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Opinion: The Second Derivative of Health
by Matthew Downey on 07/31/11 08:35:00 pm   Featured Blogs

The following blog post, unless otherwise noted, was written by a member of Gamasutra’s community.
The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company.


Two health-centric blogs (1 & 2).  I thought I’d add my perspective to the mix.

Health should follow intuition or convention; otherwise, the designer risks alienating his/her audience.  I believe most health rule sets are based off logical fallacy: while most work, they are rarely fair to risky players.  Ever since Halo, regeneration has been the newest trend in health; today I offer a new solution.

Consider the following:

A player with 100 health instantly regenerates to full after five seconds without receiving damage.  In case one an AI enemy shoots the player with a sniper, dealing 98 damage, waits six seconds and repeats.  For the purpose of this experiment this AI enemy could safely do so forever without killing the player.  In the second case, the AI enemy fires one pistol round at the player through eight concrete walls every four seconds, dealing less than one point of damage per bullet forever.  The difference?  In case two, the player will eventually die, assuming the damage isn’t rounded down to zero.

To me, regeneration is most frustrating when, on the brink of regenerating, a stray bullet resets the timer.  After all, if a pistol round is nothing like a sniper round, why do they reap the same benefits?

A relatively simple solution would be to make regeneration constant, while putting regeneration in queue based on the amount of damage received.  For instance, 98 damage puts the regenerate function in queue for almost five seconds, whereas one damage puts regeneration in queue for a few frames. 

While this implementation alone would lead to less frustration, I will go a step further to detail a more elaborate system.

 In physics, the derivative of position is velocity, and the second derivative of position is acceleration.  Similarly, I propose health has velocity (regeneration/degeneration) and acceleration (recovery).  Regeneration, unlike Halo, can be any number from the player's maximum regeneration to an infinitely negative number (to simulate damage from bleeding, poison, fire, etc).  Recovery is a positive constant, similar to gravity, which seeks to normalize regeneration and, consequently, health.

In this system, I generally consider the bullet to deal two types of damage: impact damage and bleed damage.  Although impact damage can be thrown out altogether, it is particularly useful for the verisimilitude of headshots and high-powered rifles.  To further stress the usefulness of impact damage, damage types can be separated into two levels of lethality, both of which can only kill after a certain threshold.  For instance, to prevent stalemates, a designer can make impact damage kill when the player is already at half health or lower, whereas bleed damage will instantly kill the player when they get to zero health.  This gives health adequate room to recover before the player “bleeds out” after an average firefight, since dead players can no longer dish out impact damage.

Three-dimensional health assists in player recovery after easy fights while inhibiting recovery after long, drawn out battles, making post-fight disadvantages scale accordingly to difficulty level, which I believe will speed up pace and flow in the majority of firefights.  Furthermore, since players are always “recovering,” they will be more willing to risk encounters at lower than full health.

Halo set the precedent for upgrading health systems back in 2001; I feel it’s time to shift health up in depth.  If you take nothing else away from this post, know this: when coding health, there are more than two options, some of which may be more intuitive to players than health packs. 

Feel free to comment.

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Luis Guimaraes
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It's an interesting conpect you have here. The only problem, if not really a problem, is that nothing can please everyone.

Indeed an interesting (gameplay-wise interesting) tridimensional health/damage system can catch the attention of some players, but not all of them. What would be good was if a game came with opitional configs for this, ranging from more casual to more hardcore, with proper explanation as to how each one affects the gameflow and strategy.

You have to explain that a game was design to have combats that last longer, with not so strong direct damage and not so quick headshot system, and this way a player with 30% of the health could almost never kill one with 100%, and that there's also a focus on melee combat that needs highes survivability to work well (Halo).

Or you could say that your game can have firefights ending with a single bullet, with a higher proposal of tatics and team work, but not exactly team packing being the best strategy, and round-based respawn system with no health recovery at all, which can change the way you play when you're hurt, and makes any damage you can cause to be helpful to your team, even if a player with 1% can still take your whole team down with skill and luck. (Counter Strike)

Or you can bring a whole new system. More or less hardcore. With different effects on overall gameplay.

