Saturday, January 23, 2010

Moving between scales

Recently I've been discussing a more fleshed out set of rules for "Hexploration." Hit the tag at the bottom to see the post series.

Previously, I discussed the "rule of three's" ability to help you move between different scales. Keeping a consistent ratio between the levels of scale certainly helps with this!

Now that I have come up with a relatively stable set of time/distance relationships, let's flesh out how you can move between one scale and another. For now, I'll just cover movement. We can extrapolate to other issues later.

PRINCIPLE #1: A character moves 4+/-MOD hexes every time unit at a normal walking pace. So, in one segment, 4+/-MOD hexes are covered. The MOD could include bonuses and penalties for factors such as ability scores, terrain, burden carried, armor worn, race, etc.

PRINCIPLE #2: The ratio between the distance covered on the initial scale and the distance covered on the next higher scale is, on average, 4:10 (reduced to 2:5, or 1:2.5). Even though one chain is about 10 paces, remember, the average character covers 4 paces in a segment, not one.

PRINCIPLE #3: The ratio between the first order of magnitude and the second order of magnitude is 1:10. There are about 10 chains in a furlong. For now we'll also assume a perfect 1:10 ratio between each scale level even though we know our customary units don't quite match up perfectly.

Here's some data points:
  • MARATHONS: A world-record athlete can run a marathon (about 8 leagues -- about 2/3 of a hex on the weekly scale) in about two hours (one "chunk"). The "average" time in the US is about 4:30 for men (~2 chunks) and 6:00 for women (3 chunks). Just walking would take around 4 chunks (1.5 miles x 4 hexes = 6 miles per chunk).
  • 10K (2 leagues -- the hex size on the daily scale): A world record time is about 30 minutes (3 turns). An average time for a novice runner might be around 60 minutes (6 tuns). Just walking we'd expect it to take about 12 turns.
  • 5K (1 league): A world record time is about 12 minutes (1 turn). An average time might be about 3 turns. A walking pace would be about 6 turns.
  • SPRINTERS: A world-record athlete in the 200 meter sprint covers 1 furlong (10 chains or 132 -- we will assume 100 -- paces... Normally, 4+/-MOD are covered in a ~10 minute turn) in about 20 seconds (3 segments). An average time for a decent athlete might be around 25 seconds (~4 segments). I don't have a good time for an "average" person, but 5-6 segments might be accurate. I should go run one... Just walking, we'd expect it to take 26 segments.
  • HORSE RACES: The record for a horse running a two-mile race (normally the size of a hex for a "chunk") is just over three minutes (3 rounds). I don't have a time for an average horse trotting. Walking, we'd expect a horse covering 6 chain-sized hexes per round to take 26 rounds.
  • HORSE SPRINTING: The record for a one furlong horse race would be around 10 seconds; I'm extrapolating from records for two furlong races here. So, we're going from a furlong (normally measured in turns), skipping a round, and ending up with ~1-2 segments. Walking, we'd expect a horse to cover a furlong in about 22 segments.
What do I extrapolate from these admittedly limited data points?

  • There is a noticeable difference between expert and average performance. The difference becomes most marked in the middling distances, and less pronounced when sprinting.
  • The ratio between an expert's performance, an average performance, and a performance requiring no extra expenditure of energy is about: 1:2.5:7. That is, the expect can accomplish in about 1/2 the time what the average to above average person can do. The average person can exerting effort can cover a distance in about 1/3 the time expected.
    (If you reduce the ratios above you get, with a bit of rounding: 1:2:4... 1:2:4... 1:3:6... 1:3:6... 1:2:9... Horses -- 1:X:9... 1:X:11...)
  • "If you are operating on Time Scale X, an expert can cover one distance unit of Scale X+2 with great effort using approximately 3 Time Scale X units. An average individual also exerting effort requires approximately 7 Time Scale X units. Just walking would require an average individual to expend 27.5 Time Scale X."
    Example: "If you are operating in Combat Segments/Paces, an expert can skip chains and cover one Furlong in around three segments. An average individual exerting great effort requires about seven segments. Just walking would require about 28 segments."

    Exceptions: Exceptions are required when you start dealing with the transition to weeks/12 leagues; a different ratio is needed for the strategic scales as they are based on a 1:4 ratio rather than a 1:10 ratio.
Let's talk recovery time. Recovery time after a marathon takes 1-4 weeks. Sports medicine has found that it takes about 2 days for a fit runner to recover from a 10K. It takes 10-30 minutes or so to recover from being winded after a 200 meter sprint. Less well trained athletes take longer to recover. Interestingly, that's the amount of time that corresponds to the distance scale! So, let's add another point:

  • "Expending significant effort means that, you expend a resource that is recovered on the Time Scale of X+2. One way of implementing this would be to require you to expend a resource each and every Time Scale X that elapses, with an approx 50% to avoid expending it."
Let's put this into game rules terms.

1) Make an appropriate check, for example, "Athletics," "CON + Athletics," etc (system dependent; if no skills are utilized, the DM shall utilize a 2/3 chance of success for expert characters and a 1/3 chance of success for amateurs).
2) You take a wound appropriate to a scale equal to your current one + 2. For example, tactical combat (Segment) wounds are often measured in individual HP; a wound taken in combat measured over turns would be about 25 times as intense, or would take several turns to recover. For example, the DM may rule that you expend healing surges or temporarily gain negative levels. You may make a saving throw (system dependent, but should have approx 50% odds of success) to avoid this damage.
3) Move the normal distance allowed at your scale.
4) Once you have accumulated two successes, you automatically move one hex of the distance two scales greater. Special: If your move is 8 or greater, then you accumulate two successes with one good check. If your move is 2, then you accumulate 0.5 successes with every good check. If your move is reduced to 1, then accumulate only 0.25 successes with every good check!

Example of Play: Running a Marathon
The players need to cover 12 leagues in a hurry to deliver a critical message. This is 36 miles -- longer than a traditional marathon -- but in the same ballpark.

One character, a dwarf in heavy armor trained in running has a 66% of success every check he makes. However, because his modified speed is two, he will need to accumulate four successes, not just two. On average, this will take him six checks (six chunks). He will finish the race in about 12 hours, and is likely to expend about three healing surges as wounds.

Another character, a human who is untrained in running, has but a 33% of success. It will also take them about six checks to accumulate the required successes. On average, this character will finish with the dwarf!

Another character is a human athlete with a 66% of success. This athlete will, on average, run the course in three checks (six hours). This is a pace of 6 miles per hour. If fortunate, he could finish in two chunks for a pace of 9 MPH. These are a bit slower than real world marathon paces but not far off. He will probably incur one or two healing surges as damage.

A final character is mounted on an exceptionally swift courser with speed 8! He could finish in as short as one chunk (two hours), but it will probably take 2-3 chunks depending on his horsemanship and the courser's training.

Example of Play: Running a Marathon
A character seeks to disengage from a melee occuring at the segments/paces scale. He is trained in athletics and has a move of 4.

The first segment, he moves his normal speed and must make a saving throw to avoid taking some sort of significant damage that will take turns to recover from. He makes his check and succeeds! One success. He is still in the melee however and can certainly be chased or targeted.

The second segment he fails his check -- no success accumulated -- but must still check for fatigue damage. He still gets to move his speed, however, and is still part of the melee.

The third segment, he succeeds. He checks for final fatigue and moves a whole furlong away. He's probably removed from the melee, although missile fire may be a factor. Unless pursued, the character can be assumed to have disengaged.

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