Jan 052012
 

This article will bring to a close, at least for now, our series on effective health (EH). In this article you’ll find a summary of the findings from our three previous analyses on effective health. Moreover, we included four sortable tables with the effective health and cost per unit of EH for five of Leona’s levels: 1, 6, 11, 16 and 18. They roughly correspond to the early, mid and late game which are the most distinguished phases in the game.

Leona, the Radiant Dawn

Levels 6, 11 and 16 were chosen because at those levels a new skill point can be placed on Leona’s ultimate, Solar Flare. Those levels are well spread and provide a good place to evaluate the benefits that an item provides at different important stages of a match.

What is Effective Health?

We answered this question by explaining how damage reduction works and how it’s related to effective health. We continued analysing the possible diminishing returns of increasing EH, comparing pure health to armour and magic resistance (MR) and concluded that both health and defence are practical ways of rising EH.

Items’ Effective Health Comparison

For our second entry we accepted Leona’s offer to become a test tank and analysed her effective health as she leveled up using each of the items that provided health, armour or MR. We divided the analysis between physical and magical EH, one for each type of damage. We found out that Warmog’s Armor is the best single item for EH due to its vast health bonus.

Nonetheless, items that provided a combination of health and defence or huge amounts of defence were also viable alternatives. The former were Randuin’s Omen, Sunfire Cape, Banshee’s Veil and Odyn’s Veil; which combine health and armour or MR. The latter were Thornmail, Frozen Heart and Force of Nature; which provide armour or MR alone.

Effective Health Items’ Cost Effectiveness

To examine the cost per unit of EH provided by each item we needed Leona’s help again. For each of Leona’s levels we divided each item’s price in gold by the amount of EH that Leona has with the item equipped. The calculations were separated into physical and magical EH for each type of damage once more.

The graphs were quite clear showing how as Leona’s base EH grows by gaining levels the cost of increasing EH tends to fall below one gold per unit. The conclusion drawn was that as all items become cost effective by late game, items that provide the most EH are the recommended investment.

The Tables

The four sortable tables below correspond to the analysis made in the last two articles: Items’ Effective Health Comparison and Effective Health Items’ Cost Effectiveness. The first table shows the physical effective health that Leona has, per level, with each of the items that boost health or armour. Abyssal Scepter was included to show the evolution of Leona’s base EH and to serve as a base line to compare other items.

