leverage (and clutch) in street fighter

Sonic Hurricane recently analyzed two very important parts of Street Fighter and fighting games in general: the importance of momentum and the ability to play without taking damage. I want to take a moment to analyze both of these, relate them somewhat to each other while I introduce a concept I've been thinking about for a while that most players already innately understood but have been unable to quantify or explain.

That concept is leverage.

This may seem odd, but let's first see how leverage is defined in baseball. More importantly, we're going to analyze two statistical concepts in baseball, Win Expectancy and Leverage Index, because they are the basis of what we'll be working with when trying to define our own statistics for Street Fighter.

Baseball Reference defines Win Expectancy (and Win Probability) as the following:

Given a particular inning, score, and base-out situation (for example, bottom of 3rd, home team down two with runners on 1st and 3rd and one out), we can estimate the probability of an average home team (and therefore the road team) winning the game (40% in the case above). This is the win expectancy. We have this for every single possible situation in a game: for all 24 base-out situations, for the top and bottom of each inning (extras are just repeats of the ninth inning), and all range of score differentials (-11 to 11, in this case any lead of more than 11 is treated as 11).

Given the win expectancy at the start of the play, we can then look at the change in the win expectancy at the end of the play (for example, assume a bases clearing triple in the above, bottom of 3rd, score tied, runner on third and one out, WE = 61%) and determine the difference. This difference is the win probability added to the batter and subtracted from the pitcher. In this case 21%. We sum these values across the entire game and season and produce the numbers you see on the site.

Note that in this case all of the credit goes to the batter and all of the blame goes to the pitcher. These stats do not assign credit or blame to the fielders or the baserunners (except as listed below), even though they surely deserve some of the credit or blame.

Then, they define Leverage Index thus:

Within a season, there are plays that are more pivotal than others. We attempt to quantify these plays with a stat called leverage index (LI). LI looks at the possible changes in win probability in a give situation and situations where dramatic swings in win probability are possible (runner on second late in a tie game) have higher LI's than situations where there can be no large change in win probability (late innings of a 12-run blowout).

The stat is normalized so that on average the leverage is 1.00. In tense situations, the leverage is higher than 1.00 (up to about 10) and in low-tension situations the leverage is between 0 and 1.0.

How about the word leverage, defined by Wikipedia as a matter of statistics?

In statistics, leverage is a term used in connection with regression analysis and, in particular, in analyses aimed at identifying those observations which have a large effect on the outcome of fitting regression models.

A lot of this may be a little difficult to digest if you're not into baseball or statistics, so I'll try to translate it for you into layman's terms and translate it into Street Fighter.

For what we want to describe, Win Expectancy is the probability of a single player winning at any moment during a match. There are no pauses in fighting games as there are in baseball. Determining the Win Expectancy of any player at any given moment would only really be able to be calculated live by a computer, or after review of a game. Calculating it live is rather difficult, although you can sort of make a decent calculation of a player's Win Expectancy simply by eye, but it would tend to be somewhat off.

Leverage, however, is a lot easier to determine. Leverage is something that any person can see in a game. It's easy to determine when a situation is much more important to the outcome of a fight than others. Here's a thought exercise: let's say that we have a Sagat v Ryu matchup. Sagat is leading Ryu on life, Sagat has about 80% of his life left while Ryu only has 40% of his own. Ryu has been focusing through certain attacks, so despite not being quite there yet in terms of life, he already has a full revenge meter. He's stuck in the corner against Sagat's fireball pressure and looking for a way to advance. Let's say Sagat throws a slow high tiger shot and FADCs forward and moves in to put pressure on Ryu. How much leverage does Sagat have in this situation? If we define leverage as an action that can have a dramatic impact in the result of a fight, Sagat's offensive move to shut Ryu into the corner is a fairly high leverage action.

Something that might confuse things here, however, is that fighting games track three separate variables for winning: two life bars and a timer. It's not like baseball, where the person with the highest score at the end of 9 innings is the winner. Running out of life in SF makes you the loser, regardless of how much time there is left and how much life your opponent has left. So how do we determine the actual leverage of any given situation in fighting games? Think about it: in baseball, the pitcher will come in to any given situation, and each situation has a different leverage index -- some situations are more "important" than others. How do we determine a situation that's more important in a fighting game? The only variable that we have that is easily quantifiable in this situation is life remaining.

Let's talk about momentum for a moment. Momentum is very important in fighting games. We'll define "having momentum" as having offensive control over a situation, being in an advantageous position and forcing your opponent to make guesses and decisions in unfavorable conditions. You are essentially taking advantage of their forced defensive reactions -- you are in motion and they are not. There are times of course where having the momentum, you will eventually arrive at an impasse. This impasse usually comes when you've reached the point where the possibility of you forcing a guess has reached a situation equal to or worse than 50/50 in your favor. A situation where your opponent guessing right puts you either in a neutral or disadvantageous position is usually a good time to stop pressing your momentum and letting the situation naturally reset to a neutral position.

Being able to hold and maintain the momentum of a fight allows you to create higher leverage situations. A player who is on defense in a high leverage situation -- in other words, he has a very low amount of life remaining, or is at risk of losing a large amount of it -- is mentally forced to decide whether to make riskier decisions knowing that making a mistake results in losing the most important resource you have (life) and which you have very little of already.

The only problems here, of course, are how we can observe leverage in reverse: if someone has a low amount of life, but they are on offense, are they still not in a good amount of trouble? Having the momentum when you are low on life is desirable, but still extraordinarily dangerous in the events of a bad guess. Your offense cannot be the same as when you are stocked full of life.

Why find all of this out, anyway? The goal is simple: statistically quantify those players that handle themselves better under pressure. Yes, you can visually see that a lot of players can be very clutch in dire situations (a famous example being Daigo against Justin in 3rd Strike, and of course more famous examples being Justin himself in Marvel -- against Yipes and against Xecutioner). More importantly, quantify those players that can do this with consistency -- you can occasionally find some players being rather clutch, but the moments they do it are rare. Is it possible to put a number to how clutch a player is?

Is it possible to find out how much more often a player can be clutch? Is it possible to be able to define which situations are higher leverage than others in a fighting game? Is it even possible to make a blanket assumption of leverage across all characters, or should matchups be involved?

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