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View Full Version : Logarithmic scaling problems.

xBlackWolfx
2013-02-02, 10:59 PM
I'd like my supers game to use logarythmic scaling, only issue is I'm having trouble working out the math. Right now, there is only a scale for how much weight a character can lift.

I'm actually considering just giving up on the idea, and going for a more free-form method (if your strength ranks says you can lift it, you can throw it at someone, regardless of how far away they are), but I decided to try and get some help to make it work, mostly just bc I want some official rules on travel speed.

Here's how the lifting chart works:

Your average human has a strength of +0, this would mean they can lift 20 lbs. This multiplies by 10 every five steps (a bit fast I know, but it works well in my opinion). The lifting capacities for +0 to +5 are as follows:

+0: 20 lbs
+1: 40 lbs
+2: 80 lbs
+3: 120 lbs
+4: 160 lbs
+5: 200 lbs

These values were chosen so that the math would result in perfectly even tons. Infact, all of them are simply the values (in pounds) for one ton, two tons, four tons, six tons, and eight tons divided by 100.

I need scales for time and distance, but I can't think of any that makes sense, and doesn't result in stupid stuff like 10 hours, 34 mintues, and 13 seconds somewhere down the line. The main problem is obviously time isn't metric (neither is SAE weights, but obviously the scaling still works fine since tons are divisible by 10, 100, and 1000) so multiplying a set time by 10 every five steps isnt going to result in perfectly even times; its hard just to get the scaling to hit a perfectly even 1 hour, and its impossible to achieve an even minute and an even hour in the same progression. Another problem is of course distance, since SAE distances are about as un-metric as you can get, I even contemplated changing all the measurements to metric (including the lifting chart). Sole reason I didn't do that is because I'm only familiar with american rpgs (which tend to measure things in five-foot intervals, like DnD), and five feet comes out to be something wierd in metric.

I'm not even sure if I want to do this or not, bc I'm trying to go for a simplistic design (thus the reason for the low attribute numbers, as evidenced by the fact that a character with a strength of 15 can throw a 10-ton object), and I'm thinking all this stuff about logarithmic scales is just getting too complicated. Can anyone help me?

Grod_The_Giant
2013-02-02, 11:58 PM
Have you seen the Ranks and Measures (http://www.d20herosrd.com/home/ranks-and-measures)chart for M&M? It has exponential scaling (I think; things double every rank), but it might shake something loose.

TuggyNE
2013-02-03, 12:14 AM
Another problem is of course distance, since SAE distances are about as un-metric as you can get, I even contemplated changing all the measurements to metric (including the lifting chart). Sole reason I didn't do that is because I'm only familiar with american rpgs (which tend to measure things in five-foot intervals, like DnD), and five feet comes out to be something wierd in metric.

You may want to reduce it to 1-meter increments (which are a bit over a yard), and just eat the squeeziness. Conveniently, metric tonnes are almost the same as imperial tons, so that won't be too bad either.

2013-02-03, 01:40 AM
Just use an exponential function to do the time. I mean, you're already doing it for the weight (as your function is 20*2^t), so it just makes sense to continue to use it.

: You have some decay on your previous formula, as the rate of change between intervals never goes over 40 lbs. I didn't notice that before.

xBlackWolfx
2013-02-03, 02:27 AM
Have you seen the Ranks and Measures (http://www.d20herosrd.com/home/ranks-and-measures)chart for M&M? It has exponential scaling (I think; things double every rank), but it might shake something loose.

Yes, I am aware of M&M's chart (or at least the 3rd edition one), and I hate it. Why? Scales too fast for one, but mostly, bc the math is wierd. According to DC adventures, batman can lift over 800 lbs, which btw would allow him to pick up a thug, and throw him over 100 feet away. And all that comes from him having a strength of +4. I would strongly prefer a game that could model the characters more realistically (or, actually, or accurate to how they're depicted, I mean seriously, Batman has a strength value that would be more appropriate for bane or killer croc)

Just use an exponential function to do the time. I mean, you're already doing it for the weight (as your function is 20*2^t), so it just makes sense to continue to use it.

: You have some decay on your previous formula, as the rate of change between intervals never goes over 40 lbs. I didn't notice that before.

Like I said, the values were chosen so that they would result in even tons later down the line. Specifically:

+10: 1 ton
+11: 2 tons
+12: 4 tons
+13: 6 tons
+14: 8 tons
+15: 10 tons

Yeah, the scaling's a bit weird this way, since its essentially linear with an exponential bump every 5 ranks, but I still like it for some reason.

You may want to reduce it to 1-meter increments (which are a bit over a yard), and just eat the squeeziness. Conveniently, metric tonnes are almost the same as imperial tons, so that won't be too bad either.

Yes, I noticed that, infact online it claims a metric ton is equal to 2200 lbs, which surprised me. Though the only issue beyond that is I have a hard time grasping just how much a kilo actually weighs, or how long a kilometer is. I can't even remember if a kilo is more than a pound, or less than a pound. You normally don't see metric here in the US, the only time I ever used it was in science class in high school, and I think my scooter also measures kilometers-per-hour alongside miles-per-hour.

TuggyNE
2013-02-03, 05:45 AM
Yes, I noticed that, infact online it claims a metric ton is equal to 2200 lbs, which surprised me. Though the only issue beyond that is I have a hard time grasping just how much a kilo actually weighs, or how long a kilometer is. I can't even remember if a kilo is more than a pound, or less than a pound. You normally don't see metric here in the US, the only time I ever used it was in science class in high school, and I think my scooter also measures kilometers-per-hour alongside miles-per-hour.

A kilogram is about 2.2 lbs, so a metric tonne (1000 kg, 1 million grams) is only a bit over an imperial ton.

A kilometer is about 0.62 miles long.

(I'm a bit of a metric nut, despite living in the US most of my life. :smallwink: Despite that, I don't remember exactly how big a hectare is off-hand, only that it's roughly the size of an acre; turns out a hectare is actually 2.47 acres.)

xBlackWolfx
2013-02-04, 07:35 PM
Okay, I think I got a scaling for time that might work.

+0: 1 second
+1: 5 seconds
+2: 15 seconds
+3: 30 seconds
+4: 45 seconds
+5: 1 minute
+6: 5 minutes
+7: 15 minutes
+8: 30 minutes
+9: 45 minutes
+10: 1 hour

Sadly, the thing will probably go all wierd beyond that. I'm thinking I'll just ditch the whole idea and go with a chart cross referencing time and mph. It'll be a lot more realistic, and straight-forward, than logarithmic scales anyway.

Though I still need distances for throwing things, which would be pretty easy in all honesty:

0: 1 space
1: 2 spaces
2: 4 spaces
3: 6 spaces
4: 8 spaces
5: 10 spaces

Same scaling as the strength chart too. Note that I'm really leaning towards multiplying all of these values by 2.