Why are some people sprinters, while others are distance runners? The differences between short races and long ones aren't very clear in PB, because detailed rules for running races, jumping, and throwing are hard to find. I've been told that there are rules for determining jumping heights in the HU GM's Guide, but I don't want to buy that book. Besides, given the problems I have with the way PB implements attributes, I doubt the info given in the GM's Guide would satisfy me. I'll start from scratch, and let anyone that reads this page decide which is better. I'll do my best to keep the game mechanics simple, and the implementation "megaversal." All of my proposals are motivated by my knowledge of kinematics, as well as my experience as a former high school athlete.
One of the strangest, most confusing aspects of the Palladium system is how it separates PS attributes into different categories. The whole point of having universal attributes is to allow ready comparison between characters; allowing different strength levels and different PS multipliers, damage scales, etc makes the game much more complicated than it needs to be. In any event, because of these different strength levels, I'll refer below to the maximum amount of weight a character can lift instead of referring to a character's PS attribute. As a reference, from HU2, lifting limits are determined as follows:
Max Lift (lbs)
There are tables given in various books, but none are very satisfying. A simple rule of thumb that I've used:
The distance (in yards) an object can be thrown by a character
is the amount of weight
that character can lift divided by the weight of the object to be thrown.
d = distance character can throw object = [ weight character can lift ] / [weight of object ]
This assumes that the character gives a full two attack effort to throw the object. A one attack throw will reduce the distance to 2/3 maximum, and a restrained toss will have a range of 1/3 maximum. If trying to strike a specific target, the character has to compare the distance to the target with his maximum throwing distance. Additional modifiers, due to the sizes of the target and the object, may be appropriate.
Distance to Target
Because small objects will be thrown much faster than large ones and strong characters will throw objects much harder than weak ones, it doesn't seem fair for the size of the object to determine the damage inflicted. If the object is thrown at a target, the damage done will be determined by the character's combat damage. Using two attacks to throw an object means the damage will be that character's power punch damage, using one attack to throw will inflict the character's normal punch damage, and a restrained toss will inflict the character's restrained punch damage.
The simplest, most accurate method I can come up with is:
Characters can jump a total vertical height, in feet, determined
by the amount of weight
that character can lift divided by his body weight:
h = height character can jump = [ weight character can lift ] / [ character's body weight ]
This means an average person (PS: 10, 165 lbs) can jump about 14 ½ inches off of the ground. A character who's a little heavy for his strength (PS: 10, 200 lbs) can jump one foot. On the other extreme, a character with Superhuman Strength (PS: 35, 250 lbs) can jump 42 feet off the ground! This may seem too high to some, but I think that's because most people have misconceptions about what very high strength-to-weight ratios would allow people to do. Someone who can lift over five tons won't have much trouble dealing with their own body weight, and that should be reflected. How many TV shows have characters, usually very attractive teenage girls with moderately enhanced strength (by HU standards), that can easily jump over 10 foot fences?
Assuming that characters don't have a running start, they'll be able to jump a maximum horizontal distance of about twice their maximum vertical height. This means our average character (PS: 10, 165 lbs) will be able to jump about 2 feet, 5 inches, and our Superhuman character can jump over 84 feet. Again, this last jump may seem very long, but I think that's the fault of existing misconceptions.
Running Start: A Complication...
Characters will be able to jump further with a running start. A reasonably accurate way to determine the additional jumping distance (in feet), assuming the character can get up to maximum speed, is:
xadded = Spd ( hmax
/ 8 )½
[Additional jumping distance: feet] = [Speed Attribute] * ( [Maximum jumping height: feet] / 8 )½
This means an average character (PS: 10, Spd: 10, 165 lbs) can make a total horizontal jump of about 6 feet, 4 inches. A character with Superhuman Strength, a Speed attribute of 30, weighing 250 lbs, can with a running start, make horizontal leaps of over 150 feet! Characters with average strength and weight, gifted with Sonic Speed (PS: 10, Spd: 100, 165 lbs) can make horizontal leaps of about 40 feet, but characters with both Superhuman Strength and Sonic Speed (PS: 35, Spd: 100, 250 lbs) can make leaps of over 270 feet!
