2436 574.96
Night Stalker 2416 498.82
Nyx Assassin 2462 680.41
Ogre Magi 2437 576.06
Omniknight 2364 519.64
Oracle 2361 324.20
Phoenix 2443 580.95
Primal Beast 2437 567.65
Pudge 2427 534.94
Riki 2472 695.85
Rubick 2462 504.10
Sand King 2491 691.52
Shadow Demon 2471 502.05
Shadow Shaman 2443 401.23
Silencer 2465 574.06
Skywrath Mage 2455 647.12
Slardar 2438 481.19
Snapfire 2437 538.50
Spirit Breaker 2423 528.36
Tidehunter 2438 486.55
Tiny 2427 590.69
Treant Protector 2424 376.54
Tusk 2411 499.34
Underlord 2420 605.78
Undying 2418 384.11
Vengeful Spirit 2400 384.86
Venomancer 2457 676.61
Warlock 2442 530.58
Windranger 2466 691.54
Winter Wyvern 2466 582.33
Witch Doctor 2467 601.64
Duration Hero Damage
Arc Warden 2445 988.57
Axe 2481 784.58
Bloodseeker 2475 773.94
Bristleback 2476 872.21
Drow Ranger 2493 728.65
Ember Spirit 2430 932.55
Medusa 2484 853.13
Muerta 2477 854.23
Queen of Pain 2458 845.25
Razor 2486 744.42
Sniper 2526 858.25
Spectre 2534 1004.57
Techies 2490 755.53
Tinker 2465 1016.93
Viper 2515 749.93
Weaver 2480 742.32
Zeus 2526 947.05
Duration Hero Damage
Beastmaster 2328 611.35
Broodmother 2272 500.82
Chen 2276 243.31
Io 2280 190.27
Lone Druid 2270 508.06
Lycan 2305 476.28
Meepo 2263 698.11
Visage 2310 571.44
Duration Hero Damage
Alchemist 2380 673.97
Batrider 2396 622.75
Chaos Knight 2402 669.36
Clinkz 2394 751.92
Dawnbreaker 2399 586.96
Death Prophet 2430 669.08
Huskar 2371 747.98
Juggernaut 2397 721.96
Legion Commander 2397 796.32
Leshrac 2437 715.60
Lifestealer 2406 645.64
Luna 2402 677.20
Monkey King 2409 736.91
Morphling 2365 672.35
Naga Siren 2399 631.56
Necrophos 2420 833.01
Outworld Destroyer 2435 794.57
Pangolier 2449 686.77
Phantom Assassin 2423 755.70
Phantom Lancer 2435 717.22
Puck 2431 774.66
Pugna 2414 677.93
Shadow Fiend 2389 779.18
Slark 2408 622.04
Storm Spirit 2444 712.64
Sven 2434 736.62
Templar Assassin 2385 749.91
Terrorblade 2410 681.58
Timbersaw 2430 798.31
Troll Warlord 2420 700.10
Ursa 2441 773.61
Void Spirit 2396 788.37
Wraith King 2419 685.53