Assuming the world speed is x1,, and ignoring the farm upgrades, warehouse upgrades or any resource upgrading, here are some numbers to consider:
Starting at a village with:
HQ10, Barracks 5, Stables 3, Smithy 10, Market 5
Upgrading your HQ first to the levels listed below, followed by Barracks 20, Stables 15, Workshop 2, Smithy 20 + Academy + Market 10 to represent a post-noble stage:
HQ20 = 325.58 Hours
HQ21 = 314.57 Hours ~ 11.01 Total Hours Saved ~ +11.01 Extra Hours Saved
HQ22 = 304.78 Hours ~ 20.80 Total Hours Saved ~ +9.79 Extra Hours Saved
HQ23 = 296.24 Hours ~ 29.34 Total Hours Saved ~ +8.54 Extra Hours Saved
HQ24 = 289.01 Hours ~ 36.57 Total Hours Saved ~ +7.23 Extra Hours Saved
HQ25 = 283.15 Hours ~ 42.43 Total Hours Saved ~ +5.86 Extra Hours Saved
HQ26 = 278.74 Hours ~ 46.84 Total Hours Saved ~ +4.41 Extra Hours Saved
HQ27 = 275.88 Hours ~ 49.70 Total Hours Saved ~ +2.86 Extra Hours Saved
HQ28 = 274.69 Hours ~ 50.89 Total Hours Saved ~ +1.19 Extra Hours Saved
HQ29 = 275.31 Hours ~ 50.27 Total Hours Saved ~ -0.62 = Wasted Time
Now, let's assume that you have a farm level 25 by the time you your HQ finished, so you will raise your farm 25-29 to be conservative. As well as your warehouse, let's assume 18(required for HQ25) as a starting point, and you will need to raise it to level 24 to afford a farm 29. So farm 25 -> 29 and warehouse 18 -> 24. Note, I'm ignoring other buildings because they are not required to build nobles.
HQ20 = 418.14 Hours
HQ21 = 402.73 Hours ~ 15.41 Total Hours Saved ~ +15.41 Extra Hours Saved
HQ22 = 388.74 Hours ~ 29.40 Total Hours Saved ~ +13.99 Extra Hours Saved
HQ23 = 376.20 Hours ~ 41.94 Total Hours Saved ~ +12.54 Extra Hours Saved
HQ24 = 365.16 Hours ~ 52.98 Total Hours Saved ~ +11.04 Extra Hours Saved
HQ25 = 355.67 Hours ~ 62.47 Total Hours Saved ~ +9.49 Extra Hours Saved
HQ26 = 347.81 Hours ~ 70.33 Total Hours Saved ~ +7.86 Extra Hours Saved
HQ27 = 341.66 Hours ~ 76.48 Total Hours Saved ~ +6.15 Extra Hours Saved
HQ28 = 337.34 Hours ~ 80.80 Total Hours Saved ~ +4.32 Extra Hours Saved
HQ29 = 334.98 Hours ~ 83.16 Total Hours Saved ~ +2.36 Extra Hours Saved
HQ30 = 334.73 Hours ~ 83.41 Total Hours Saved ~ +0.25 Extra Hours Saved
Your nobles will be available faster but it will be more time consuming and demanding with your day to day farming. How high your raise your HQ during this stage is strictly dependent upon how much money you have available. The bottom line is, it is faster, but it is more costly in terms of resources: but if the resources are aplenty then all that matters is that it is faster to get to nobles in terms of time. If you are unable to keep your HQ upgrades queue'd 24/7, while queuing the stables/barracks of course, then you should upgrade resources to keep the queue going. Again, upgrade your farm & warehouse only as needed during this stage. Remember it is vital not to upgrade your stables and barracks or smithy prior to your HQ at this stage.
Some people have tried to argue that raising your barracks and stables prior to your HQ is better for troop production. Well, I assure you that it is not.
First, let's ignore the farm and warehouse upgrades required to achieve nobles. Because it is clear that raising the barracks/stables prior to your HQ would increase the time to nobles simply because your troop production will be higher during your pre-HQ20+ stage which means that you will need to raise your farm and warehouses to a higher level during your pre-HQ20+ stage. This will make you save less time from upgrading your HQ because you will not take advantage of the farm/warehouse decreased build time because you're not upgrading your HQ, you're upgrading your stables/barracks.
Secondly, we can ignore the resource upgrades, wall upgrades, because they are not required to produce nobles. We'll also ignore workshop upgrading, because it is independent of nobles also. And finally, we can ignore the market and smithy upgrades because they'll be done post-barracks/stables upgrades anyway.
So we will assume that the only build times to be considered are the barracks, stables and HQ.
Starting with HQ10, and ending with HQ23 in a straight run:
HQ10 -> HQ23 = 31.09 Hours
Add:
Barracks 5 -> Barracks 20 @ HQ23 = +29.18 Hours
Stables 3 -> Stables 15 @ HQ23 = +37.11 Hours
-----------------------------
Totalling: 97.38 Hours
Now lets say you go stables 10, before upgrading HQ to 23.
Stables 3 -> Stables 10 @ HQ10 = 22.84 Hours
HQ10 -> HQ23 = 31.09 Hours
Barracks 5 -> Barracks 20 @ HQ23 = +29.18 Hours
Stables 10 -> Stables 15 @ HQ23 = +25.00 Hours
-----------------------------
Totaling: 108.11 Hours
That is a 10.73 hour difference.
That means that if you go HQ last or during, and only bring your stables up to 10 from 3, excluding the extra farm and warehouse space you'd need as well as excluding any barracks upgrading, which would lead to more farm space required pre-HQ23, making it take a longer time. Which means, for 10.73 hours you are producing LC's at stables level 15 as opposed to stables (at most) level 10. I don't have to quote production times to show that stables 15 will produce more LC's than stables 10 for that period of time.
Again, this is only true if you can afford 24/7 production. The time you save on build times of your stables or barracks independently will yield more troops than if you were to upgrade them first. This is because you will be producing units at barracks 23 + stables 15 for about an extra 20 hours instead of 20 hours at Barracks 5, Stables 3 or any level between the two groups. Producing troops at a higher level of production for the barracks and stables simply yields more troops pre-noble in the same time period. Anyone who does not upgrade their HQ in this manner and opposes an opponent that does will lose every time.
Karmalot, 2008. Tribal Wars Forum. [Online]
Available at: https://forum.tribalwars.net/index.php?threads/guide-from-hq1-500-villages.137637/
[Accessed 04 01 2017].
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