This applies to games of Standard the same way it used to apply to games of Limited. If you discover a matchup in Modern or Legacy where Pack Rat is appropriate, it applies there too. Proper activation of Pack Rat is frequent activation of Pack Rat, and you need a damn good excuse to do anything else that prevents an activation. To see this, think about the last time you played Limited against Pack Rat and what was going through your mind. I bet it was a little something like this:
"Don't have land three . . . Oh no, you have land three . . . Cast spells . . . Please cast spells . . . No way I can beat not casting any spells . . . Please cast spells . . . Nice, you cast a spell, so I get an extra turn . . . Nope, not good enough . . . Please cast another spell . . . Nope, still dead."
Remember that because that's what's probably going through your opponent's mind when you play Pack Rat unless you're behind and Pack Rat would lose the race or there's a Supreme Verdict, Detention Sphere, or other good answer waiting for you if you go down that path. Figuring out which of these two things your opponent is thinking and acting accordingly is the way to get the most out of Pack Rat.
One Pack Rat on its own is a 1/1 and is terrible. Two Pack Rats are each 2/2 and are pretty bad. Three Pack Rats are more powerful than they appear, as three 3/3 creatures can hit hard. A bigger army than that is usually impossible to deal with unless a sweeper is used. The reason you put Pack Rat into your deck is to be able to make three to five of them and blow your opponent away.
Looked at purely in terms of power and toughness, the third Rat is +5/+5, and the fourth Rat is +7/+7. Most decks have few things better than 5/5, and only Master of Waves or an active God can make a reasonable claim to be better than a 7/7. Rats beyond that are even bigger but less impactful because the game is probably already over at that point. Looked at this way, it's easy to see that it's usually a mistake to play a spell like Desecration Demon instead of a third Rat. You're getting a slightly bigger upgrade right now, but you're giving up the future option of even more power.
Protect Your Pack
There are two types of protection that your Pack Rat needs. The first type of protection is making sure your opponent doesn't kill all your Rats with removal, leaving you unable to make more. This is huge if you know you want to be on the Pack Rat plan, either because your hand dictates this by not having a good alternate plan or the matchup or situation tells you the Pack Rat plan will work. Under those circumstances even if your opponent has already had a chance to break up your Rat army and failed to do so, there's no reason to give your opponent the chance to draw a solution to the problem or realize their mistake.
Also keep in mind that it's very hard for Pack Rat to lose when your opponent has no removal; the nasty surprise of all your Rats getting smaller when you least expect it is the best way to lose a Pack Rat game. If you're going to go on the Pack Rat plan, you want to get on it now unless your opponent has done something that makes this look like a losing path.
The other type of protection is making sure your Rats can't be productively blocked. As the game goes on, your opponent will be able to play bigger and bigger creatures, activate their Gods, and otherwise complicate matters. If your plan is to overwhelm your opponent with Rats, the other way to lose (besides falling prey to removal at the wrong time) is for your Rats to be unable to win fights because your opponents creatures are getting bigger faster than your Rats, and once you start losing even a few of them in combat, you'll be in a downward spiral.
The more Rats you make now, the less likely you are to be unable to fight. Anything your opponent has now is going to get outclassed by your growing army, so don't use removal now even if it lets you hit for a bunch of damage. Giving up the four damage from two 2/2 creatures means little if you're going to be hitting with three 3/3s and then four 4/4s soon. That removal could also be your way to eliminate the one thing that can stand in your way later on.
Your goal is to get into the Rat endgame where the Rats are bigger and meaner than anything they are up against, not to tempo your opponent out quickly. A quick tempo attack makes cards they play likely to be able to compete with your Rats as they move up their mana curve, whereas letting your army grow makes all your options steadily better because you save your key removal spells for their top end while they are forced to play lands and watch every card in your deck become more and more awesome.
Extra Damage vs. Optionality
Often the Rat player will have the choice whether to activate a Pack Rat during their attack in order to get a few extra points of damage in. There are three disadvantages to doing that. One is that it takes away your optionality during your opponent's turn or to choose the right discard, the second is that it lets them go after all your Rats at sorcery speed, and the third is that it reveals information to your opponent. In exchange for all of that, you get to do free damage. When are these disadvantages important?