Physical Effective Health Items Table
Name EH Lvl 1 EH Lvl 6 EH Lvl 11 EH Lvl 16 EH Lvl 18
Abyssal Scepter 626.087 1300.432 2109.627 3053.672 3469.048
Aegis of the Legion 1189.157 2035.852 3017.397 4133.792 4618.108
Atma’s Impaler 858.737 1728.832 2733.777 3873.572 4367.248
Banshee’s Veil 1080.212 1812.682 2680.002 3682.172 4120.798
Catalyst the Protector 977.277 1696.572 2550.717 3539.712 3973.068
Chain Vest 858.737 1728.832 2733.777 3873.572 4367.248
Cloth Armor 719.147 1471.792 2359.287 3381.632 3828.328
Doran’s Blade 747.187 1437.032 2261.727 3221.272 3642.848
Doran’s Ring 747.187 1437.032 2261.727 3221.272 3642.848
Doran’s Shield 835.107 1571.552 2442.847 3448.992 3889.208
Elixir of Fortitude 910.672 1621.442 2467.062 3447.532 3877.478
Entropy 959.112 1676.082 2527.902 3514.572 3946.998
Frozen Heart 1137.917 2242.912 3482.757 4857.452 5445.088
Frozen Mallet 1473.787 2256.632 3174.327 4226.872 4685.648
Giant’s Belt 1146.817 1887.812 2763.657 3774.352 4216.388
Glacial Shroud 858.737 1728.832 2733.777 3873.572 4367.248
Guardian Angel 977.647 1947.792 3052.787 4292.632 4826.328
Haunting Guise 868.287 1573.632 2413.827 3388.872 3816.648
Heart of Gold 928.837 1641.932 2489.877 3472.672 3903.548
Hextech Sweeper 989.387 1710.232 2565.927 3556.472 3990.448
Ionic Spark 928.837 1641.932 2489.877 3472.672 3903.548
Kindlegem 868.287 1573.632 2413.827 3388.872 3816.648
Leviathan 1619.107 2420.552 3356.847 4427.992 4894.208
Madred’s Bloodrazor 755.337 1538.432 2456.377 3509.172 3968.048
Madred’s Razor 744.997 1519.392 2428.637 3472.732 3928.128
Ninja Tabi 755.337 1538.432 2456.377 3509.172 3968.048
Odyn’s Veil 1049.937 1778.532 2641.977 3640.272 4077.348
Phage 898.562 1607.782 2451.852 3430.772 3860.098
Prospector’s Blade 868.287 1573.632 2413.827 3388.872 3816.648
Prospector’s Ring 868.287 1573.632 2413.827 3388.872 3816.648
Randuin’s Omen 1700.187 2755.032 3944.727 5269.272 5836.848
Rod of Ages 1389.017 2161.012 3067.857 4109.552 4563.988
Ruby Crystal 844.067 1546.312 2383.407 3355.352 3781.888
Rylai’s Crystal Scepter 1231.587 1983.432 2870.127 3891.672 4338.048
Shurelya’s Reverie 1025.717 1751.212 2611.557 3606.752 4042.588
Soul Shroud 1255.807 2010.752 2900.547 3925.192 4372.808
Spirit Visage 928.837 1641.932 2489.877 3472.672 3903.548
Sunfire Cape 1606.187 2546.032 3620.727 4830.272 5351.848
Thornmail 1143.087 2252.432 3496.627 4875.672 5465.048
Trinity Force 928.837 1641.932 2489.877 3472.672 3903.548
Warden’s Mail 884.587 1776.432 2803.127 3964.672 4467.048
Warmog’s Armor 2164.057 3035.252 4041.297 5182.192 5676.308
Wriggle’s Lantern 781.187 1586.032 2525.727 3600.272 4067.848
Zhonya’s Hourglass 884.587 1776.432 2803.127 3964.672 4467.048

The second table is the equivalent to the previous one but on magical effective health; all items in the table grant health or MR. Atma’s Impaler was included as baseline for Leona’s base EH as it doesn’t contribute any health or MR.

