[RPG] How fast (in game-time) would you go from level 1 to level 20 using the DMG encounter guidelines

First off RAW gives the referee the authority to decide whether downtime activities are required.

Between adventures, the DM might ask you what your character is doing during his or her downtime

In the PHB on page 187, we have a rule requiring the player to choose a lifestyle for their character and pay the appropriate expenses.

Between adventures, you choose a particular quality of life and pay the cost of maintaining that lifestyle, as described in chapter 5.

Living a particular lifestyle doesn't have a huge effect on your character, but your lifestyle can affect the way other individuals and groups react to you. For example, when you lead an aristocratic lifestyle, it might be easier for you to influence the nobles of the city than if you live in poverty.

If your referee keeps strict track of time between adventure this expense can add up. If the income from adventuring doesn't cover it then the player may have to have their character do something in between adventures i.e. downtime activities to cover their expenses.

Now the lowest lifestyle is Wretched which cost nothing per day. However the description of Wretched is.

You live in inhumane conditions. With no place to call home, you shelter wherever you can, sneaking into barns, huddling in old crates, and relying on the goad graces of people better off than you. A wretched lifestyle presents abundant dangers. Violence, disease, and hunger follow you wherever you go. Other wretched people covet your armor, weapons, and adventuring gear, which represent a fortune by their standards. You are beneath the notice of most people.

While there no direct mechanical consequence of living a Wretched lifestyle, the part highlighted in bold give the referee ample authority per RAW to make the character's life a hell between adventures. The character would win at first but likely be worn down by the incessant attacks and interruptions.

So while engaging in downtime activities is not specifically required, it would not be smart not to at least do something to insure a decent lifestyle..

Let's do some math, assuming we take an average 4 people party, starting at 0XP.

The Encounter Budget Chart helpfully tells us, that every encounter should contain at best 400 XP for the first level, 500 XP for level 2 etc. The tables for for the budgets has a few jumps, but that doesn't help with speed... yet. It only gives us XP/Encounter, which can be calculated into the XP per player and hour, which we ultimately need to get the time per level.

$$\frac{{XP}_{Group}}{Encounter}\times\frac {Encounter} {Encountertime\text{ [in h]}}=\frac{{XP}_{Group}}{\text h}=N_{Players} \frac{{XP}_{Player}}{h}$$

Filling in with a 4 player group, 75 minutes per Encounter (=1.25 hours), this gives $$\frac {{XP}_{Group}} {4 \times 1.25\text h}= {{XP}_{Player}}$$

Now, how much XP we need? Character advancement table time! Ok, 1000 for level 1, 2250 for level 2 etc.

Let's have FUN with MATH! OR... we do it easy: Let's make an excel table! or rather, a Google Spreadsheet!

112.5 hours of encounters to gain level 10, it is reached in Session 28, assuming 4 hour per session are dedicated to encounters and encounters can be seamlessly split up; nobody ever comes late, ruleslawyers, investigates abandoned wells^* or just derails the plot; interludes are part of the encounters and take up no extra time; etc.

All in all, I estimate that these 112.5 hours of encounters to level 10 will be overshot by at least 50% for interludes, Plot reasons, prolonged battles and just bad mood, etc.

Now, the tricky part: we have 100-150 total hours available. One of 5 hours is dedicated to arrival and cleanup, so 20% loss. That is 80 to 120 hours available... That makes it a bit tight, leaving at worst halfway between Level 7 and 8, and in best leaving two sessions after acquiring level 10 - as long as the estimated 1.25 hours are fixed.

Now, a short experiment of what happens if we manage to drop encounter time to 60 minutes flat! Hours per level... drop to 10 hours of encounter per level, and we only need 90 hours of encounters for level 10. In THAT case, you will very likely manage it.

Conclusion

To squeeze in the 10 levels into the 150 hours of sessions (of which about 20% are dedicated to arrival and cleanup) and reach level 10, you might want to fix one or more of the three screws that are relevant to the calculation:

• Tweak XP needed per level downwards
• Give more XP per encounter than calculated per player (netting more \${XP}_{Player}\$)
• Achieve faster encounter times (however you manage that - it directly increases the XP/h rate)

As an alternative: switch to milestone Level-Ups.

* The story behind the well goes rougly like this:

^{I was GMing a campaign. After a night rest in the wilds, the group encountered a hole in the ground the next morning. It was intended as a simple "fail your perception and reflex roll, and you take some damage" at first. Nobody fell, but they started to investigate the abandoned well without walls with increasing stubbornness and despite my maniac laughter (were they expecting a TPK because of that?!). Over their discussions they went from throwing mere stones to tossing their bard into it, almost forgetting a tether for the later. I didn't budge, it stayed a deep hole in the ground with black rock lining and water at the floor deep below, and it didn't wanted to tell any of them anything because none had Knowledges or Professions that could be applied. But they had lots of fun doing it for two hours, when I finally told them "Guys, do you want to continue searching or do you want to continue the adventure?!"}