About a year ago, you may recall, my brother and I attempted to derive the product of Pac-Man's metabolic functions. In that spirit, Kotaku has now created its own Bureau of Weights & Measures.


The Bureau's mission: To needlessly expose the wide gulf between video game physics and the laws of the real world; to pursue, to a pointless degree if necessary possible, the logical extremes of any mathematical given; to ask the questions that do not really deserve to be answered; and as an ultimate, Quixotic pursuit, to finally define the real world value of one hit point. We do this in the name of science for all mankind.


Our first journal of study is hereby submitted, dealing with three metrics - weight, speed and momentum.

Dr. Owen S. Good

Director, Kotaku Bureau of Weights & Measures

WEIGHT

Game: Fallout 3

Test Subject: Vault Dweller

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In an RPG, you'd expect to have some distorted encumbrance measurements. Players have been hauling around a full cabinet of arms, plus full plate armor, plus a spare set of armor, plus dual-wield crossbows, plus 500 bolts, plus turkey dinner, since this kind of game was played on paper. It's why D&D invented the Portable Hole.

Fallout 3 measures weight in vague units of "WG." Of any RPG that caps carrying weight, it seems to let you carry a lot. Like a U-Haul's worth. In my latest game I deliberately created a guy with 4 strength because I wanted him to travel light and carry only that which was useful. But as you can see in this recent loadout below, I'm still stowing a spare set of recon armor in case a Glowing One makes me dump in my Brotherhood suit.

Weapons: A3-21's Plasma Rifle, Combat Shotgun, 28 Frag Grenades, 15 Frag Mines, Mesmetron, 3 Plasma Grenades, 4 Plasma Mines, Plasma Pistol, 9 Pulse Grenades, Scoped .44 Magnum (56 WG)

Apparel: Enclave Officer Hat, Power Armor, Power Helmet, Recon Armor. (71)

Aid: Blood Pack, 9 Buffout, 3 Dirty Water, 14 Med-X, 15 Mentats, 2 Nuka-Cola Quantum, 4 Psycho, 17 Purified Water

9 Rad-X, 25 RadAway, 6 Stealth Boy, 79 Stimpak, (sue me, I'm a HP whore), Sugar Bombs. (28)

Miscellaneous: 16 Bobby Pins, Carton of Cigarettes, Cherry Bomb, Conductor, Fire hose Nozzle, Ink Container

Leaf Blower, Pack of Cigarettes, 5 Pre-War Money, 12 Scrap Metal, Key ring with 14 keys on it (29)

Ammo: 202 rounds .44 magnum, 20 darts, 285 Energy Cells, 50 Mesmetron Power Cells, 493 Microfusion Cells, 280 Shotgun Shells. (0 WG)

Total WG: 184


What bothered me about Fallout was not so much that the heavy weapons, like a Flamer, weighed only "15." Maybe they're made from futuristic lightweight metal. No, it's more that a pair of freaking TWEEZERS was equivalent in weight to a motorcycle helmet. It's not even that the WG figure represents a total encumbrance factor – that either the item's size or fragility makes it difficult to carry - because a pool cue has the same WG figure: 1.

So I chatted up Todd Howard of Bethesda Softworks, Fallout 3's game director, about this. First off, is "WG" equivalent to anything?


"Not really," Todd said. "It's sort of close to pounds, but we intentionally don't really say what it is. It actually started based on the weights we used for The Elder Scrolls, which most people don't know are the also-amorphous ‘stones.'"


OK, fine. If they didn't peg WG to something, I will. And I'm going to base it on the weight of beer. A bottle in Fallout is 1 WG. In real life, a bottle of beer, depending on how stout it is, will weigh roughly three-quarters of a pound when you figure in the glass. By figuring my total burden as it relates to at least one item in my possession, I could start imagining how large a load I was carrying around.

But what I couldn't measure is ammo, meds and chems, which have no weight value - and I wasn't going down to the local needle exchange to weigh whatever approximates a Jet syringe. Why didn't Bethesda give them a weight? Because in the game, these are very valuable items. Why wouldn't an RPG, which is more based in realism and more dependent on choice-making than other genres, also require players to be more conscientious about what they're carrying?


"In regards to ammo and money, it's just too granular a decision for the player, if they had weight," Todd said. "You don't want to make that a choice for the player; he already has to manage so much in his inventory and you need things he can find that are an instant win - ammo, money, drugs, etc, things that help keep him alive and playing. It would just bog the game down too much to find ammo and be thinking, ‘Do I want to pick up two of these bullets or the whole stack?' We felt that decision should be on [which] weapons to carry, not what ammo."


Yes, but when a Gatling Laser weighs the same as a frosty 18-can fridge pack of Miller, your decision to carry two is not because of their combat utility but the resale value in Rivet City. Todd said that's entirely valid reasoning, and strength is meant to enable it.

"Much of your character's power comes from his stuff. The more he has, the better he is. Even if he's not using it, it becomes money," Todd said. "Players get pretty good at the value versus weight game quickly."


