Another hack at appropriate scales

I wanted to take another hack at the scales to try and come up with a system that preserves a consistent ratio between each scale.

This is the original system:

• 1 month: 48 leagues (consider rounding to 40, 45, or 50) -- ~850 x 1300 miles (empire or small continent)
  
• 1 week: 12 leagues -- ~215 x 325 miles (kingdom)
  
• 1 day: 2 leagues -- 36 x 54 miles (duchy?)
  
• 2 hour "chunks:" 2 miles (if you require 2 chunks/day for downtime)...or 0.5 leagues (if downtime is abstracted -- 12 x 18 miles or 9 x 13.5 miles (barony?)
  
• 1 turn (~10 mins): 1 furlong (220 yards) -- 6/8 mile x 9/8 mile (manor)
  
• 1 round (~1 min): 4 rods (22 yards) -- ~130 x 200 yards (5 acres)
  
• 1 segment (~10 seconds): 2 paces (10' or ~3 yards) -- 20 x 30 yards (1/2 rood; about 1/8 acre)
  
• 1 segment (~6 seconds): 1 pace (5' or ~1.5 yards) -- 10 x 15 yards (perch, or 1/160th of an acre)

Here's a hack at a system that attempts to maintain a 1:10 ratio as best as possible. In keeping with my love for "7," we'll start with a segment as 7 seconds long!

• 1 year (12 months, 6 x 2 month periods, or 4 quarters): 576 leagues -- Could represent the entire world's circumference with 14 hexes!
  
• 1 quarter or season (12 weeks): 144 leagues -- Larger continents
  
• 2 months (8 weeks): 96 leagues
• 1 month (4 weeks): 48 leagues -- (consider rounding to 40, 45, or 50) -- ~850 x 1300 miles (empire or small continent)
• 1 week (7 days): 12 leagues -- ~215 x 325 miles (kingdom)
  
• 1 day (24 hours or 10 chunks + mandatory downtime or 12 chunks): 2 leagues -- 36 x 54 miles (duchy?)
  
• 1 chunk (2 hours or 10 turns): 0.5 leagues -- 9 x 13.5 miles (barony?)
• 1 turn (~12 mins or 10 rounds): 1 furlong (220 yards) -- 6/8 mile x 9/8 mile (manor)
  
• 1 round (~1.166 min or 10 segments): 4 rods or 1 chain (22 yards) -- ~130 x 200 yards (5 acres)
  
• 1 segment (~7 seconds): 1 pace (5' or ~1.5 yards) -- 10 x 15 yards (perch, or 1/160th of an acre)

This maintains a strict 1:10 ratio all the way up to "chunks." You have to fudge a bit for Chunks:Days. Days:Weeks also poses a problem, unless you create 10 day weeks.

Another way you could deal with the week issue would be to rejigger the system so as to use 1 hour chunks. Then you can have half-days instead of days, and then use 10 half days for a week (plus a weekend where activity is discouraged).

You could also use odd units; for example, 10 day weeks, like in the ancient Egyptian calendar, or seasons of two months length like the Bangledeshi calendar. Straying from well known units however can cause confusion.

The downside to this system is that rounds and turns are no longer nice even numbers of 1 minute and 10 minutes respectively. The upside is that its very easy to shift between the tactical and early operational scales. Everything is a factor of 10, which allows for easy transitions for the most part.

CONSEQUENCES OF DIFFERING SCALES

Let's think about consequences of differing scales. Say you can expend 1 Mana Point to cast a spell that has a duration of 1 segment. Since all of our scales are linked, you could say that it costs 10 MPs to affect something for a round, 100 MPs to affect a turn, and 1000 MPs to affect a chunk. Everything scales neatly by 10s. This is also great for things like map paper. You can print up a bunch of sheets of hex paper that have large hexes subdivided into 10 x smaller hexes in width. Then you can use them for comparisons between any two scales in the game. It also holds true for consumption of resources: If someone consumes X resources in a one period of time, then they consume 10X resources in the next scale up. A token representing 1 soldier in one scale represents 10 soldiers in another.

However, if the ratio between time units is >10 and the cost continues to increase by 10, then you basically get something for free. For example, let's scale up from a chunk to a day. The cost is now 10,000 MPs, but the player basically got four hours for free when casting the spell! This creates increasing returns: its more efficient to cast the spell to last all day than it is to cast it again every two hours. Alternatively, if you have to drink 1 unit of water every chunk, or 10 units of water each day, its better to just pay by the day.

If the ratio between time units is <10, then it introduces entropy. For example, going from a day (10,000 MPs) to a week (100,000 MPs) costs 10 times as much but you only get 7 times the duration. This creates diminishing returns. Its actually more efficient to play out casting the spell every day than it is to opt for the longer duration of a week. The same would go for, say, food consumption. You're better off ticking off one unit of food every day than ticking off 10 for the week.

One work around is to have a table that let's people know when the ratio is not exactly 1:10. For example, your rule could say, "In general, to go up a scale, multiply by 10. However, if going from days to weeks, you only have to multiply the cost by 7." This obviously increases complexity however.

Another work around would be to somehow compensate for either consistently diminished or augmented returns with a random variable. For example, say you get consistently augmented returns and wish to discourage people from exploiting them by casting all their spells for a day instead of two hours. You could rule that any spell with a duration of 1 day has some percentage chance of backfiring or otherwise failing. If dealing with consumables (say, water) then maybe there's a small chance that extra is expended. If you want to compensate for diminished returns (say, going from 1 day to 1 week) then do the opposite: there's some chance that a random boonful event occurs.

CONSISTENTLY AUGMENTING RETURNS (Ratios >=10):

• 1 Day --> 1 Fortnight (1:14) --> 1 Semester of Six Months (1:12) --> 1 Lustrum of Five Years (1:10)

CONSISTENTLY DIMINISHING RETURNS (Ratios <=10):

• 1 Day --> 1 Week (1:7) --> 1 Month (1:4) --> 1 Season or Quarter of Three Months (1:3) --> 1 Year (1:4) -- 1 Olympiad of Four Years (1:4)
• 1 Day --> 1 Week (1:7) --> 1 Month (1:4) --> 1 Trimester of Four Months (1:4) --> 1 Year (1:3) -- 1 Olympiad of Four Years (1:4)

This system suggests using two scales; Perhaps a 1:10 cost explosion all the way up to weeks (perhaps with a random bonus/penalty system to deal with the awkward 1:12 ratios for chunks to days and 1:7 for days to weeks), then switch to a 1:4 cost ratio for the "strategic" scales. So, if it costs you X units of resources to do something in a week, it only costs 4X units to do it for a month, season, year, or olympiad. Again you might need a random bonus to deal with the season (or trimester-->year) discontinuities.

This is why the world went to metric!