Let's Bring Back Big Chances

Entropy and a Unified Model of Goal Probability

The Big Chance is an intriguing artifact of soccer analytics history. In the early times, Opta defined Big Chances as shots where a player should reasonably be expected to score: a one-on-one with the goalkeeper, an open-net tap-in, or perhaps a free header in the six-yard-box with a prone goalkeeper. These tags were subjective, applied by analysts watching the game, and while they were inconsistent, they were undeniably powerful.

Big Chances worked because they acted as proxies for many things that weren't systematically collected at the time: the pressure on the shooter, the positioning of defenders (particularly the goalkeeper), and various additional attributes of the buildup play. These were moments when the likelihood of scoring wasn’t just high – it felt inevitable. But as the event data specs improved and xG models started incorporating these elements directly, the need for the Big Chance qualifier faded. They lacked consistency, tied chance evaluation too closely to outcomes, and led to some very weird bi-modal distributions of chance quality.

But what if the original concept of Big Chances deserves a second act? Not as a subjective evaluation of shots, but as a tool for identifying repeatably dangerous moments within possessions where scoring becomes genuinely probable, regardless of whether a shot is even taken.

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Inflection Detection

Soccer is a game of uncertainty, and one way to understand that uncertainty is through the lens of entropy – which we will interpret as the variability in possible outcomes as a sequence unfolds. At the start of a possession, entropy might seem intuitively high because the ball could end up anywhere, but the likelihood of a goal is overwhelmingly low. Almost every possession ends without a goal, so the outcome entropy at the beginning of a possession is usually correspondingly low.

However, as a possession progresses and nears dangerous areas, entropy rises alongside the probability of a goal. Entropy peaks at the moment when the uncertainty about whether the possession will result in a goal is at its highest. This peak often corresponds to moments when a team is poised to make a decisive action, such as taking a shot or attempting a key pass.

Entropy – measured in bits between zero and one for binary outcomes – correlates closely with the probability of a goal for values between 0.0 and 0.5. As xG values continue to rise toward 1.0, entropy logarithmically dwindles back down toward zero. It makes intuitive sense that entropy would reach an inflection point around 0.5 xG since that value represents the highest possible degree of uncertainty for the outcome of a possession.

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Breakaway Entropy

Consider a breakaway situation. An attacker races toward goal and the goalkeeper rushes out to close the angle. At this point, entropy is high: the possession might end in a 0.99 xG tap-in if the attacker rounds the keeper, or no shot at all if the goalkeeper manages to smother the ball. The entropy only collapses as the attacking player and the opposing goalkeeper collide and the play resolves with either a goal scored or a heroic save.

(Of course, there could also be a penalty or a rebound. For that – let’s get a refresher on conditional probability)

Plotted over time, entropy will occasionally demonstrate asymptotic-like behaviour. In the split seconds before-and-after a ball is struck, it will jump instantly between values derived from the pre-shot and post-shot xG values.

In most cases, this entropy spike coincides with the moment the ball is struck for a shot. But there are instances, like the breakaway, where the moment of highest uncertainty can occur a few moments earlier. This brings the problem with cumulative xG into focus and earns Expected Goals a reputation of having an outcome bias.

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Reframing Big Chances

Let’s start by detaching Big Chances from shots entirely. Instead of focusing on shots, we could reframe Big Chances as possessions where the goal probability crosses an arbitrary threshold along a relatively smooth entropy path. The arbitrary threshold to be determined later, of course, by someone else. Minimal math in this blog post.

This definition will filter out chaotic moments where a chance falls into a striker’s lap and emphasize moments of deliberate, repeatable opportunities created through controlled progression and decision-making.

Under this reframed concept, provided that it didn’t emerge from a sudden defensive blunder, a breakaway would qualify as a Big Chance even if a shot was never taken. This approach avoids rewarding unearned xG tied to chaotic or situational factors. Instead, it focuses on whether the team successfully created a repeatable, high-value opportunity.

A penalty, however, would not qualify as a Big Chance due to the dramatic entropy whiplash – a residual of the xG of the possession suddenly exploding. I’d argue this is a formulation of the intuition behind why we’ve generally excluded penalties from cumulative xG totals.

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Unified Model

This also plays nicely with an important soccer analytics discovery from the early times – shooting ability seems to be deeply unstable. An entropy-based approach may imply a unified theory since post-shot xG values can reach far above the 0.5 entropy/xG inflection point, suggesting there shouldn’t be much signal to be detected in the xG stratosphere.

The motivation of this approach is the hypothesis that teams and players don’t have much control over these extraordinary xG values that are occasionally attributed to individual moments. And if they don’t have much control over these moments, they probably don’t reflect a pattern of behaviour that would lead to similar moments occurring in the future.

I suspect that counting Big Chances in this manner might serve as a better predictor of future goals than the current established practice of using xG to predict future goals, as long as you carefully select the right xG threshold. This can probably be tested. On here, I’m just a theorist – but I’d gladly grant a guest Central Winger blog post to someone who constructs a compelling experiment.