You might figure that, in the long run, it all balances out. Tweezers are overweighted, bazookas are underweighted, and everyone gets along. But my previous loadout would weigh 138 pounds (1 WG = 0.75 pounds) and still fill up a Public Storage room. Todd insisted that developers discussed the question of how much a player should be able to carry, "right until the end. … We kept narrowing and narrowing what a low-strength versus high-strength gave you, because it was too powerful."


Was too powerful? In the finished game, a Fallout 3 character with the bare minimum strength of 1 can carry 160 WG. I searched for a real world comparison, and this is the best I could do: The Improved Load Bearing Equipment in use by the U.S. Marine Corps since 2005 can carry - ready for this? - 120 pounds. If beer is our unit of measure (and why shouldn't it be?) that converts to 160 bottles of beer (or WG). In other words, any vault reject a notch above total weakling - a 2 strength or better - will out-lug any Marine, even the one assigned to carry the mortar and shells.

Partly to spite Bethesda, I created a character with 1 Strength and assigned the rest of the points to more useful attributes. I never use melee weapons, anyway. I also manually assigned weight to my ammunition and chems (1 for units of 10). I quickly saw how right Todd was.


In Fallout, your ability to meet more difficult challenges depends a lot on the equipment you have, and it's usually items you build or buy that prove the difference. Financing that comes from the resale of surplus items, not the discovery of treasure. Realistic strength would leave you endlessly grinding before starting the next job.

As for ammo, I gave up on that shortly after a raid at the Super-Duper Mart. I was robbing Raider corpses for spare rounds to fight off the survivors and writing down the totals. It was indeed too granular a decision, and got in the way of more pressing challenges.


So, even though with a 5 strength, you can run from Megaton to the Arlington Public Library loaded down like a Peruvian donkey, let's just say the future is made of super-light plastics. And the radiation turned everyone into Lou Ferrigno.

[Images from the Fallout Wiki]


SPEED

Game:Grand Theft Auto: San Andreas

Test Subject: Carl "C.J." Johnson

Originally, I wanted to test the scale speeds of the Team Fortress 2 characters, especially Scout, who could probably outrun Carl Lewis like a Porsche outruns Stephen Hawking. The problem with this, as with other games, is measuring the distance those guys cover in real world units. I'd have to know, say, Heavy's IRL height (6'5?") and be able to lay him end to end over a straightaway to get its real distance. I'm not a modder, and I wouldn't have that kind of time anyway.


So I then looked to the Grand Theft Auto series. From Claude to Niko, you've always had the ability to overtake a moving car on foot and jack it. I really wanted to know these guys' running speeds, and they live in cities with structures based on real world ones. Unfortunately, everything in Liberty City is a compressed distance, so running Niko across the Broker Bridge still wouldn't tell us much.


But in Grand Theft Auto: San Andreas, there's this Easter egg, which identifies the specific dimensions of the Gant Bridge, including a length of 159.7 meters. During the first few tests, something seemed way off. First, 159.7 meters isn't even a 10th of a mile, and C.J.'s runs - at a sprint - were keeping up with traffic and returning mile times of 17:41. So I had to measure this bridge for myself. If I knew the actual scale speed of a vehicle in the game, I could derive its length. This database lists all such attributes.

Thus aboard an NRG-500 motorcycle running at its top speed of 118 mph, I made five maximum-speed trips across the bridge, at a flying start, with a median time of 18.15 seconds. If the Gant Bridge really was 159.7 meters, the bike would have been doing 20 mph, not 120 mph. It's possible they're talking about a distance shorter than the one I was using - toll booth in San Fierro to concrete strip at Tierra Robada - but at top speed, the bike should be able to cross 159.7 meters in just under 3 seconds. Either way, 160 meters is a fraction of the bridge's length as it relates to C.J.


So, at top speed, the bike is traveling at 173.16 feet per second. Multiplied by 18.15, we discover the length of the Gant Bridge is 3,142.85 feet, which is nearly 1 kilometer. As another control, I went back and rode with traffic, matching its speed. We crossed the bridge in 1:09.16, which is 30.98 miles per hour. I damn for sure could see a developer setting standard traffic speed to something round, and 31 mph is almost 50 kph. So, I'm pretty confident the sign is incorrect, and I got this measured as close as possible.

Now, back to running it. C.J. has five paces on foot: a walk, a "brisk walk," a "jog," and then two sprints, one with the A button held down, and another that provides a burst of speed by rapidly tapping it. The C.J. I was playing had maxed all of his physical stats, so he could achieve top running speed and not tire out, at any distance. Back at the bridge on foot, I took him through the five paces.




Walking

At his slowest C.J. covered the distance in 8:22, which equates to 4.2 miles per hour. Frame of reference: 4.0 is the fastest most walk on a gym treadmill. At the "brisk walk" pace, C.J. covers the distance in 4:44.03. Remember our treadmill? This "walk" is more than a jog, it's 7.54 miles per hour. It's equivalent to a 7:57 mile time. My best time in the mile - running - is 8:21, five years ago.


