Since actually playing the game has become a bit too easy until things get patched up, I decided to get started on running through some of the numbers for GCL. Because it’s easier to manage, I’ll focus on pure gems for the moment. I’ll mainly be looking at scaling, in particular: what powers get broken and what powers get useless past about grade 12?

For this first post, I’m taking a look at the effectiveness of specials for gems. Basically all you need to know is in the graph below

**About this graph**

- This graph uses a log(2) scale for the vertical axis. This means every time you go up one step, the power of the special *doubles*. For example, the orange power at grade 20 is about 100 times higher than the red one.

- Purple and yellow look a bit weird because they almost overlap in terms of strength. Looking at either line will give you a feel for the other though.

- If pictures give you a headache, the numbers are included below.

**About the results**

What does this actually tell us about the power of our gem types? Let’s look at them one by one:

*lime*: becomes insanely powerful at higher levels. Your damage potential is actually dozens of times higher as long as there are multiple enemies to hit. And we’re not even talking about double gems here.

*yellow*: The second sick gem. Once again, your damage potential is dozens of times higher, as long as you have big beefy targets, instead of lots of swarming monsters that die in one hit regardless. When you make a dual gem with lime, you have a gem that hits dozens of targets for dozens of times base damage, giving hundred of times the damage output of a base gem: you are now a God!

*orange*: looks really fancy as the top contender in the graph, but looks can be deceiving. For remember: the cost of a higher grade gem almost doubles every grade. So for orange to keep up, it would have to go up a factor of two (one line in the graph) per grade. However, it only averages about a doubling in mana drain for every two grades.

That doesn’t make it useless though, for there are two extra factors to consider. First, your gems firing speed increases. More firing speed means more hits per second, means more mana drained per second. Second, your mana pool will be getting larger, so your mana gain multiplier will go up too.

So what we want to look at is: take the cost of building a tower (let’s say 200 mana on average) and add the cost of your gem. That’s the amount you need to spend to get your gem set up.

Then you take the mana gain per hit and multiply it by the firing speed: this is your mana gained per second.

Compare the two, and you’ll see how fast you need to increases your mana gain multiplier to keep the gem scaling well.

If we do all this, we get the following base effectiveness (shown in both a linear and a log graph):

formula used: 60 * [mana gain per hit] * [firing speed] / {[gem cost] + 200}

*Note*: I didn’t actually have the firing speed for orange on hand, so I cheated and used the one for yellow gems. A fair approximation because yellow is around 10% faster, but it scales roughly the same.

So what we see is, to keep this gem gaining the same amount of mana per minute, you need to double the mana pool multiplier going from grade 4-8, double it again by grade 12 (to 4X), get it to 8X by grade 15 and to 16X by grade 18.

Overall, an orange gem scales acceptably, but it won’t make you rich without some serious investment in mana pool (and if you can invest in that, what do you need the gem for?)

It doesn’t get really interesting until you throw it in a trap combined with a lime gem and get a chance to multiply your mana gain by the number of chains as well!

*red*: this is one of the weirdest scaling gems. It’s sucky early on, because your kill count is still a lot lower than the base damage of the gem (it starts at 0 after all). But after a few waves, when you’ve racked up maybe 100-200 kills, it really starts adding up. By end game though, it is a useless piece of junk.

Let me explain that last one: As you can see in the graph, the base multiplier scales fairly poorly. Starting at 36% it isn’t doubled to 72% until grade 9 and you’ll have to wait until grade 14 to hit 3X the multiplier you started with (110%).

You’ll be racking up more kills though, doesn’t that mean the gem keeps getting stronger and stronger? Sure it will, but not fast enough.

If monsters kept giving the same amount of mana per kill, that meant by the time you had collected double the mana (needed to upgrade your gem one rank), you’d also have doubled your kill count. So every time you upgraded your gem, you’d have doubled your damage bonus too. A pretty sweet deal. In that case the increasing damage multiplier would just be icing on the cake.

