It is a fairly complex problem and highly dependent on efficiency of the item, hero, and matchup.
Efficiency
The concept is kind of similar to a spell like Dragon Knight's Dragon Tail stun which gives you amazing worth for one level, but very marginal gains for additional levels.
As a hero that is constantly getting things that benefit the team (i.e. consumables, Arcanes, Force Staff, etc.), it's hard to pass up the value of Magic Stick, but hard to justify the upgrade to Magic Wand on grounds of efficiency, at least until you get some core items.
You can justify it sometimes in events like:
- There is a lot of spam (e.g. Batrider Sticky Napalm)
- You are heavily involved in fights (in which case an Urn of Shadows may also be worth it)
- You are rolling in money
Considerations
You do need to take a lot into consideration for any decision in a game. Especially as the community gets bigger and players become better, efficiency becomes core.
You want to take into account:
- Starting Items - if you already had Iron Branches to begin with, then the relative cost of upgrading to Magic Wand is lower --> easier to justify the expense
- Usefulness - you get the most use out of Magic Wand when you are heavily involved in fights, and when lots of spells are cast. If you are split-pushing, or farming more towards late game, that may not be as useful to you.
- NOTE: burst healing is one of THE MOST beneficial things. Anything that allows for mind games or warping another player's sense of risk/reward is hugely powerful.
- Comparative Use - the benefit of upgrading needs to outweigh the benefit of another item. If you're prioritizing Magic Wand over something like Blink Dagger on Batrider, then you really need to have a good reason. Same goes for supports - 150g for Wards, or 100g for Smoke can easily have far more impact than 150g for a Magic Wand recipe.
- How Likely It Is To Change Your Fate - some heroes will basically be dead if caught out no matter what they do. Like a Nature's Prophet may get relatively low use out of a Magic Stick.
Basically, it's nice to not have Iron Branches clogging your inventory, but there are other ways to deal with that. You need to consider the worth still.
Misc
Just remember the breakdown of the item:
Magic Stick
- 10 Charges
- 15 HP/Mana per Charge ==> 150 Max Burst HP/Mana
- 200g Total
Magic Wand
- 15 Charges
- 15 HP/Mana per Charge ==> 225 Max Burst HP/Mana
- 500g Total (150g for Recipe)
- Gold Efficiency of Heal
- Magic Stick ==> 150/200 = 0.75
- Magic Wand ==> 225/500 = 0.45
- However, you never know when that extra 75 HP/Mana will make the difference
- You also get +3 Stats, which is 39 Mana, 57 HP, and some regen, armor, and attack speed as well
Heroes
While the vast majority of heroes get Magic Stick, the amount that get Magic Wand varies quite a bit.
Supports
The heroes you're LEAST likely to see upgrade it are supports.
This is because:
- Supports often start with Observer Ward + Animal Courier/Sentry Ward + Smoke of Deceit, Tangos, Clarity, and Healing Salve--> this means they do not have Iron Branches to start with, thus nothing clogging up their inventory for a long time
- Magic Stick is incredibly efficient because burst heals are amazing for baiting opponents into stupid decisions
- Often, paying the extra 300g (3 branches + recipe) is not worth it to a support since that is a large chunk of Arcane Boots, Mekansm, Force Staff, etc.. All of which benefit the entire team, not just you
Offlane
This depends quite a bit on the hero.
Someone like Tidehunter or Batrider may get one, but usually not before their core items (i.e. Blink Dagger). They are both heavily involved in rotation and ganks, so there should be plenty of opportunity to get use out of the upgraded stick.
A hero like Nature's Prophet may not be as inclined to because he split-pushes, can port back to base at will, and often when he's caught out he dies regardless of whether he had Stick charges or not.
Other Cores
This will often depend on matchups and builds. Like, maybe you're Outworld Devourer and getting a Mek so having a Magic Wand could be a bit redundant and slow down your Mekansm timing. Now you have burst healing and decent mana recovery.
Some 1v1 matchups may not need it, like if you're 1v1 against Drow Ranger, she has only 1 spell that can trigger charges and she doesn't spam it (i.e. silence).
It can also be a player preference thing, efficiency thing, or otherwise. I notice Universe does not seem to pick up Magic Stick or Magic Wand all that often (at least in the later TI games), so there is some wiggle room for it on cores.
Magic Wand also contains up to 15 charges, while Magic Stick only holds 10.
How useful a Magic Wand (or a stick for that matter) is to you will depend on how quickly you can rack up charges. If you're laning against someone who spams abilities, you're going to have no problem filling up 15 charges on a frequent basis. Against someone who uses abil mainly just right clicks? Not so much. In that situation, you might as well just skip the stick all together.
I wouldn't upgrade it just because you have the branches, either. Mekansm and Pipe of Insight use branches too, so the are other ways to use them up. Even if you sell the branches, you only lose 25 gold - much less than the cost of a Magic Wand that you didn't really need.
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