Running

Now it gets good. At the third pace, "jogging," C.J. crossed the span in 2:43.16. If he held that pace he would run a marathon in under two hours, which is unprecedented. Holding down the A button, C.J. crossed the bridge in 1:38.11, or 21 miles per hour. That's a mile in 2:44.84, which is inhuman. Remember Roger Bannister? The first mile under 4 minutes? C.J. would run the first one under three. He would beat the world record holder by a larger margin (in seconds) than he would have lost this year's Kentucky Derby.

Sprinting

Rapid-tapping the A-button gave C.J. just a 16- second advantage, which means this loses its effect pretty quickly. Still, at minimum one can assume some world-class sprint times. How world class? Try torching Usain Bolt's records in the 200 and 100 by two and one seconds, respectively - 17.1 and 8.58 seconds. Granted, that speed figure is derived from a running start. Real-life sprinters have to react to a gun and get up to speed. But, remember, C.J.'s sprint lost effect, I'm not sure exactly how far in, so most of this time was derived from a run at the standard "A" pace.


Incidentally, C.J.'s motion capture actor was Eddie Goines, a star wide receiver at North Carolina State University and a classmate of mine. I knew him pretty well, as well as a sports writer knows one of the team's stars, anyway. As a flanker, he set all the receiving records that Torry Holt and Koren Robinson would later break. As a freshman, Eddie was the fastest on the team, clocking a 40 yard dash in 4.35. A 4.09 is thought to be the NFL record. CJ's time is 3.15. I'm sure Eddie would be delighted to know that, at least in a video game, he's by far the fastest human alive.

MOMENTUM

Game: Assassin's Creed

Test Subject: Altair


No one would expect to fall 40 stories onto the top of a parked car and survive. However, at least it stops the body from crashing all the way through to the ground. Now imagine falling that height into a pile of hay that's roughly 2 meters wide by a meter and a half tall.

That's the first "leap of faith" in Assassin's Creed, from the tower at Masayaf. Holy catfish, that poor bastard who jumped with Altair at the beginning was lucky to get off with just a broken leg. And it is far from the steepest drop in the game. The infamous steeple on the cathedral at Acre is nearly twice as tall. Fresh off our victory in San Fierro, the Kotaku Bureau of Weights & Measures set out not only to fix its height, but also to calculate how much hay you'd need to land safely.


Ubisoft verified that Altair's height and weight, for purposes of the game's physics, was 6 feet and 190 pounds. This would be useful in calculating his stop. But that's all we got from them. However, one of the locations in the game is Jerusalem's Dome of the Rock, whose dimensions are known. The structure's walls are 11 meters tall. Putting all this information in the hand of a trained scientist - devoted reader Matt M. - we were able to come up with some good estimates.


Matt worked up all three heights, but let's use Acre's as it is the most impressive. We were able to time the drop from the top of the steeple -4.1 seconds - using this video (which I downloaded and measured frame by frame). Working backward, we found that its real-world height would be 82.37 meters - about 270 feet. In the game, Altair is accelerating to 39.69 meters per second, acquiring a momentum of 3,420.48 kilogram-meters per second.


That's certainly a large number, but what does it mean? Matt breaks it down:

Basically, whatever catches him has to has to reduce that momentum to zero in under 0.05 seconds, which is the difference in time between Altair falling 82.05 meters and falling 80.05 meters at that speed. That means in the space of 2 meters - which is a little lenient since the floor of the cart is, what, half a meter off the ground? - the hay has to provide 68,298.25 Newtons of force. It's 136,596.5 Newton meters of work, which is a ridiculous thing to ask of hay.


Certainly, Kotaku Weights & Measures does not want to be unreasonable in its dealings with dead vegetable matter. And I'm not sure what could provide that kind of stopping power in that space, other than Kevlar. Or pavement. So I asked Matt if he could figure how large a haystack would be required to cushion a fall from such a height. We used the elasticity of military-grade bungee cords as a guide (using specs found here).


In the case of Acre, the haystack would be so big it would dwarf most other buildings in the game - 40 meters (131 feet) at its point, 67 meters (219 feet) wide at the bottom, if the dimensions conform to the original tiny pile. The freefall into such a mass of hay would last only 2.87 seconds. In terms of volume, it's more than 2.7 million cubic feet of hay - 2,695 times greater than what Altair is leaping into. I kept picturing Phil Hartman sitting atop the amazing mountain of Colon Blow cereal.

Alongside this you can see comparisons, to scale, of the heights Altair falls at the Dome of the Rock, Masayaf, and Acre, and of the size of hay he hits in the game relative to the size he would need to survive. "Leap of Faith" indeed. Sounds more like Altair's in a suicide cult.


The Kotaku Bureau of Weights & Measures gratefully acknowledges the contribution of Matt M. to this post. Follow him on Twitter.