Magical Effective Health Items Table
Name EH Lvl 1 EH Lvl 6 EH Lvl 11 EH Lvl 16 EH Lvl 18
Abyssal Scepter 966.79 1780.24 2593.69 3407.14 3732.52
Aegis of the Legion 1330.03 2065.18 2800.33 3535.48 3829.54
Atma’s Impaler 672.1 1237.6 1803.1 2368.6 2594.8
Banshee’s Veil 1605.6 2388.6 3171.6 3954.6 4267.8
Catalyst the Protector 1049.1 1614.6 2180.1 2745.6 2971.8
Chalice of Harmony 827.2 1523.2 2219.2 2915.2 3193.6
Doran’s Blade 802.1 1367.6 1933.1 2498.6 2724.8
Doran’s Ring 802.1 1367.6 1933.1 2498.6 2724.8
Doran’s Shield 828.1 1393.6 1959.1 2524.6 2750.8
Elixir of Fortitude 977.6 1543.1 2108.6 2674.1 2900.3
Entropy 1029.6 1595.1 2160.6 2726.1 2952.3
Force of Nature 1065.02 1961.12 2857.22 3753.32 4111.76
Frozen Mallet 1582.1 2147.6 2713.1 3278.6 3504.8
Giant’s Belt 1231.1 1796.6 2362.1 2927.6 3153.8
Guardian Angel 868.56 1599.36 2330.16 3060.96 3353.28
Haunting Guise 932.1 1497.6 2063.1 2628.6 2854.8
Heart of Gold 997.1 1562.6 2128.1 2693.6 2919.8
Hexdrinker 853.05 1570.8 2288.55 3006.3 3293.4
Hextech Sweeper 1062.1 1627.6 2193.1 2758.6 2984.8
Ionic Spark 997.1 1562.6 2128.1 2693.6 2919.8
Kindlegem 932.1 1497.6 2063.1 2628.6 2854.8
Leviathan 1738.1 2303.6 2869.1 3434.6 3660.8
Lich Bane 827.2 1523.2 2219.2 2915.2 3193.6
Mercury’s Treads 801.35 1475.6 2149.85 2824.1 3093.8
Negatron Cloak 920.26 1694.56 2468.86 3243.16 3552.88
Null-Magic Mantle 796.18 1466.08 2135.98 2805.88 3073.84
Odyn’s Veil 1560.6 2343.6 3126.6 3909.6 4222.8
Phage 964.6 1530.1 2095.6 2661.1 2887.3
Prospector’s Blade 932.1 1497.6 2063.1 2628.6 2854.8
Prospector’s Ring 932.1 1497.6 2063.1 2628.6 2854.8
Quicksilver Sash 961.62 1770.72 2579.82 3388.92 3712.56
Randuin’s Omen 1127.1 1692.6 2258.1 2823.6 3049.8
Rod of Ages 1491.1 2056.6 2622.1 3187.6 3413.8
Ruby Crystal 906.1 1471.6 2037.1 2602.6 2828.8
Rylai’s Crystal Scepter 1322.1 1887.6 2453.1 3018.6 3244.8
Shurelya’s Reverie 1101.1 1666.6 2232.1 2797.6 3023.8
Soul Shroud 1348.1 1913.6 2479.1 3044.6 3270.8
Spirit Visage 1227.2 1923.2 2619.2 3315.2 3593.6
Sunfire Cape 1257.1 1822.6 2388.1 2953.6 3179.8
Trinity Force 997.1 1562.6 2128.1 2693.6 2919.8
Warmog’s Armor 2323.1 2888.6 3454.1 4019.6 4245.8
Wit’s End 930.6 1713.6 2496.6 3279.6 3592.8

Based on the table on physical effective health per Leona’s level, the first table, the following table divides the price of each item by the EH Leona has at each level. The value calculated corresponds to the cost of each unit of EH the combination of Leona’s base EH and each item’s EH offer.

