How Tough Is Your Game? Creating Difficulty Graphs: Part II
Games Development
Recap
So, let's recap the steps:
- First, you have to determine what the game's standard conditions are. This is the minimum power level the player has during a determined segment of the game (be it a stage, a level or the whole game). This can vary often due to permanent power-ups.
- Find the base enemy (generally the weakest or most generic enemy) and set its threat level to 1, and adjust the threat level of all other enemies in accordance to its stats.
- Playtest. A lot. Have different players with different play styles move through the level so that you can get the average time (if doing time-based difficulty charts) or average distance (if the chart is distance-based) of each enemy encounter.
- Check which situations you find the enemies in, and assign values to those situations depending on how the mechanics and enemy behaviors allow you to fight them.
- Determine how the encounters work. Figure out how many waves there are in each encounter and what enemies they are composed of.
- Ʃn=0 = (Etn)(ESn) Multiply each enemy's threat level by the situation multiplier and add them all up for each wave.
- Plot them in a graph according to the time when they appeared or the distance from the starting point where you meet them.
Examples
Just to show an example of how they look, I followed this method to plot three different 2D sidescrolling shooters using time-based difficulty graphs. The games chosen come from different consoles and different eras just to show that this method is universal (and because they're the ones I had easy access to).
The example games are Metal Slug (published by SNK in 1996 for arcades), Shank (developed in 2010 by Klei Entertainment; this test is based on the PC version) and Hard Corps: Uprising (created by Arc System Works in 2011 for Xbox Live Arcade and PSN).
Now, they might seem quite similar on the surface, but they have several nuances that make them different. This is important to mention, because the difficulty graphs do not actually show which game is harder. Remember that the difficulty is measured based on the game itself; a 1 in Shank is not the same as a 1 in Metal Slug.
What the graphs do show us is how the difficulty changes throughout the game, and this in turn gives us clues on the pacing and tension building of the game. Lots of spikes and you can bet it's a fast-paced, tense game; lots of plateaus and it's likely it is calmer.
Note: A great method for directly measuring pacing is Ben Cousins' method of counting player actions. He describes it in his article Elementary Game Design, which you can find at his personal website, http://www.bencousins.com.
These graphs show the first level of each game from start to right before the boss. I'm leaving out boss encounters because they generally change the rules, requiring specific mechanics for victory. Comparing them directly with the rest of the level can cause gargantuan spikes in the chart that are not really representative of how hard the game is overall.
First up, Metal Slug, the shortest of the bunch (clocking at around 1:20). We can see that it presents enemy encounters every two to three seconds. Besides your standard pistol, the game starts you with some grenades, which are a hard-hitting, though limited, weapon. Unlike the other two, it features one-hit-kills (another way to say all enemies do the same amount of damage) and hefty temporary power-ups, including the titular Metal Slug (a tank, basically). As an arcade game, death isn't a big deal, as each continue will respawn you at the point of death. This is, of course, until you run out of quarters.
We can see that the basic trend is quite close to the horizontal axis, with a smooth rise throughout the level. There are two large spikes which represent helicopters. Under standard conditions they are quite tough (taking around 40 shots from your basic pistol to take down). The camera freezes and stops your movement until you kill them, making sure you can't just skip ahead, explaining the plateaus.
To help you out, the game provides you with power-ups (red vertical lines) right before facing them. As all power-ups in Metal Slug are temporary, the game makes sure you have at least one by dropping a bunch of them really close to one another.
There is another rather large spike near the end, once you start facing other tanks. Provided that you still have your Slug, they should be no problem; however, if you lost it to the helicopter, you could be in a tough spot. The game balances this by giving you health for your tank (the green vertical lines) right after the second chopper and just before the tank section, again trying to make sure you don't miss out.
Next we have Shank, whose first level is around five and a half minutes long. Contrary to Metal Slug, you have a health bar in the game, so enemy attacks aren't so devastating. Also the game starts you out with four weapons (pistols, knives, a chainsaw, and limited grenades) allowing you to take on several enemies at once. On the flipside, there are no power-ups except health and more grenades, so what you start with is what you get.
