Most metrics used to analyse football are accumulated over a whole match – for example, goals, shots and shots on target. Even Expected Goals, the new paradigm for football analytics, which takes multiple information (e.g. distance, angle and type of shot) to assess the goal-scoring likelihood of each chance, simply accumulates these values over the duration of the game.

All of these (particularly Expected Goals), when averaged over a number of matches, can do a good job of assessing a team’s attacking and defensive strength. However, they all miss subtle, but important, information about how a team plays in different game-states – i.e. when they’re winning, drawing or losing. If a team is able to successfully adjust its tactics to take account of their objective in each game-state, then this won’t fully show in these metrics.

An example of this is when a team scores a goal to take the lead – in this game-state they don’t need to score any more, as long as they don’t concede – so they may adjust tactics to prioritise stopping their opponents creating chances. Some teams do this, and if they’re successful it reduces the number of chances for the rest of the match, which means they’re likely to be undervalued by most metrics (including Expected Goals) compared to teams that don’t change their tactics.

So, how can a football match be modeled allowing for how teams react to each game-state? I use a model that splits a particular match into 95 separate minutes (assuming 2 minutes injury-time in the first half and 3 in the second). In each minute the likelihood of either team scoring depends on the game-state at the time as well as the current duration of the match (because more goals tend to be scored later in a match). I than stochastically (randomly) simulate the match 5000 times to get a better understanding of the likelihood of different outcomes for that match.

For example, if we expect a team to play in a way that would produce an average of 1.2 goals per game in the draw game-state – and the match is tied after 10 minutes, a random number determines whether they score in the 11^th minute based on a goal rate of 1.2/95 per minute. If they do score, the model moves to a win game-state in the 12^th minute and their goal scoring rate may also change – to (say) 1.1 goals per minute (with a corresponding change to their opponent’s goal scoring rate).

This is great in theory, but paucity of data about teams’ performance in different game-states makes it difficult to reliably model actual matches (although it doesn’t stop me trying). Even so, this type of model can help assess the theoretical implications of different tactical strategies.

To illustrate this I’ll start with a simple example of two equally matched teams, playing at a neutral venue (to ignore home advantage) – where the goal scoring rate for both teams is 1.3 goals per match. Initially there is no adjustment for game-state. This produces a win probability for both teams of around 37% and 26% for a draw. Reassuringly this is similar to probabilities that are generated by a Poisson distribution (a statistical distribution commonly used a way to model goals scored in a football match).

This outcome is not far off the average actual outcomes for two evenly matched teams – but it underestimates draws, which for actual (English league) matches tend to be around 30% for two equal teams. The reason it underestimates draws (in the same way a Poisson distribution does) is that it doesn’t yet allow for game-state differences.

When two closely matched teams play, a draw isn’t too bad an outcome for either team, so they may play conservatively in the draw game-state. If the model’s game-state is adjusted to 1.4 goals for each team in a win/lose game-state and 1.2 in a draw game-state it generates probabilities closer to those expected from observation – i.e. 35% for win/lose and 30% for the draw. This is probably closer to what happens in an actual match, rather than a constant goal scoring rate throughout the game.

We can also explore what would happen if a team adopted the tactical approach described earlier – i.e. they had the tactical ability and flexibility to successfully defend a lead. So again we have two equally matched teams (team A and team B) except that Team A is able (through tactical adjustments) to reduce the game’s goal scoring rate when in a winning position. So in this example in a draw or losing game-state – both teams’ goal-scoring rate is 1.5. But in a winning game-state Team A is able to sacrifice its own goal scoring rate to ensure that team B’s is also reduced (e.g. a goal-scoring rate of 1.0 for each team). The new probabilities are Team A win 39%, Team B win 35%, Draw 26%.

This demonstrates that, even though Team A and Team B have an equal goal-scoring rate throughout the match, because team A has the tactical flexibility to change both team’s goal-scoring rates when in the lead, Team A has a better chance of winning. The average goals, over the 5000 simulations, are the same (1.27) for both teams in this example.

In practice it won’t be as simple as this because team B is also likely to change its tactical approach when losing – especially in the later stages of the game. But I think it does show that tactical flexibility does matter, is an attribute that improves a team’s quality – but doesn’t get measured by common metrics, including Expected Goals.

I intend to use the model to explore other tactical approaches – for example, the impact of high intensity attacking over short periods at different times in a match. In the meantime various hypotheses I have from this analysis are:

• Metrics simply accumulated over a match undervalue tactical flexibility.
• To properly measure a team’s attacking and defensive strength we need metrics that properly allow for game-state. Expected goals in winning, losing and drawing game-states would be perfect.
• Tactical flexibility is an important (and possibly under-valued) team attribute. It obviously has to be deployed successfully – for example, I suspect some teams try to defend a lead but in reality just reduce their own scoring rate rather than their opponent’s.
• A higher value should be placed on players that can perform in different tactical situations (e.g. attacking and defensive). This may be against popular wisdom – my heart always sinks if I hear the team I support are about to sign a “utility player”.
• The ability to adjust tactics is an essential managerial quality.
• One of the reasons leagues in different countries display different characteristics – e.g. more draws or fewer goals – is because they deploy tactical flexibility in different ways (either because of ability or cultural acceptability).