Greetings, my minions... I mean, class! When last we met, we glossed the basic idea that characters can and should be evaluated on their own merits, divorced from such harder to quantify things as ease of use or player skill. Today we’ll be engaging with the mechanics of such evaluation.
There can be no doubt that psychology, creativity, good reads, and mental toughness—all subjective qualities—are critical to achieving success in competitive fighting games. The stage on which these particular player qualities are brought to bear is, by contrast, decidedly objective, being defined by hard numbers. That being the case, when it comes to evaluating character match-ups and mixup scenarios, it stands to reason that we can use these numbers to gain valuable insight into which characters, discrete options, and so on, give us the most dramatic advantage. Don’t worry, it’s not as daunting as it seems. I think. Screw it. Go ahead and worry. Maybe pop some Advil before we get started, too, just in case.
Definition Time
Some useful terms:
Mixup Scenario
A situation, post-hit, -block, wakeup, or in the open field, wherein a player is forced to make a guess of some sort.
Example: after Astaroth or Voldo’s ground pick-up throws, the player being picked up must usually guess between defending against a throw or a safe mid.
Zero-Sum Mixup
Borrowing obliquely from game theory’s usage of the term zero-sum, this defines a situation wherein guessing correctly nets a player damage while guessing incorrectly costs him damage. This is in contrast to mixups wherein a player might guess correctly and be rewarded only with escaping damage and perhaps frames.
Example: Any mixup involving forcing an opponent to choose between defending one of two unsafe options.
Mathematical Advantage
This term applies to any match-up or mixup scenario in which, after equalizing for player skill, the underlying raw numbers favor a particular character over time. The highest levels of competitive play are all about maximizing mathematical advantage and repeatedly forcing these situations onto an opponent.
Calculating Mathematical Advantage
First, to be clear, I’m not demanding that anyone break out their TI-86s. Just getting an idea of a range like “Very Good/Good/Bad/Abysmal” can be enough to act as a general guideline. To that end, I’ll only be engaging with the numbers to an extent; once the general tenor of a mixup becomes apparent, I see no reason in pursuing it down to microscopic detail.
A basic scenario would be Astaroth, in a position of advantage, running up to another character and mixing between a throw and a Bullrush (66K). In most cases, the defending player’s options are crouching, which defeats the former, and sidestep, which defeats the latter. (Note that, given these parameters, the defender is forcing Astaroth into a zero-sum mixup. Electing to block a bulrush instead of stepping it makes the scenario far more favorable for Astaroth because it gives him an option wherein the defender guesses correctly but he does not, in fact, take damage.) Astaroth’s general reward structure, assuming he guesses correctly, is as follows:
*Note on how throw damage is calculated here: I added the damage for his A and B command grabs, roughly 65 and 80 damage, then divided by two. I then divide by two again to account for a 50% chance to break each grab.
Now let’s plug in the punishments for Astaroth guessing incorrectly. We’ll use Cervantes for this example:
Let’s observe how the numbers change if Cervantes decides to stand and block bullrush rather than commit to stepping. Astaroth’s numbers remain unchanged; he’s still getting an overall average of about 32 damage every time he initiates this mixup. By blocking bullrush rather than stepping and punishing, however, Cervantes’ numbers become (0+50)/2=25 if we take the lower damage option, (0+70)/2=35 for his more difficult punish. In the first case, Astaroth has a marginal mathematical advantage. In the second, Cervantes’ mathematical advantage is negligible. Doing the math tells us why it is important to minimize your own zero-sum mixups while working, as in the case of stepping instead of blocking in the above example, to maximize the number of zero-sum mixups your opponent utilizes.
Application and Caveats
Before you start frothing at the mouth and exclaiming things like “b-b-but if I was Astaroth I’d throw out 66A and etcetera, etcetera,” remember that we’re talking about guidelines, not absolutes. There are myriad ways in which basic mixup scenarios can be made more complicated. That said, these complications tend to undermine the effectiveness of the original mixup, introducing new risks and rewards into the occasion. Circumstances will invariably shift and evolve, and that is where your own skills as a player have an opportunity to shine.
What’s more, it’s important to remember that evaluating mixups and match-ups in this fashion addresses averages over time. There are no guarantees that these numbers will bear out 100% in any given match, or even any given five or ten matches. When you’re flipping a coin, sometimes it just comes up all tails. Even so, possessing a strong understanding of any situation’s mathematical underpinnings allows a savvy player to subtly shift the match into his favor, and these results will manifest themselves over time.
One important way to utilize this is the concept of “trading down.” Mathematical advantage helps us determine when it is appropriate to generate particular mixup scenarios. While it’s always in a player’s best interest to engage in as many mathematically advantaged mixups as possible, there are times when roughly equal scenarios become desirable. If you find yourself with a life lead, for example, it’s perfectly reasonable to open up your game and push mixups that favor neither you nor your opponent because, over time, the averages dictate that you’ll lose roughly the same amount of life. When you’re already ahead, equal losses just magnify your advantage while potentially further limiting your opponent’s options if his life drops low enough.
Homework:
Think about match-ups you play frequently, or those that give you particular trouble, and run the numbers on some of the most common scenarios. See how the math favors or disfavors you. If the math’s on your side, it means your opponent is reading you like a book—get better. If the math’s against you, look for alternatives which might allow you to shift the numbers in your favor, then go play somebody and test it. And, of course, report back here.
Also, next week we will be deviating from the norm a little bit. Be prepared for the worst.