Physical Effective Health Items Cost Effectiveness Table
Name EH Lvl 1 EH Lvl 6 EH Lvl 11 EH Lvl 16 EH Lvl 18
Abyssal Scepter 4.232638595 2.037784367 1.256146229 0.867807675 0.763898338
Aegis of the Legion 1.618793818 0.945550069 0.637967095 0.465674132 0.416837371
Atma’s Impaler 2.800624638 1.391112612 0.879735253 0.620873963 0.550690046
Banshee’s Veil 2.513395519 1.497780637 1.013058945 0.73733655 0.65885297
Catalyst the Protector 1.355808026 0.780986601 0.519461783 0.374324239 0.333495425
Chain Vest 0.815150622 0.404897642 0.256055999 0.180711756 0.160284005
Cloth Armor 0.417160886 0.20383315 0.127157061 0.088714561 0.078363191
Doran’s Blade 0.635717699 0.330542396 0.210016505 0.147457278 0.130392484
Doran’s Ring 0.635717699 0.330542396 0.210016505 0.147457278 0.130392484
Doran’s Shield 0.568789389 0.302248987 0.194445252 0.137721398 0.122132835
Elixir of Fortitude 0.27452255 0.154183745 0.10133511 0.072515643 0.064474898
Entropy 3.716979873 2.126984241 1.410260366 1.014348262 0.903218091
Frozen Heart 2.438666441 1.237230886 0.796782549 0.571287169 0.509633637
Frozen Mallet 2.20520333 1.440199377 1.023839069 0.768890092 0.693607373
Giant’s Belt 0.96789636 0.587982278 0.401641738 0.294090217 0.263258505
Glacial Shroud 1.775863856 0.882098434 0.557836283 0.393693469 0.349190154
Guardian Angel 2.65944661 1.334844788 0.851680776 0.605689004 0.538711832
Haunting Guise 1.710264003 0.943676794 0.615205646 0.438198905 0.389084872
Heart of Gold 0.888207511 0.502456862 0.331341669 0.237569226 0.211346191
Hextech Sweeper 1.890059198 1.093418905 0.72878145 0.525801975 0.468619062
Ionic Spark 2.476214879 1.400788827 0.92374041 0.662314206 0.589207562
Kindlegem 0.978938991 0.5401517 0.352137912 0.250820922 0.222708513
Leviathan 0.787471118 0.526739355 0.379820707 0.2879409 0.260512017
Madred’s Bloodrazor 5.030867017 2.470047425 1.546993804 1.08287653 0.957649706
Madred’s Razor 1.342287284 0.658158 0.411753589 0.287957723 0.254574189
Ninja Tabi 1.125325517 0.552510608 0.346038088 0.242222382 0.214211118
Odyn’s Veil 2.585869438 1.526539865 1.027639529 0.745823389 0.665873995
Phage 1.463449378 0.817896954 0.536329273 0.383295655 0.340664926
Prospector’s Blade 1.094108284 0.603698959 0.393565902 0.280329266 0.248909514
Prospector’s Ring 1.094108284 0.603698959 0.393565902 0.280329266 0.248909514
Randuin’s Omen 1.808624581 1.116139486 0.779521625 0.583572076 0.526825437
Rod of Ages 2.184998456 1.404434589 0.989289918 0.738523323 0.664988602
Ruby Crystal 0.562751535 0.307182509 0.199294539 0.141564879 0.125598643
Rylai’s Crystal Scepter 2.521137362 1.56546834 1.081833661 0.797857579 0.715759715
Shurelya’s Reverie 2.144841121 1.256272798 0.842409337 0.609967084 0.54420584
Soul Shroud 1.819547112 1.136390763 0.787782442 0.582137129 0.522547526
Spirit Visage 2.460065652 1.391653248 0.917716016 0.657994766 0.585364904
Sunfire Cape 1.624966458 1.025124586 0.720849708 0.540342242 0.487682012
Thornmail 1.749648102 0.887929136 0.571979797 0.410199866 0.365962019
Trinity Force 4.381823721 2.478787185 1.634618899 1.172008183 1.042641207
Warden’s Mail 1.526135926 0.759950282 0.481605008 0.340507361 0.302213005
Warmog’s Armor 1.386285112 0.988385808 0.742335938 0.578905606 0.528512547
Wriggle’s Lantern 2.048165164 1.008806884 0.633480974 0.444410867 0.393328364
Zhonya’s Hourglass 3.504460274 1.745071019 1.105907795 0.781905792 0.693970604

Finally the same treatment is given to magical effective health. For each of Leona’s levels and each item that supplies health or MR we calculate the cost per unit of EH that Leona has.