Optionality matters when there are scenarios where you would use that optionality. If you're holding an instant such as Hero's Downfall, you're giving up the chance to kill a creature if your opponent plays something more important than the third Rat you are likely to make. Even if you end up making a Rat anyway, you get to choose which card to discard after learning what your opponent is up to, which can be valuable down the line.
Most of the time it would be fine to wait until your turn to cast the spell you are thinking of casting on their turn. If you make a third Rat now, then you're two life points ahead and then can untap and cast your removal spell later, which also lets the Rat attack. That's only likely to be substantially worse than casting the removal spell on their turn if you have more spells you'd also want to cast, and at that point you're moving far away from the game plan you want to be on. This road is usually a mistake.
Even when there is a clear advantage to waiting when they play the right card, the big danger is that by making you worse off in the scenario where you make more Rats you turn it from a likely winning play into a plausibly losing play, which then causes you to compound your error by choosing the non-Rat path when you would have been better off with the Rat path and the two extra damage in hand. It's easy to think about how often you'll cast the spell over the Rat without considering how often you'll cast the spell while wishing you'd made a Rat while you had the chance.
Choosing the right discard can be important, but players overestimate the chance that it will matter. If you're on the Pack Rat plan, it probably means you're going to be discarding or not using a bunch of the spells in your hand, which means it doesn't matter which one you still have for a future discard. Even when it does matter, it is likely to be a small mistake to choose the wrong card. It's fine to be wrong so long as it doesn't have too big an impact since you got something important in exchange.
You want to keep the cards that can be strong complements to your core Rat strategy and lose the rest, keeping in mind you won't get to draw more cards before making your decision. A good heuristic here is that you should postpone for this reason only when you can think of a line for all options in which that discard costs you the game and each of these lines is common while the damage mattering seems less so than each of these scenarios coming up.
The second downside is a problem against decks that can use mass removal against you. Right now that usually means Esper and U/W Control and occasionally a deck with Anger of the Gods. In these cases there's a very good reason to hold back, but a key question to ask is whether you'd be happy or sad if they choose to pull the trigger for that reason instead of holding it back. If you're fine with the game proceeding that way, go for it. This is especially true if you can't beat the removal spell in any case or the card you'd be discarding doesn't matter to your game plan in a world where they kill your Pack Rats.
The last downside is that your opponent gets to choose their line of play knowing that you've made a Pack Rat. This can be a great advantage to them in some situations, especially if this will be your second Rat token and they don't know if you intend to play the Pack Rat game, but again you need to have a concrete idea of what play they might change based on this information. If they will frequently have a choice on their turn between removal and a creature, perhaps holding back puts them in a bind where if they use removal on a Rat then you can abandon the Rat plan, whereas if they cast a creature you can overwhelm them with Rats. What you don't want is to pay a price to avoid revealing information without an idea of what your opponent will do with that information.
Also note that making a Rat now can also be misleading, implying that you have no other options when you do in fact have other options. Your opponent may play into a removal spell as a result.
Black vs. Anderson: A Case Study
(Game 3 of Black vs. Anderson starts at 22:30.)
This is the amazing third game of the match between Sam Black and Todd Anderson at Grand Prix Albuquerque. It's a classic example of why you should stick to your ABCs (Always Be Cloning your Pack Rats!) rather than casting more spells. The "dreaded Pack Rat" comes out on turn 2, and Sam Black is both going second and misses his two drop, so things are looking pretty great for Todd. His third turn second Pack Rat is an easy decision for him. Contrary to Randy Buehler, who has been doing an amazing job with commentary lately, playing the fourth land is an easy call since it is good for Todd in every scenario.
It's easy to come up with reasons to cast Desecration Demon rather than activate Pack Rat on Todd's fourth turn. Playing the Demon forces Sam to deal with the Demon if he wants to attack with Nightveil Specter. If Sam uses Cyclonic Rift on the Demon, it saves Todd a card and takes a lot of optionality away from Sam, but that seems unlikely since Sam would have burned the Rift on turn 2. This line denies Sam a card, but it lets Sam develop his game plan with a hand we know doesn't have any one- or two-drops, making it likely he can work towards some very powerful effects.