There can be no doubt that psychology, creativity, good reads, and mental toughness—all subjective qualities—are critical to achieving success in competitive fighting games. The stage on which these particular player qualities are brought to bear is, by contrast, decidedly objective, being defined by hard numbers. That being the case, when it comes to evaluating character match-ups and mixup scenarios, it stands to reason that we can use these numbers to gain valuable insight into which characters, discrete options, and so on, give us the most dramatic advantage. Don’t worry, it’s not as daunting as it seems. I think. Screw it. Go ahead and worry. Maybe pop some Advil before we get started, too, just in case.
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Definition Time
Some useful terms:
Mixup Scenario
A situation, post-hit, -block, wakeup, or in the open field, wherein a player is forced to make a guess of some sort.
Example: after Astaroth or Voldo’s ground pick-up throws, the player being picked up must usually guess between defending against a throw or a safe mid.
Zero-Sum Mixup
Borrowing obliquely from game theory’s usage of the term zero-sum, this defines a situation wherein guessing correctly nets a player damage while guessing incorrectly costs him damage. This is in contrast to mixups wherein a player might guess correctly and be rewarded only with escaping damage and perhaps frames.
Example: Any mixup involving forcing an opponent to choose between defending one of two unsafe options.
Mathematical Advantage
This term applies to any match-up or mixup scenario in which, after equalizing for player skill, the underlying raw numbers favor a particular character over time. The highest levels of competitive play are all about maximizing mathematical advantage and repeatedly forcing these situations onto an opponent.
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Calculating Mathematical Advantage
First, to be clear, I’m not demanding that anyone break out their TI-86s. Just getting an idea of a range like “Very Good/Good/Bad/Abysmal” can be enough to act as a general guideline. To that end, I’ll only be engaging with the numbers to an extent; once the general tenor of a mixup becomes apparent, I see no reason in pursuing it down to microscopic detail.
A basic scenario would be Astaroth, in a position of advantage, running up to another character and mixing between a throw and a Bullrush (66K). In most cases, the defending player’s options are crouching, which defeats the former, and sidestep, which defeats the latter. (Note that, given these parameters, the defender is forcing Astaroth into a zero-sum mixup. Electing to block a bulrush instead of stepping it makes the scenario far more favorable for Astaroth because it gives him an option wherein the defender guesses correctly but he does not, in fact, take damage.) Astaroth’s general reward structure, assuming he guesses correctly, is as follows:
- Bullrush hits, opponent takes 28 damage, and is knocked down.
- Throw connects, opponent takes an average of around 36 damage*, and is knocked down.
*Note on how throw damage is calculated here: I added the damage for his A and B command grabs, roughly 65 and 80 damage, then divided by two. I then divide by two again to account for a 50% chance to break each grab.
Now let’s plug in the punishments for Astaroth guessing incorrectly. We’ll use Cervantes for this example:
- Bullrush is stepped, Cervantes punishes with 3B, iGDR, 28B for 65 damage, Astaroth grounded.
- Throw is ducked, Cervantes punishes with FC A+B spam for ~70, opponent grounded, or WR A, aK for roughly 50 damage and significant advantage, Astaroth left standing.
Let’s observe how the numbers change if Cervantes decides to stand and block bullrush rather than commit to stepping. Astaroth’s numbers remain unchanged; he’s still getting an overall average of about 32 damage every time he initiates this mixup. By blocking bullrush rather than stepping and punishing, however, Cervantes’ numbers become (0+50)/2=25 if we take the lower damage option, (0+70)/2=35 for his more difficult punish. In the first case, Astaroth has a marginal mathematical advantage. In the second, Cervantes’ mathematical advantage is negligible. Doing the math tells us why it is important to minimize your own zero-sum mixups while working, as in the case of stepping instead of blocking in the above example, to maximize the number of zero-sum mixups your opponent utilizes.
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Application and Caveats
Before you start frothing at the mouth and exclaiming things like “b-b-but if I was Astaroth I’d throw out 66A and etcetera, etcetera,” remember that we’re talking about guidelines, not absolutes. There are myriad ways in which basic mixup scenarios can be made more complicated. That said, these complications tend to undermine the effectiveness of the original mixup, introducing new risks and rewards into the occasion. Circumstances will invariably shift and evolve, and that is where your own skills as a player have an opportunity to shine.
What’s more, it’s important to remember that evaluating mixups and match-ups in this fashion addresses averages over time. There are no guarantees that these numbers will bear out 100% in any given match, or even any given five or ten matches. When you’re flipping a coin, sometimes it just comes up all tails. Even so, possessing a strong understanding of any situation’s mathematical underpinnings allows a savvy player to subtly shift the match into his favor, and these results will manifest themselves over time.
One important way to utilize this is the concept of “trading down.” Mathematical advantage helps us determine when it is appropriate to generate particular mixup scenarios. While it’s always in a player’s best interest to engage in as many mathematically advantaged mixups as possible, there are times when roughly equal scenarios become desirable. If you find yourself with a life lead, for example, it’s perfectly reasonable to open up your game and push mixups that favor neither you nor your opponent because, over time, the averages dictate that you’ll lose roughly the same amount of life. When you’re already ahead, equal losses just magnify your advantage while potentially further limiting your opponent’s options if his life drops low enough.
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Homework:
Think about match-ups you play frequently, or those that give you particular trouble, and run the numbers on some of the most common scenarios. See how the math favors or disfavors you. If the math’s on your side, it means your opponent is reading you like a book—get better. If the math’s against you, look for alternatives which might allow you to shift the numbers in your favor, then go play somebody and test it. And, of course, report back here.
Also, next week we will be deviating from the norm a little bit. Be prepared for the worst.