At first glance, we can see that the game is a slower-paced than Metal Slug, due in large part to having clearly-defined encounters in which the player can't move ahead. We can also see that in most encounters, enemies appear drip by drip, leading to the stair-like form of the curve. The obvious point of this is easing the player into combat, instead of presenting the challenge all at once.
Between large encounters (which can be distinguished by the high plateaus), we find that the game always presents a couple of enemies, so that the challenge never gets too low.
Just like in the previous example we have a spike near the end -- however, this is an absolute spike, presenting the hardest part of the level. After this we see a steep decline until we get to zero, the complete absence of enemies and obstacles, in preparation for the boss battle.
Interestingly, we see that health packs are commonly found in the middle of the encounter (usually because they are enemy drops) and tend to be found more frequently at the later stages of the level. On the other hand, only once can we restock grenades; this is most likely due to the game trying to get the player to learn to use his three main weapons.
Lastly we have Hard Corps: Uprising. In this game, the player has a segmented health bar, with the base enemies taking a full segment with each hit. Though the player only starts with a weak machine gun, she is able to pick up several power-ups which are lost when hit. The first level (minus the boss) clocks in at around 6:20 and is easily the longest of the bunch.
Despite having an Arcade Mode (no character building), the game's star attraction is the Rising Mode, which allows the player to gain experience and permanently upgrade her character even if she dies. In other words, it allows for grind.
First off, you'll notice the off-the-chart spike; I intentionally left it there. This is the miniboss (the typical Contra wall). Clearly its power is off the roof -- it takes many hits to bring down and has powerful attacks. However, once you battle it, you'll notice the terrain gives you a great advantage against it, so in the end it's not really that tough. This is why it's recommended to treat your boss fights as special cases. They work differently, often with different rules and game mechanics -- hence, they don't really relate with the whole level.
Putting the miniboss aside, we can see that the game has a very spiky difficulty curve, with short plateaus and lots of ups and downs. This is decidedly a fast-paced game. Despite its ups and downs, the mean does tend to go up throughout the level, with longer confrontations and more enemies being faced at a time.
While encounters near the beginning of the level are at around seven, near the end they reach 30. This is a massive slope in difficulty, perfect for a grind-friendly game. Near the end we once again find a major confrontation followed by a brief respite before fighting the boss. Notice that power-ups are evenly distributed throughout the level, as they form an integral part of the game mechanics. On the other hand, health is much rarer, though it is also found at equal intervals.
Conclusion
We can compare all games' graphs by simply normalizing the time (dividing it by their total length) and plotting them together. Once more, this is not a measure of how difficult a game is, but how that difficulty changes. Here we can see that in all three games, the difficulty curve's mean is below 10, which is quite usual for first levels. Hard Corps is the one with the highest change in difficulty, while Shank is a lot more constant. Metal Slug is also quite constant with few (though large) spikes.
If we start thinking about the overall design of each game, we see that these differences make a lot of sense. The grind and permanent power-ups of Hard Corps allow it to have a steep difficulty curve throughout the level, and actually encourages the player to start over several times to pass it. Meanwhile, arcade Metal Slug, which is trying to suck you out of quarters, depends on minibosses to provide challenge, allowing you to beat them in multiple tries (as long as you pay). Shank, on the other hand, seeks accessibility, having a smooth curve, which allows new players to ease into the game.
Analysis by difficulty graphs tells us a lot about a game -- not only about the way it's structured, and the way it looks for engagement, but also about the design philosophy behind each game. It's also useful while designing your own games as an analytical way to find spikes and valleys that shouldn't be there.
Of course, this is not the only method of measuring difficulty; however, this has been very useful as it is independent of individual player skill. Once the results are in, everyone in a team can easily see where the trouble spots are, and it makes tackling them together a lot easier. I really recommend you give it a go. You'll be surprised how much this makes difficulty easier.
Further Reading:
Linear algebra for Game Developers
How to create hyper-casual game ?