The Protoss race's Photon Cannons are easily the most powerful defensive structures in the game of Starcraft. They're the only weapon of any sort which can attack units on land, in the air, and act as a detector, at no population cost, no Vespene gas expense, and a fairly low mineral price. They make the difference in many games in ways that other defensive structures cannot duplicate.
So, a question. When the time comes that you absolutely must attack a Photon Cannon emplacement, what is the best way to do so: by attacking the Photon Cannons themselves, or the Pylons which power them? The Pylons are exactly 3 times as durable as the Cannons, having 300 shields and hit points to the guns' 100 shields and hit points. Thus, we can model an attack on such a placement by assuming that our forces take some time, t, to dish out 100 shields & hit points worth of damage (i.e., t long to destroy a Photon Cannon, and 3t long to destroy a Pylon).
From a purely tactical standpoint, the most compelling consideration is: how much damage, or number of shots, can the Cannons return on our forces during our attack? Let's assume that there are c Photon Cannons powered by a single Pylon, and that a single Cannon can shoot x times over time t (that is, at a rate of x/t). Since it takes 3t time to destroy the Pylon, clearly the associated Cannons will fire off c·(x/t)·3t = 3cx shots in the time it takes to cut off their power. Alternatively, if the Cannons themselves are attacked, then it will take ct time to destroy them all (one time factor for each Cannon). During the first segment of time, cx shots will be fired (since all are shooting), during the second period (c-1)·x shots (since one has been destroyed), and so forth: hence, the total shots fired will be Σi=1..cix = xΣi.
These numbers are compiled in the table below, for a variety of Pylon : Photon Cannon support ratios, with the entries in bold indicating the best option. Additionally, I've included figures for the total time spent, and the mineral expense of damage inflicted, which may be important for larger strategic considerations.
| Attacking Pylon | Attacking Cannons | |||||
|---|---|---|---|---|---|---|
| Pylon:Cannon | Shots | Time | Expense | Shots | Time | Expense |
| (1:c) | (3cx) | (3t) | (100) | (xΣi) | (ct) | (150c) |
| 1:1 | 3x | 3t | 100 | 1x | 1t | 150 |
| 1:2 | 6x | 3t | 100 | 3x | 2t | 300 |
| 1:3 | 9x | 3t | 100 | 6x | 3t | 450 |
| 1:4 | 12x | 3t | 100 | 10x | 4t | 600 |
| 1:5 | 15x | 3t | 100 | 15x | 5t | 750 |
| 1:6 | 18x | 3t | 100 | 21x | 6t | 900 |
Now we can see that the break-even point for shots returned during an assault on a Photon Cannon emplacement occurs at the ratio of 1:5 Pylon per Cannon; less than this, it is optimal to attack the Cannons, while greater than this, it is clearly best to attack the Pylon itself. If the most important issue is to incapacitate the Cannons as quickly as possible (so as to move on to some different threat), then attacking the Pylon is definitely justified at any ratio over 1:3. If you wish to cause as much building-expense damage as possible in the time allowed, then attacking Cannons is always the better choice (since a single one is more expensive than a Pylon). Personally, at the break-even point of 1:5 Pylon per Cannon, I would recommend still attacking the Cannons, since it causes the greatest facilities damage and prevents the Cannons from all being re-powered by a single new Pylon.
Perhaps equally important in this analysis is the realization that a Protoss player is justified in building Photon Cannon placements at a 1:5 ratio of Pylon per Cannon, since this optimizes the return fire that it will lay down on any attacking force. Terra Adun!