Switch to group initiative. It's not like weakening the value of the Dex stat will be bad for game balance overall…
How would this speed things up, since everyone still has to take their turn?
We've switched to group initiative in our game recently. The GM didn't announce it being for any particular reason, though there's the implication that he wants to speed up the combats since we're approaching the end of the campaign.
The implementation is a bit more spartan than others have described. Each side rolls a single d6 (the person who rolls changes each round), no modifiers added. Highest value goes first. On a tie, everything all happens at once. (If someone had the Alert feat, I personally would rule that that gives the players first move on a tie.)
On the players' turn, the GM just goes around the table asking for each person's action. If someone isn't immediately ready, he moves on, and gets back to that player after everyone else is finished. And while it hasn't come up, if someone isn't able to decide on an action at that point, setting their action to Dodge seems reasonable.
Now, why is this faster?
- We don't have to sort out everyone's turn order, whether we'd only do that at the start of combat, or every round. There's only a single pair of numbers to compare, instead of potentially a dozen or more.
- There is only one 'turn' for the players, so everyone's consideration of what to do happens in parallel. With normal initiative order, the sequential nature means any single person taking a long time bogs things down for everyone.
- By default, each player tends to only consider what to do on his turn. If it's not his turn, he's more likely to "check out". That means that on average, each player doesn't really need to engage for 80% - 90% of the round (for anywhere from 4 to 6 players). In addition, the disengage-reengage cycle will slow down each individual player's turn, since he has to figure out where he is, and what's going on all over again each time his turn comes up.
- It's easier to skip a player who's not sure what he wants to do, and get back to him after going through the other players' actions. With standard initiative, it's harder to legitimately do that because it can screw up how the actions get resolved, particularly if monsters have actions between players. If you have [ Player A > Monster A > Player B ], then if Player A is put on pause until after Player B, he can find out what Monster A does, and how it was resolved, before deciding on an action. This can be problematic in some scenarios. With group initiative, there's no way for that to happen, so reordering players is easy.
- Continuing #4, there's also none of that, "I delay my turn until after Player B goes" (which also isn't really legitimate in 5E), often used so that players can coordinate their actions. If Player A the rogue has to wait til Player B the barbarian gets next to the monster so that the rogue can use his sneak attack, the standard initiative order means people have to fiddle around with figuring out what order people are moving in, and how much that delay may cost them in other ways (such as the monster moving away, or Player C killing it with a spell, etc). All actions in a round are supposed to be roughly simultaneous anyway, so the group initiative just gets rid of the extra bookkeeping involved.
- The GM can move on to the next player immediately after the prior player has declared his actions, even if that prior player has not yet resolved the actions. For example, Player A declares he's going to attack. GM says, "OK, make your attacks. Target AC is 17. Let me know how much damage you do." Then the GM immediately moves to Player B. Player A is then free to do all the rolls he needs, including double checking if other features come into play (eg: a Cavalier using Unwavering Mark, or a Barbarian using Brutal Critical, etc) without the pressure of needing to get done so that the next player gets his turn, and possibly losing out on some of his special benefits because he forgot.
- While it's not explicitly using a timer, the GM doesn't have to wait for each person to sit around and think. It's much easier to do a rapid-fire run through the table, and have the table as a whole under the virtual effects of a timer (without singling any one person out). And on the flip side, once one person is done, he is free to help out anyone else at the table resolve more complicated actions or ideas. With a sequential order, even if someone is ready to perform a quick action, he has to keep that 'suspended' in mind until his turn comes up, which makes it more difficult to help others since the anticipated action may be lost, and then time spent figuring it out again dilutes the value of being prepared.
Most of those are only small improvements in overall speed, but together, and particularly in parallel, it really helps speed things along, and keeps people from disengaging. It is likely to reduce total combat time by at least 15%, and potentially up to 50%.
I'll note that this is all at a live game, not a virtual one, though. My gut feeling is that it would be a little harder to manage in a virtual game, but I'm not entirely sure. The virtual game I'm playing hasn't tried anything like this.
Also also, someone mentioned the Greyhawk Initiative system option. We've tried that in my group before, and I wouldn't recommend it if your goal is reducing round times in combat. It adds an extra layer of complexity in figuring out which actions correspond to which dice, and then translating that to a new initiative each round. While we eventually got used to it, it was definitely not a fast system.