Magical Effective Health Items Cost Effectiveness Table
Name EH Lvl 1 EH Lvl 6 EH Lvl 11 EH Lvl 16 EH Lvl 18
Abyssal Scepter 2.741029593 1.48856334 1.021710382 0.77777843 0.709976102
Aegis of the Legion 1.447335774 0.932122139 0.687418983 0.544480523 0.502671339
Atma’s Impaler 3.578336557 1.943277311 1.333813987 1.015367728 0.926853707
Banshee’s Veil 1.690956652 1.136649083 0.856034809 0.686542255 0.636159145
Catalyst the Protector 1.262987322 0.82063669 0.607770286 0.482590326 0.445857729
Chalice of Harmony 1.075918762 0.584296218 0.401045422 0.305296378 0.278682365
Doran’s Blade 0.592195487 0.347323779 0.245719311 0.19010646 0.174324721
Doran’s Ring 0.592195487 0.347323779 0.245719311 0.19010646 0.174324721
Doran’s Shield 0.573602222 0.340843858 0.242458272 0.188148618 0.172677039
Elixir of Fortitude 0.255728314 0.162011535 0.118562079 0.093489398 0.08619798
Entropy 3.462509713 2.234969594 1.650004628 1.30772899 1.20753311
Force of Nature 2.450658204 1.330872155 0.913475336 0.695384353 0.634764675
Frozen Mallet 2.054231717 1.513317191 1.197891711 0.991276764 0.927299703
Giant’s Belt 0.901632686 0.617833686 0.469920833 0.379150157 0.35195637
Guardian Angel 2.99346044 1.62565026 1.115803207 0.849406722 0.775360244
Haunting Guise 1.593176698 0.991586538 0.719790606 0.564939512 0.520176545
Heart of Gold 0.827399458 0.52796621 0.387669752 0.306281556 0.2825536
Hexdrinker 2.110075611 1.145912911 0.786524218 0.59874264 0.546547641
Hextech Sweeper 1.760662838 1.148930941 0.852674297 0.677880084 0.626507639
Ionic Spark 2.306689399 1.471905798 1.080776279 0.853875854 0.787725187
Kindlegem 0.911919322 0.567574786 0.412001357 0.32336605 0.29774415
Leviathan 0.733559634 0.553481507 0.444390227 0.371222268 0.348284528
Lich Bane 4.194874275 2.278098739 1.563626532 1.190312843 1.086548096
Mercury’s Treads 1.497473014 0.813228517 0.558178478 0.424914132 0.387872519
Negatron Cloak 0.804120575 0.436691531 0.29973348 0.228172523 0.208281732
Null-Magic Mantle 0.502398955 0.272836407 0.187267671 0.142557772 0.130130391
Odyn’s Veil 1.739715494 1.158474142 0.868355402 0.694444444 0.642938335
Phage 1.363259382 0.859420953 0.627505249 0.494156552 0.455442801
Prospector’s Blade 1.019203948 0.634348291 0.460472105 0.361409115 0.332772874
Prospector’s Ring 1.019203948 0.634348291 0.460472105 0.361409115 0.332772874
Quicksilver Sash 1.497473014 0.813228517 0.558178478 0.424914132 0.387872519
Randuin’s Omen 2.728240618 1.816731655 1.361764315 1.089035274 1.008262837
Rod of Ages 2.0354101 1.475736653 1.157469204 0.952126992 0.889038608
Ruby Crystal 0.524224699 0.322777929 0.233174611 0.182509798 0.167915724
Rylai’s Crystal Scepter 2.348536419 1.644945963 1.265745383 1.02862254 0.95691568
Shurelya’s Reverie 1.998001998 1.320052802 0.985618924 0.786388333 0.727561347
Soul Shroud 1.694978117 1.194084448 0.921705458 0.750509098 0.698605846
Spirit Visage 1.26303781 0.805948419 0.591783751 0.467543436 0.431322351
Sunfire Cape 2.076207143 1.432020191 1.092919057 0.883667389 0.82080634
Trinity Force 4.081837328 2.604633303 1.912504112 1.510989011 1.393931091
Warmog’s Armor 1.2913779 1.038565395 0.868533048 0.74634292 0.706580621
Wit’s End 2.149151085 1.16713352 0.801089482 0.609830467 0.556668893

Conclusion

The tables presented allow an easy comparison between items so that item purchases can be planed according to the expected length of a game. Matches in Summoner’s Rift will likely last enough for champions to reach level 18 so items with better late game performances are preferred.

On the other hand, Dominion is very fast paced so planning for items with good mid game performance might be the best option. Additionally, early game champions can benefit by obtaining strong early game items. The tables can be sorted at any level so items can be easily compared and a plan can be set.

If you have any doubts or would like to recommend additional topics to cover don’t forget that you can leave a comment. We’d appreciate your feedback and thank you for your preference.

– Acronyms: AD: attack damage, AP: ability power, AS: attack speed, CD: cooldown, CDR: cooldown reduction, CS: critical strike chance, Gp10: gold per 10 sec., Hp5: health regen per 5 sec., LS: life steal, MD: magic damage, Mp5: mana regen per 5 sec., MR: magic resist, MS: movement speed, PD: physical damage, SV: spell vamp




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