However, the mana you get per kill *does* go up, by a lot! Not only does the base mana you get per monster you kill increase (easily by a factor of 10 throughout longer levels), but so does your mana pool multiplier. Pretty soon you’ll be raking in dozens of times as much mana per kill, but still only be getting a percentage of 1 damage added to your total. That’s where the increased special multiplier should kick in to keep the gem worthwhile, but it doesn’t. At that point, the red gem starts to suck.

Now don’t get me wrong, this gem can serve you well easily into grade 10 – even grade 12 when boosted in a trap – but you’ll see it become useless soon after that.

*Purple*: This gem scales fairly well, as you can see in the graph. The interesting part though is how fast the armor decreases as a function of your damage per hit. If you do twice as much damage with each hit, the armor had better go down twice as fast to keep things worthwhile as well. This gives us the purple effectiveness:

formula used: 60 * [armor drain per hit] * [firing speed] / [damage per hit]

*Note*: once again, I cheated and used my yellow data for both firing speed and damage per hit.

As you can see, purple scales well. With a good base scaling and higher firing speeds to stack up the armor drain, you actually cut through armor a bit faster compared to your damage as you level up.

In other words, purple would be a good choice *if* armor went up as fast as gem damage. It doesn’t though. Armor scaling is pathetic in the game right now, not even going over 100 until your gem is doing thousands of damage easily. That doesn’t just means you’ll cut through the armor with a single hit, it also means cutting through the armor will never give you a boost of more than a few % of base damage at most.

The purple mechanic is solid, but monster armor scaling is broken at higher levels to the point of making it useless.

*Blue*: Peter has told us slowing actually works as speed = 100% / (100% + slowing %). Plugging this in gives:

The problem is it’s hard to measure how you scale this, but the basic idea is: slowing doesn’t become ‘less useful’ as monsters get tougher, so an increase in slow % is an increase in effectiveness. In that sense, a higher grade slowing gem is more worthwhile than a lower grade one. How good it is compared to others though, depends completely on your style and strategy.

*Cyan*: Cyan works different from slowing. Every time it hits an enemy, they have a chance of being stunned (for 3 seconds). However, they also have an ever increasing ‘stun immunity’, going up by a random amount ranging from around 5% to 11% each stun, for an average of about 8%. Especially at higher grades, your attack rate is so high you can expect to have a guaranteed stun at some point even with a fairly small chance to stun. That means we can calculate the expected time a monster can be stunned by your gem at each level, overestimating it a bit for lower levels, but becoming pretty accurate at higher levels.

formula used: {3 * [stun %] / 0.08} – 10/[gem speed]

*Note*: the last term you subtract is an approximation of the lower level tendency to not get the max stun values. Because of their low firing speed, they don’t get enough hits in for guaranteed stun on low stun chances per hit.

Those times go pretty high. Does it actually work like that? Oh yes

Add to this the fact you can spread the stun to multiple targets, as long as you get back to each one every 3 seconds, and you have a pretty sweet alternative to blue gems. Once again, usefulness of slow/stun is situational, but if you have to pick, blue is not the only option.

*Green*: Green looks pretty underwhelming in terms of scaling, and it is. The percentage of base damage you do over 5 seconds stays pretty much the same (around 80%) regardless of level. Now it can be argued with higher firing speeds and larger range, you can apply it to more targets. This is actually not as silly as it sounds. With the ‘random’ targeting option, you can actually apply the poison to lots of targets.

Sound good? By grade 6, you’re already making 33.5 attacks in 5 seconds. Factor in the 80% and you need to have 42 targets poisoned at all times for the poison damage to break even with the normal gem damage. By grade 12, you’re looking at over 100 targets to break even.

Now putting it in a trap seems like a good option, with it being one of the specials that doesn’t become less useful from reduced base damage like yellow and lime do. But at that point your target pool goes way down, with your tiny range, meaning a lot less mobs can stay poisoned. So while this may work at lower levels – when your range and firing speed are too low to get lots of targets poisoned anyway, it really drops off in effectiveness at higher grades.

Overall, green can be a decent starter in a trap, and doesn’t even totally suck outside one for a while, but it can’t hold up at higher levels.

NEXT UP: Gem scaling. Do I want one grade 9 gem, or eight grade 6s?