The way health/damage works can change the whole game strategy. And some players will simply prefer a more casual one or not.

Matthew Woodward
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If we're going to talk about second derivatives, here's a much simpler system to consider:

Health regeneration occurs at a rate that is both constant and related to the amount of damage you've taken. The more wounded you are, the faster you heal. Balance the regeneration curve to taste and serve.

(Properly balanced, this should allow the player to balance on the edge of death in combat, which is desirable from a tension-building perspective, while also making regen in the top half of the health bar slow enough that working to maintain full health and/or using medpacks is still desirable.)

Matthew Downey
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That's very interesting, reminds me of this article.

As much as I like this idea, this might make damage-all-at-once weapons more powerful than they were initially intended to be. Weapons like snipers, which are generally the most powerful weapon, could potentially be the only viable option for competitive play, assuming the sniper can have a one-hit kill. If you can't get a one-hit kill with a sniper, it might be too weak (assuming it has high recoil and/or slow rate of fire).

Matthew Downey
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[A Response from one year later, a lot of education, and a metric ton of introversion.]

While this may seem like a cool idea, for the sake of networked multiplayer it causes a few problems.

The physics equation y = y' + v't + (1/2)*a*t^2 can have all of the required unknowns sent over the network: timestamp,health,regen (acceleration is constant). This means you can calculate the current "position" of the player any time in the future by taking the delta-time (Time.currentTime - Network.timestamp) as "t", health as " y' ", regen as " v' ", and the constant recovery as "a", which is very convenient, for anything else you would need to integrate (or make approximations that might not be consistent on all clients) for the curves.

Also, you can have near-infinite accuracy for a players health and you only have to send new information when they are damaged.

Justin Speer
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This sort of thing really has to be tuned on a game by game basis, and there are many ways to approach it. I wish more people had played Vanquish, which despite not having the most accessible model, has a really interesting way of dealing with this issue.

Michael Joseph
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Regenerating health makes for lazy gameplay (for lowest common denominator players) and is a sign of heavy handed game design (which we're seeing more and more of).

When you hear designers overly concerned with controlling the eb and flow of the game it feels more like they're trying to choreograph the gameplay of an entire level to look the same no matter who is playing.

That's less of a game and more of a button masher on rails... or at least bowling with gutter guards.

Nick Harris
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Very interesting article.

Those who criticise Halo's regenerating shields and 100% instant recovery health packs miss the point of the system. You can set up a multiplayer custom game where no one has a shield and find that your Spartan is in much the same predicament as one of their hapless UNSC Marines - indeed, despite being stronger and being able to jump higher they are a lot taller and stand out on the battlefield as a much larger brightly coloured target. Such games can have their setting tuned so they resemble Call of Duty and seem entirely fair until someone starts sticking pink explosive barbs into you with the alien Needler gun which can fire around corners - then you notice that there is a lot more that is prone to explode near you than in Call of Duty and whilst splash damage wasn't much of a problem when you had a shield you now find formerly navigable routes through a map a death trap. Obviously, the maps could be redesigned in the Forge and all vehicles removed, but then it wouldn't be Halo anymore.

Halo empowers the player and then rebalances the game by throwing multiple enemies at them at once. The same was true of Goldeneye 007 on the N64: make the player feel as capable as James Bond, but then throw ten Spetsnaz commandos at them. On the whole you take on the role of a one man army, rather than part of a coordinated squad, as in Call of Duty or Ghost Recon.

Halo's Mjolner armor makes Master Chief into a walking Tank, indeed he is capable of single-handedly taking down an enemy Tank, or hijacking a passing aircraft in mid-air due to the layer of impact reducing gel in his suit. This makes him ready for the most brutal, dramatic, frontline combat. What would be suicidal insanity for a Marine is just work-a-day heroics for a Spartan provided that they have planned their strategy to stop behind intervening cover in order to make the final assault with a full recharge. These pauses aren't boring, but an opportunity to reload, swap weapons and cycle between different types of grenade. They provide an opportunity to assess the battle, develop situational awareness and formulate tactics. Halo is Chess.

