Field Note · Forms Methodology

Markov Chains in Football: Stochastic Processes, Technique and the Case for Patient Youth Development

How transition probabilities, chance and maturation explain why Forms Academy builds technique before tactics and small formats before large ones.
September 27, 2026By Ron HogsettRead on Substack ↗

Every possession in football ends. The ball is shot, kicked out of play, or taken by the other team, and everything between the first touch and that ending is a run of moves from one situation to the next. Markov chains in football write that run down precisely. They belong to the wider class of stochastic processes, sequences of events in which each step occurs with a probability instead of with certainty.

This paper uses that mathematics to set out what Forms Academy believes about youth development. A young player’s technique sets the odds of each step in a possession, those odds multiply, and the product becomes visible only over many repetitions.

What Markov chains in football actually model

A Markov chain is a stochastic process in which the probability of the next state depends only on the present one:

In a football model, the transient states are situations in possession, the p_ij form a transition matrix whose rows sum to one, and the absorbing states are the ways a possession ends: a goal or shot, a dead ball, a turnover. Sarah Rudd’s 2011 presentation at the New England Symposium on Statistics in Sports used 39 states with two absorbing ones.

Karun Singh’s Expected Threat (xT), published in 2019, divides the pitch into 192 zones and defines each zone’s value through the zones that follow it:

Here, s_z is the probability of shooting, g_z the probability of scoring given a shot, m_z the probability of moving the ball, and T the matrix of destinations. This is a Bellman equation (Bellman, 1957) in its policy evaluation form, with the league’s average behaviour as the policy. Singh solved it by value iteration. Kemeny and Snell’s (1960) treatment of absorbing chains gives the same object in closed form. With Q the matrix of transitions between transient states, the fundamental matrix

has entries n_ij equal to the expected number of visits to state j by a possession starting in state i, and its row sums give the expected number of steps before absorption, which is possession length.

Stochastic processes in football: chance, rare goals and the patience compounding requires

Goals are rare events. Maher (1982) showed that English league scores are described reasonably well by treating each team’s goals as Poisson, with its own attacking and defensive strength:

where lambda is the expected number of goals. Dixon and Coles (1997) refined it with a correction for low scores. A score, in these models, is one draw from a distribution with a knowable average and a wide spread.

Researchers have also tried to measure how often chance is involved in goals. Lames (2018) examined 1,931 goals from the 2011/12 Bundesliga and Premier League seasons and found that 47.0% involved at least one chance factor, such as a deflection, rebound or defensive error. Wunderlich, Seck and Memmert (2021) checked 7,263 Premier League goals from 2012/13 to 2018/19 and found some random influence in about 46%, more often for weaker teams. These figures count chance involvement in goals, a narrower quantity than the share of a result owed to luck.

The consequence is that a better underlying process needs many repetitions before it shows up reliably in results. In a constructed illustration, suppose one team averages 1.2 goals per match and another 1.0, a 20% edge. Treating goals as Poisson, the better team wins a single meeting 40.6% of the time, and in simulated head-to-head series it finishes ahead on points only 58.1% of the time after ten matches and 74.7% after forty (Figure 1). Monte Carlo simulation, used for those series, returns the whole distribution of outcomes instead of an average. Tournament data show the same pattern: across 262 matches, goals picked the stronger side less than half the time even over three matches, while penalty-area entries reached 59% (The Recurrence Rate, 2026; Figure 2). A season of results is too short to reveal a real but modest improvement in a youth team. That is why patience in development is a mathematical requirement: a process that compounds pays out in the long run, and the short run is where it looks most like losing.

What 18,803 tournament possessions show

FORMAX Research fitted a simple chain to StatsBomb open data from the 2022 World Cup and Euro 2024: 115 matches, 18,803 possessions, 2,525 shots and 56 team-tournaments (The Arrival Rate, 2026). The pitch was split into three rooms, Build, Progress and Create, joined by doorways (Figure 3). The product of the three doorway probabilities, called the chain index, correlated with expected goals per possession at r = 0.705. Entry into the final third was the strongest single doorway, at r = 0.636.Teams in the top quarter of the chain index produced 0.0197 expected goals per possession against 0.0100 in the bottom quarter, and 17.8 shots per 100 possessions against 9.0, both ratios of 1.98. The quality of their shots barely differed (0.111 against 0.107 expected goals per shot). The better chains won on how often they arrived, which is a transition probability.*Figure 3: The possession chain: three rooms, three forward doorways. Each possession moves through Build (x Markov chains in football describe the game as a sequence of states with odds attached, and the wider theory of stochastic processes shows why those odds reach the scoreboard slowly and unevenly. The odds that matter most belong to individual players, multiply across a possession, and can be changed by coaching. Raising them one player at a time, in designed formats that give each child the most varied repetitions, sequenced by capacity as the Forms Methodology prescribes, is the approach whose results arrive late and compound for years.

References

Ron Hogsett is the founder of Forms Academy and architect of the Forms Methodology, a neuroscience-driven framework for youth football development focused on technical mastery, cognitive speed, and motor efficiency.

The Forms Methodology and the FORMAX 5x5 framework are set out in more detail at FormsAcademy.com.

Deepens these Manual chapters
Ch 1 · The Philosophy of Forms: Why Technique Before TacticsCh 13 · The City System: Positional Play and Collective IntelligenceCh 15 · Integrating Technique and Tactical Awareness

Learn the whole methodology

Field Notes are the thinking behind the Forms curriculum. The full interactive program and coach certification live inside the LMS.

Explore the curriculum →
© Forms Academy · Field Notes · Curriculum