[RPG] Are shields a numerically significant defensive boost

I had thought there were other already answered questions concerning the benefits of shields, but when I looked, I couldn't find one here, but did find a few on Reddit. However, the bottom line is really that Raising a Shield reduces incoming damage by roughly 20% under typical circumstances (assuming a shield, and not a buckler). The +2 bonus to AC makes you 10% less likely to get hit, so on average that prevents 10% of the damage you would otherwise have taken. Further, since most opponents you will face will have a sufficient to hit bonus to allow critting on rolls well below 20 (usually about 16-18 for same level), the shield will also drop 10% of hits that are crits to just hits.

That is back of the envelope math, of course. The 10% increase to miss chance could result in even more savings if the attacks in question have additional effects that would result in more damage (reducing your defense, or reducing your offense, thus adding another turn to the combat in which you then get hit, etc), and many attacks don't target AC, so the shield will do little to reduce damage from them. So I suppose it's more accurate to say AT LEAST 20% damage reduction vs. AC targeted attacks. But I digress.

Considering that the Multiple Attack Penalty (MAP) for a third action attack is typically sufficient to prevent a hit on anything but a natural 20, it is often considered a poor use of the action to attack, and so often you aren't giving up much to raise your shield.

So, at this point, we have a 20% reduction in damage for almost free - the shield does not take damage (and thus incur repair/replacement cost) if all you do is raise it, and the action you spend to do so is usually not competing with better options. With this alone, a shield is frequently a solid investment.

Further, feats such as Reactive Shield can allow you to not even have to use an action if you do decide that you often have better things to do with it. However, it can be argued that a reaction is even more valuable than an action, especially for Fighters and Champions.

Shield Block is potentially more controversial. Again, using a reaction is fairly expensive for some builds. Secondly, you now risk damaging the shield, which then requires repair or replacement. Lastly, most classes do not have the Shield Block feat by default, requiring them to spend one of their general feats on it.

However, if you aren't using your reaction (most classes) and at least one member of the party has the repair skill, using Shield Block can be a reasonable option.

So, to compare with other options, we should look at the two uses separately (Raise Shield and Shield Block):

Raise Shield - Requires no feat investment, low money cost (can use a wooden shield), low action cost (third action often suffers from a lack of good options - hail Mary third attack or unnecessary skill use "just because"). The biggest trade off for using Raise Shield in most cases is that you are then limited to one handed weapons (and no dual wielding unless you are trained in Martial weapons to use a shield boss, which is still likely to be a sub-optimal "off hand" weapon). Again, this will have the largest impact on certain classes - Barbarians and Rangers topping that list, but many other builds can face the same issue. Of course, many classes (casters mostly) will have little use for two handed weapons (or dual wielding) and so this may not be a consideration at all for them.

Shield Block - Requires a feat for most classes, takes both an action and a reaction, and can get expensive if used to block big hits that end up destroying the shield (and you will spend quite a bit on good shields to boot). Also requires that at least one party member be trained in Crafting (not a big deal mostly) and have a repair kit (they are heavy, and expensive at first level). The loss of the reaction will most heavily impact Champions and Fighters (and Barbarians that take Opportunity Attack), but can also impact other builds that make strong use of reactions. Further, as for Raise Shield, it limits your weapon choice as well. However, the damage mitigation can be decent, especially with Sturdy shields. In my opinion, the mitigation doesn't scale as well as it should, so I'd be more likely to argue that using Shield Block is not worth the investment, but if you are already raising your shield anyway, and you have the feat for free from a class (Champion, Druid, Fighter) or because you felt your general feat options were lackluster for a particular level, then you might as well. Champions with Shield Ally and/or Quick Block are also feasible builds that make Shield Block considerably more useful, so it can obviously be said that it is good for some builds, but as a general rule of thumb, I would not recommend it.

Other options to raise armor class typically revolve around runes/magic items or feats. Runes and Magic items stack with shield use and are typically going to be readily available with little investment (as found loot), and so are a highly recommended option, though they don't really compete with shields, but rather compliment them. Feats that improve AC, either class feats (which might require multi-classing) or general feats, are few. Many folks consider the dip into Champion worthwhile for many classes in order to gain training in Heavy Armor, but at higher levels, the extra 1-3 points of armor class you gain are overtaken by better training in your class's usual armor. Plus the strength investment to wear Heavy Armor might be a steep cost in and of itself. The Armor Proficiency general feat suffers the same problem. The only other general/skill feat I could find that increased AC was Wary Disarmament, and that only helps against traps. So, competing options for AC boosts are fairly limited. There might be some spells that offer situational bonuses like Wary Disarmament, or that work in place of armor (like Mage Armor), but across the board AC boosts don't seem like a highly contested area.

Shield Cantrip - As pointed out by @YogoZuno below, the Shield cantrip can be a useful alternative to a shield for builds that do not have a hand free for a standard shield (such as dual wielders or those using two-handed weapons). While not as good as a regular shield (being roughly equivalent to a buckler), it does take a cantrip slot, but grants you the Shield Block reaction without requiring the feat. For casters, the cantrip slot cost could be more or less valuable than the feat cost, but I would still argue that for a build where the spare hand for a shield and 20% damage reduction is unavailable, spending a cantrip slot for 10% reduction is still a good trade-off. For dual wielding or two-handed weapon wielding martial builds, the feat slot (either a Class feat for a dedication feat or an Ancestry feat for those ancestries that have a cantrip option) to get a cantrip slot or two can be a worthwhile investment to gain 10% damage reduction against AC targeted attacks. Again, this analysis is based wholly upon the value of Raise Shield and the equivalent functionality of the Shield cantrip. The Shield Block being thrown in for free, while of arguable use (especially considering the downside of using it), only works to further recommend the cantrip even if that functionality is only ever used as a last ditch effort to avoid dropping to 0 HP. However, if you have the free hand, I would recommend just carrying a shield over taking the cantrip, even if it means giving up the Shield Block reaction, for the reasons stated previously concerning the value of Shield Block.

tl;dr: Raise Shield is well worth it. Shield Block not so much unless you have the feat already anyway.