Would it be better if you could carry multiple health packs and self-administer them as required? Often the health packs were unsafe to collect when weak, should this really be Risk / Reward? Maybe. It required the player to take a paranoid approach, to back-track for health and appropriate weapon combinations and that may not have been such a good thing after all. Consequently, I'm intrigued by the approach taken in F.E.A.R. 2 where you collect Medkits and use them as needed:

Something similar was done in Far Cry 2 with syrettes, whilst % Health became bodily harm:

I'd really like to see an end to players sprinting away whilst under fire when they should collapse incapacitated and gradually bleed out. The field dressing / medkit / health pack / syrette / etc. shouldn't be a single button press away, but require an inventory access, as well as not being instantaneously recuperative (some kind of absorption delay at the very least), to prevent them being used in sequence to give the player apparent invulnerability. This isn't a problem in Far Cry 2 as it forces you to fix your injuries before reengaging with the enemy. The upcoming Battlefield 3 innovates with its new ability to use light machine guns to suppress enemy positions - you force them to duck down and enable part of your fire team to move forward, you also get points for doing so even though you didn't get the kill:

It doesn't suit every game, but increased realism leads to games like Red Orchestra 2:

Of course, you can have a separate Medic class whose job is to help out incapacitated allies, although some games don't seem to get all the wrinkles worked out, as in ARMA II:

Should a player be able to Sprint with a quarter health bar? How brutal should their Melee attacks be if they are at death's door? Should the health of a player be reflected in their gait? Should location specific damage cripple their ability to throw grenades accurately? The enemies in the upcoming RAGE react this way, see presentation after 3:40 in the following video:

Of course, that's before you get into dealing with Halo's equipment: regenerator, bubble shield and deployable cover. Reach tends to overdo this with always available armor abilities and the stupidly irritating and largely ineffectual armor lock, but then any sequel is criticised if it doesn't innovate and you can't make any changes to a perfect combination of ingredients without coming up with something worse.

Matthew Downey
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With respect to these quotes:

"I'd really like to see an end to players sprinting away whilst under fire when they should collapse incapacitated and gradually bleed out."


"Should a player be able to Sprint with a quarter health bar?"
ack. html

When a player can't sprint near-death, that makes fighting back near-impossible due to "slippery slope," which (generally) leads to boring and one-sided fights. Forcing an unfair fight tends to frustrate players: people don't like dying without a fighting chance.

The setting for which tri-dimensional health is intended is the sci-fi universe, where the designer has an unlimited resource of tools to explain systems. Artificial muscle and Carbon-nanotube armor is all I have to provide for the player to believe they can run near death and take 100 bullets. Add that to the fact that nanobots are repairing the artificial muscle/carbon-nanotube hybrid suit while repopulating each other and regeneration clicks, as if it were a self-sustaining biological system.

Let it be known, I'm not up-in-arms against any of the other ideas, in fact I really like the "gradually bleeding out" idea. Also, I sort of figured out halfway through that your comments are single player-centric, whereas I purely focus on multiplayer.

Thanks for the comment.

Nick Harris
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It was interesting to read about Beat 'em ups and the alternative to resource gathering used by World in Conflict as I am unfamiliar with these genres, so thanks for the link.

I should have mentioned that I was thinking of the console version of Operation Flashpoint: Dragon Rising which would have been a decent attempt at a hardcore Military Simulator if the squad control interface hadn't been crippled beyond use. Codemasters acquired the name from its original developers Bohemia Interactive who went on to produce the (rather buggy) ARMA games:

It should be apparent from watching this that this is a simulator not an arcade game such as Call of Duty. The original Xbox game Full Spectrum Warrior was developed for the US Army to train their squads in the correct use of Bounding Overwatch:

Interestingly, Goldeneye 007 on the N64 lacked health packs, had no shield except for wearable body armour (which didn't recharge):

The highest level of difficultly let you adjust the game's settings so you only stood a chance if you used the floating reticle to headshot one enemy at a time whilst briefly leaning out from behind impenetrable cover. PC shooters are considered superior to console because of the precision and rapidity of mouselook is thought to be better than the gamepad's analogue stick. Yet, whilst games like Halo force you to slowly Turn to face every target you Aim at, Goldeneye effectively circumvented this problem four years earlier:

So, a player can avoid the "slippery slope" in these 'realistic' games through the use of stealth, observation, situational awareness, strategic use of cover, flanking manoeuvres, suppressive fire through the use of 'blind fire' and bounding overwatch.

