So, this is the first in what may become a series of blog posts I'll make about maths in PvZ. Here, I'm going to be using maths to determine what is the most cost effective attacking plant in PvZ1 or 2.
Firstly, the Peashooter. We all know that this does 1 damage per shot, and costs 100 sun. This is the base cost effectiveness: 1 damage, 100 sun, no crowd control, no special effects.
Next, onto the Snow Pea. Snow Pea costs 75% more, but its peas, by slowing down the targeted zombie, essentially double the effectiveness of not only itself, but every other plant in the row. This means that its cost effectiveness goes up the more attacking plants there are in the row. Snow Pea + Peashooter is effectively four times as powerful as a Peashooter for only 275 sun, less than three times the cost of a Peashooter. Snow Pea + 2 Repeaters is ten times as powerful as a Peashooter for only 575 sun, less than six times the cost.
10 times as powerful, for 5.75x the cost. That's close to twice as cost effective as a Peashooter. However, due to some zombies being immune to slowing, and it not being powerful against groups, it does have limitations. In PvZ2, it costs slightly less, and so can be more cost effective. But it's premium, so not really worth getting.
Fume-shroom now. At night in PvZ1, it costs 75 sun, and hits up to four spaces away, while a Peashooter can hit up to 8.5 spaces away, if placed at the far left. However, Fume-shroom's crowd control means that it can take out infinite common Zombies, and it also ignores shields, meaning it can render Newspaper and Screen Door Zombies harmless too. Peashooter would be more powerful against a Conehead, but Fume-shroom is definitely more cost effective overall. However, exactly how much more cost effective varies depending on how many zombies there are in its range.
During the day, it has double the cost due to the Coffee Bean, but it is still worth using if going just by cost effectiveness. In PvZ2, it costs 125, which I think is actually quite fair, considering it no longer needs a Coffee Bean.
Scaredy-shroom is a quarter of the cost of a Peashooter, but barring Pogos, Diggers or Bungees to scare it, it's practically equal in strength. As much as I dislike Scaredy-shroom, it's almost four times as cost effective as a Peashooter at night. During the day however, it's less effective than a Peashooter.
What else can I talk about next? Oh, the Starfruit. It fires off five projectiles at once for only 125 sun. 25% more than a Peashooter but 5x the firepower. The only problem is that due to its inaccuracy, it requires massive groups to be of any use, and is rarely cost-effective.
Let's get to the big guns now. Melon-pults. In the Almanac, he states that "Sun for damage, I deliver the biggest punch on the lawn". Is that really true though? Up against a single zombie, it definitely isn't, as the Melon-pult only delivers a Repeater's worth of damage for 50% more cost than said plant. However, splash damage in a wide radius means that it can deal almost a Peashooter's worth of damage to all zombies near the target, which can make it better than a Repeater and numerous Peashooters. In fact, comparing it to all the plants I've mentioned so far, it's definitely the most cost effective. In PvZ2, the splash radius is larger and splash damage is increased, so although it's slightly more costly, it's even MORE cost effective.
Then again, what about Melon-pult's upgrade? Winter Melon, like Snow Pea, doubles the effectiveness of itself and other plants in the row due to slowing. However it also slows groups, and can slow down THREE rows. It's definitely more than twice as powerful as a Melon-pult, and yet in both PvZ1 and PvZ2, the total cost of it is only 500 sun, only 66% more than the Melon-pult in PvZ1 and only about 54% more then the Melon-pult in PvZ2. In PvZ2, it also has the same buffs to its splash as the Melon-pult. It's tough to beat the cost effective power of the Winter Melon, definitely.
But, not impossible. Cob Cannon is up next. Every 36 seconds, it's capable of essentially shooting a Cherry Bomb wherever you want. Cherry Bombs hit a 3 by 3 area with 90 damage. It's only 2.5 damage per second, which considering that it costs 700 sun, would make it cost 180% more than it should for that dps. But then, due to the massive crowd control, and the fact that it can hit ANYWHERE, it's definitely worth the cost. It reloads than a Cherry Bomb can recharge, and is certainly the most cost-effective plant in PvZ1, even if not the most space-efficient.
But...can any plant in PvZ2 beat Cob Cannon?
Coconut Cannon does slightly more direct damage per second than a Melon-pult, but the splash dps is slightly less. Overall, nowhere near enough to equal Cob Cannon's cost effectiveness.
Citron deals 4.5 damage per second for 3.5x the cost of a Peashooter. But with no crowd control whatsoever, it's nowhere near as cost-effective as even a Melon-pult, let alone a Winter Melon or Cob Cannon.
I guess all that really leaves is Banana Launcher. A plant that I, and a few other people, hate for the reduced damage and explosive radius. But is it that bad? It deals only 60 damage per shot, but reloads faster, taking only 21 seconds instead of 36. Damage per second: 2.85. More than a Cob Cannon. The explosion hits only three spaces in one row however, making the explosion only 33% of the size of a Cob Cannon's. Then again, there's also the cost. It costs 28.57% less than a Cob Cannon. If you crunch these numbers then...
It's much less cost effective than Cob Cannon. Sorry Banana Launcher lovers, but it's not the winner of this blog. It's about 38% as powerful as Cob Cannon, so even with its reduced cost, it's nowhere near as effective. Although, as I mentioned earlier, this is cost effectiveness, not space efficiency.
And so, the most cost effective plant is...Cob Cann-WAIT! I forgot a plant!
The Puff-shroom. While weak, only around a third of the strength of a Peashooter, it costs absolutely nothing at night. In PvZ2, it never costs anything, and even with the limited existance, this technically makes it the most cost effective attacking plant ever. Bet you didn't see that coming, did you?