The Strategic Landscape of Formula 1 / F1 策略全景

The Strategic Landscape of Formula 1 / F1 策略全景

1.1 What "Good" Strategy Actually Means — 何为"好"的策略

A casual observer would say a good strategy is the one that wins the race. A team principal might say it is the strategy that maximizes championship points. An engineer in the garage, headset pressed to one ear and a printout in the other hand, might say it is the strategy that gives the driver the best chance of finishing ahead of the car in front at the moment the chequered flag falls. All three are correct, and all three are wrong. Strategy in Formula 1 is not a single objective — it is a layered set of objectives that shift in weight as the race unfolds, all of them shaped by an unrelenting set of constraints and an uncomfortably stochastic environment. The purpose of this opening chapter is to make those layers explicit, to name the constraints in plain language, and to explain why F1 strategy is a fundamentally different problem from strategy in NASCAR, the World Endurance Championship, or even IndyCar. By the end of this chapter you should be able to write down the formal objective function (形式化的目标函数) of an F1 race, identify every regulatory constraint that bears on a strategy decision, and explain in one paragraph why the same set of strategic tools, transplanted to another series, would fail.

The first step is to define what is being optimized. Race strategy is, formally, a constrained stochastic optimization over a discrete time horizon. Translating that into F1 language:

$$\min_{\pi} \mathbb{E}\!\left[\,P_{\text{final}} \mid \pi\,\right]$$

where $P_{\text{final}}$ is the finishing position of the car, $\pi$ is the strategy (the sequence of decisions the team makes from formation lap to chequered flag), and $\mathbb{E}[\cdot]$ denotes expectation over the stochastic elements of the race. The objective is to minimize expected finishing position — not to win, not to score a fixed number of points, not to lead a specific number of laps. The expected-value framing matters: a strategy that wins in one scenario and retires in another is, on average, worse than a strategy that finishes P3 in both. In a 24-race season, robustness is worth more than upside.

The decision variables (决策变量) inside $\pi$ are:

• The compound chosen at the start of each stint (stint = 赛段, a continuous run on a single set of tires)
• The lap on which each pit stop is made, including the option of not stopping at all (a so-called zero-stop strategy, which is occasionally viable at low-degradation circuits)
• The driving mode: push, conserve, or some intermediate lift-and-coast profile
• The ERS (Energy Recovery System / 能量回收系统) deployment schedule — when to use the electric boost and when to harvest
• The reaction to incidents: whether to pit under a safety car, VSC, or red flag, and how to manage a sudden weather change

The objective is constrained in four families, each of which we will treat in detail later in this chapter:

1. Tire constraints / 轮胎约束. Every car must use at least two different dry compounds during a dry race, drawn from the three compounds Pirelli (倍耐力) allocates for the event. The mandate is enforced by a time penalty of 30 seconds for non-compliance. 2. Fuel constraints / 燃油约束. Cars may not refuel during the race. They must start with no more than 110 kg of fuel and must finish with enough fuel remaining to supply a 1.0 liter sample for FIA inspection. 3. Time constraints / 时间约束. Race distance is approximately 305 km or a maximum of two hours, whichever comes first. A stationary pit stop requires a minimum of 2.0 seconds. DRS (Drag Reduction System / 减阻系统) is available only in designated zones, only when within one second of the car ahead, and only after the first two racing laps. 4. Regulatory constraints / 规则约束. Parc fermé (维修区封闭) regulations lock the car configuration from the start of qualifying. Cars may not change setup after that point without incurring grid penalties.

The time horizon is discrete, with the lap as the natural unit. Within a lap, the team observes sub-second telemetry (sub-sector times, GPS position, tire surface temperature) and the strategy team typically meets every 5-10 seconds during green-flag running to update the picture. This makes the problem an instance of a Markov Decision Process (MDP / 马尔可夫决策过程), defined by the tuple $(S, A, P, R, \gamma)$:

• $S$ is the state space — the set of all possible race situations. For a single car, this includes tire age and compound, fuel mass on board, position on track, gap to the car ahead and behind, weather state, pit cycle phase, and many derived quantities. The dimensionality is in the dozens; the cardinality is in the millions.
• $A$ is the action space — at any moment, the team can pit, stay out, push, conserve, deploy ERS aggressively, or hold it. The action set is small in cardinality but its consequences are continuous.
• $P(s' \mid s, a)$ is the transition probability — the likelihood of moving from state $s$ to state $s'$ given action $a$. This is the most poorly known element of the tuple, and we will revisit it repeatedly.
• $R(s, a)$ is the reward — a function of the immediate consequences of the action, typically a combination of track position gained, time gained, and tire preserved.
• $\gamma$ is a discount factor — a number slightly less than 1 that says "current position is worth more than distant position."

The optimal policy $\pi^*(a \mid s)$ maximizes the expected sum of discounted rewards over the race horizon. The Bellman equation (贝尔曼方程) that defines this optimality is:

$$V^*(s) = \max_{a \in A} \left[\, R(s, a) + \gamma \sum_{s' \in S} P(s' \mid s, a)\, V^*(s') \,\right]$$

In principle, dynamic programming solves this exactly. In practice, the state space is too large and the transition probabilities too uncertain. Real teams do not solve the Bellman equation. They approximate it with simulation, heuristics, and the accumulated intuition of the strategy group. The remainder of this book is, in essence, a description of how the approximation is built and where it succeeds and fails.

The stochasticity in F1 strategy is unusually rich. There are at least five distinct sources of randomness, each of which can be partially modeled but not fully predicted:

1. Weather / 天气. Rain arrival time, intensity, and duration are forecastable in the hours before the race but become much less predictable once the race is underway. A 10% chance of rain in the first stint can shift the optimal pit window by 3-5 laps. The 2024 São Paulo Grand Prix, where a 30-minute rain shower mid-race scrambled an otherwise settled strategy, is a recent illustration of how a small weather change can re-write the cost-benefit calculation of every team on the grid. 2. Incidents / 事故. Safety cars, virtual safety cars, and red flags are triggered by mechanical failures, driver errors, and debris. The base rate is roughly 0.5-1.5 incidents per race, with a heavy tail — some races have none, others have five or more. The 2020 Tuscan Grand Prix, with two red flags in a single race, is a useful upper-bound reference. 3. Mechanical reliability / 机械可靠性. A power unit, gearbox, or hydraulic failure can end a race at any lap. Modern F1 is extremely reliable — the typical DNF (Did Not Finish) rate is 3-5% of the field — but the consequence of failure is total strategic loss for that car and a permanent reshuffle of the rest of the field. 4. Rival decisions / 对手决策. Each team is simultaneously solving its own version of the MDP. The strategies are coupled, which produces classic game-theoretic complications: undercut attempts, overcut attempts, two-versus-one traps, and the implicit "no, you pit first" poker game that often unfolds in the midfield. 5. Driver execution / 车手执行. Even the perfect strategy can be ruined by a driver error, a bad pit entry, a missed apex, or a lock-up into Turn 1. Driver fatigue, especially in hot and humid conditions, can quietly c