Finding yourself under suppressive fire should be your cue to seek some hard cover, regroup with your squad - one of which is hopefully a Medic and can heal any injuries the team have - reload and reassess the situation. Health packs should be either dropped by a Medic, or carried in reserve until needed by every soldier (as in F.E.A.R. 2), with the wrinkle that they drop their hoard for someone else to pick up when killed.

I'm not knocking Crysis. I'm suggesting that Call of Duty could be more realistic provided that everyone who played it stopped running around like Rambo Jesus.

Matthew Downey
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Oh wow, reading this over a year later and I realize I cut the bleed damage can kill at 1x maxHealth, and any impact damage can kill after that based on the verticality of the shot (which was really hard to explain, no slight on anyone else, it's my fault as a designer).

I changed that weird method to "if you get below zero health, you die", which is how it should work; it's simple and the bleed shader (which isn't mentioned here but in another Gamasutra article on my profile) a lot easier.

I almost feel like I could simplify this post, although if anything I'll just reprint it.

Nick Harris
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How close is your proposal to a segmented health bar where recuperation is slower to fill up the segments that represent core health and you can't automatically recover beyond a single damaged segment back to full health without some intervention.

Far Cry 2 has this solution, although I'm unsure whether its recuperation rate slows as you get more seriously injured. The Chronicles of Riddick: Escape from Butcher Bay may also do this.

Anyway, thanks for a thought-provoking article.

Matthew Downey
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The short answer: I don't think I implied such a solution (sorry if I worded the article awkwardly).

Longer answer: I considered adding something like un-regenerating health (not segmented like Brink or FarCry; I didn't like the idea of segmentation, and being very good at math I can easily compensate in fairer and more predictable ways for the player). My obsolete method was distributing damage in short- and longterm types. Short term damage would subtract from your health and was what would kill you, long term damage could never kill you, but it made sure you wouldn't heal to the same max (until you took in some sort of medical treatment). Long term damage would subtract from the max health of about 1000, until the player hit, say, 700, whereupon their maxHealth was clamped there indefinitely, so the player didn't diminish their health to 500 or 300 or lower.

After a little bit of thought, though, I put that idea in the obsolete pile. This lies in balancing the game a different way. The idea of slowly killing players on a killing spree also seemed adrenaline revoking (and I love adrenaline, so I can't morally do that to my players). Balancing the game a different way, I can ramp up the randomized weapons the enemy team gets at spawn to compensate for any imbalances between factions in an 8v8 fight. Furthermore, the idea of nanobots repairing the skin, flesh, and blood vessels of the soldiers has been an idea I've had since inception of this game. So taking out the notion that nanobots are the best doctors in the the world makes the protagonist's tech seem a lot less badass, and I didn't want that.

This topic is more irrelevant theory of mine (and you should only read it if you prefer concepts to relevancy):

Like everything I make, this world is living and breathing to me, and I have to manage it accordingly. I can't just put in a mathematical function where 0.00001f health makes the difference between a player having, say 15.0000% more health in the long term, because that would break the stability and verisimilitude of the world. Instead I add randomness in the more traditional way. Historically players hate computer generated randomness (because it has a linear chance within a range of numbers), so I did something really unique with the logistic curve to distributes damage based more evenly around the center of the graph for stability that has occational randomness. This statistical randomness also means guns are easier to balance, in call of duty 4, a gun that does 50 damage is basically the same as a gun that does 99 damage, because the gun will require two shots to kill neglecting headshots. That being said, the logistic curve might beautifully produce results where 1.40 or 1.68 bullets are required to kill.