By giving Sam two extra life and not threatening four 4/4s, you're giving him a lot of time while cards off the top of your deck other than Nykthos, Shrine to Nyx are reasonably harmless in Sam's hands for the time being; if he steals a Nightveil Specter, he can cast it, but against three Pack Rats he's risking a huge blowout if you have Mutavault or a removal spell. Instead, you're only representing 3/3 attackers, which makes Sam's potential block safe.
In the scenario where you are attacking with three potentially 4/4 Rats and Sam is at twelve, he must block somehow or die, and the best a block can be is ugly; if he plays a Nightveil Specter and trades with one of the Rats, he's still taking eight damage, leaving him at four facing three lethal attackers again the next turn or losing outright if Todd has a removal spell unless he sacrifices the Judge's Familiar for no other gain, which leaves him dead to blank cards.
The bad scenario (if we don't assume knowledge of Todd's hand at all) would be if Sam casts Thassa, God of the Sea instead of Nightveil Specter. This loses outright to anything that can kill even the Judge's Familiar but is potentially problematic if Todd has and draws nothing. Todd can then choose to either attack for eight at the cost of a Pack Rat or to hang back and wait to attack with 5/5s or bigger Rats.
Given that a Todd with nothing likely has either another Pack Rat and land five or two more lands over the next two turns, waiting seems fine. Once the Rats get to 6/6, Todd will win every combat against anything but Thassa and still draw against Thassa since something else must join the block in order to kill the Pack Rat, and Sam should fall at the latest on Todd's seventh turn while Todd should be high enough to not be in danger of dying before that.
As it turns out, Todd's holding multiple removal spells, so Thassa, God of the Sea gets Sam slaughtered after Todd kills the Nightveil Specter. That makes it hard to see how the Pack Rat plan loses unless Sam flips a Nykthos, Shrine to Nyx and can then use that to chain into an overloaded Cyclonic Rift off the top.
Instead, Todd can't both cast Hero's Downfall and make his Pack Rats big enough to beat up on a Nightveil Specter, so he can't attack with them without offering a trade that he wants to avoid. This buys Sam valuable time, and Todd's decision to cast Devour Flesh gives Sam even more time. Now Sam is still at a reasonable life total, only facing two Rats, and starting to steal cards off Todd's library and develop his game.
Todd not making a third Rat on his next attack is arguably even worse, as he knows what he is up against at this point and how important it will be to have three Rats on the table. If you send Sam to eleven with three Rats and a Lizard, Sam is looking at a threat of lethal damage even if he has one blocker. One removal spell leaves him nominally alive but leaves him in an awful position and likely burns any Cyclonic Rift he still has. Letting Sam look at two extra cards off your deck rather than one with a Swamp already in play is bad, but giving him fewer turns of doing so is very good. And if Sam doesn't peel a Nykthos, Shrine to Nyx, the game is probably over.
On Todd's next turn, Randy comments that "Todd is doing better than Pack Rats," but this is very clearly not the case. Turn after turn Todd's failure to put Sam under bigger Rat pressure makes Todd worse off, and Sam has multiple shots at an active Nykthos, Shrine to Nyx off of Todd's deck despite Sam having about as bad a hand as he would have kept at the start of the game. Eventually, Sam's card advantage off of Bident of Thassa and Nightveil Specter carries the day. If Todd had drawn blank cards or Todd had refused to cast any more spells, Sam would have had no chance.
Conclusion: Giving Up Control
In addition to the dangers I've talked about above, there's one other big thing that holds players back and that is even more dangerous for better players—players, especially great players like Todd Anderson, hate to go down lines that leave them no control and no choices to make. Going all in on Pack Rat takes away a great player's chance to outthink the opponent and leverage superior skill instead putting the game into the hands of the opponent. It also isn't as much fun.
Decks that force players down lines like this tend to be underplayed by better players and therefore underplayed at high-level tournaments where players instead seek out decks and cards that give them more play. When players have no choice but to rely on such strategies, top players tend to hate the format. It's important to remember that your choice of deck and your choice of when to go down this path is the place you are leveraging your skill. A key part of a great player's toolbox is not to be overly attached to being great and instead to focus on what gives you the best chance of winning.