This simple system falls apart when we take air friction into account, which should definitely be done for characters with enhanced speed attributes. Everyone complains when I use too much math and/or physics, making the rules too complicated, so I'll leave that revision for another day. The above results may change many groups' conception of game balance, but I think it's appropriate. Enhanced characters are far stronger and faster than even the greatest Olympic and professional athletes.
The jumping heights above are only one aspect of a character trying to clear a height with their full body (leaping over a high shelf, as opposed to just reaching an object on that shelf). Characters trying to jump over an object, as in a "high jump" track meet event, have to add another complication. The player must roll a percentile die, adding their PP attribute as a bonus. The height they can get their body over is that percentage of their maximum jumping height. Characters specifically trained for this feat can add a one time bonus of 20%, plus 5% per level of experience of their "High Jump" skill.
If a character is only jumping over a hurdle-type obstacle it is possible to clear heights greater than their maximum jumping height. This is accomplished by shifting bodyweight to keep their center of mass below the hurdle. The maximum additional height over the character's usual maximum is half of the character's physical height. Characters leaping onto a shelf or ledge can never reach more than 100% of their maximum jumping height, regardless of a total roll greater than 100%.
According to the rules, characters can run at a maximum speed of 20 * Spd attribute in yards per minute, which is equivalent to a maximum speed of their Spd attribute in feet per second. This sprint can be sustained for one minute per PE point- The official rules allow average characters to run at maximum speed for 10 minutes! Another flaw in the rules is that bodyweight plays no part in running endurance. A high PE often represents the ability to exercise for a long period of time, but it also represents the ability to take more direct physical punishment. A short, overweight character that can take a punch can run as long and fast as a tall, thin one. Doesn't seem right.....
Using the Speed attribute, as well as the PE and PS attributes and bodyweight, I'll determine a more accurate formula for determining how long a character can run at any speed up to their maximum. For most people, full sprints shouldn't last longer than a minute or two, maximum. Slowing down to some percentage of their maximum speed allows most people to run for much longer. Looking at some actual numbers I've collected, the increase in maximum running time seems roughly proportional to the squared percent decrease in running speed. Confused? Some math to make it clear (and a table so you don't have to use the math):
vrun = n Spd
h = maximum lift / bodyweight
tn = [ 10 ( 1 - n )2 + 1/20 ]
tmax = h PE
dmax = vrun tmax = n Spd tmax
I'll make a table of values of tn for different values of n. Users of this rule will only need a small table of values, and multiply the appropriate tn by their PE attribute and strength-to-weight ratio (which is also the height they can jump according to the rule above). Looking at the table, slowing down to 90% of your maximum speed allows you run for 3 times as long, slowing to 80% allows you to run 9 times as long, etc....
An average person will have attributes PS: 10, PE: 10, Spd: 10, and weighs 150 lbs. An average athlete with the Athletics, Bodybuilding, and Running skills will have different attributes PS: 13, PE: 11, Spd: 24, 160 lbs, allowing him to run faster and longer than his average counterpart. A SPB with Extraordinary PS might have attributes PS: 28, PE: 20, Spd: 40, 210 lbs. At different percentages of their maximum running speed they'll be able to run for different amounts of time, and thus will run across longer distances before tiring out. As an example of how this formula is an improvement I'll plug in some numbers:
This revision, evidenced by the more realistic maximum times and distances characters can run, is a definite improvement over the official rule. The existing rule allows average people to run full sprints for ten minutes, which is ridiculous. The SPB can run just over one minute per PE point at maximum speed, thanks to his incredible strength-to-weight ratio (he's pure muscle!). Most importantly, this revision allows characters to run longer times if they sacrifice a bit of speed; real people don't sprint everywhere they go!
Running races is now a little more complicated, because characters can't typically sprint for incredible distances, but I think it's more realistic. Assuming that the race is longer than the character can sprint, they'll have to decide on a percentage of their maximum speed to run at. If after a certain amount of time the player decides to change their running speed, when they've already used up some of their "energy," a new maximum run time should be calculated. For example: I, an average person, decide to run at 90% speed for a race. After one minute, half of the maximum time I can run, I see that I'm losing the race. I decide to run faster, bumping my speed up to 95%. I've already used up half of my running energy, so I'll only have 30 more seconds at this new speed before I run out of steam. If I get near the end of that 30 seconds, and still haven't finished the race, I can slow back down to whatever speed I need.