How to Interpret Force-Velocity Profile: Deficit Diagnosis

Samozino et al. (2012) published a landmark paper demonstrating that the mechanical power output of a jump squat is not maximized by simply having the highest possible force capacity or the highest possible velocity capacity — it is maximized by achieving the optimal ratio between the two. Athletes with identical peak power values can differ by 15–20% in realized jump height simply because one has a balanced force-velocity profile and the other does not. For coaches and sport scientists, this shifts the diagnostic question from "how strong is this athlete?" to "where on the force-velocity continuum does their limiting factor lie?"

This guide explains the physics behind the F-V profile, walks through a practical field assessment protocol, and provides a clear decision tree for prescribing the correct training intervention based on the diagnosed deficit.

The F-V Relationship Explained

The Hill (1938) force-velocity equation describes an inverse hyperbolic relationship between muscle force and shortening velocity: as contraction velocity increases, the force a muscle can produce decreases. This is not a limitation — it is a fundamental mechanical property of actomyosin cross-bridge cycling.

In applied sports science, the F-V relationship is usually operationalized through the straight-line approximation of Samozino et al. (2010): when force output (normalized to body mass, in N/kg) is plotted on the x-axis against mean velocity of movement (in m/s) on the y-axis across multiple loaded conditions, the resulting scatter follows a near-linear descending trend. The two key parameters extracted from this line are:

• F0 (theoretical maximum force): The x-intercept — the force the athlete would hypothetically produce at zero velocity (approximated by an isometric maximum). Expressed in N/kg.
• V0 (theoretical maximum velocity): The y-intercept — the velocity the athlete would achieve with zero external load. Expressed in m/s.
• SFV (slope of the F-V relationship): = –V0 ÷ F0. A steep (more negative) slope indicates a force-dominant profile; a shallow slope indicates a velocity-dominant profile.
• Pmax (maximum mechanical power): = F0 × V0 ÷ 4. This is the area under the F-V line, and represents the athlete's peak power-producing potential.

The insight from Samozino et al. (2012) is that for any given Pmax, there exists an optimal slope (SFV_opt) that maximizes jump height. An athlete's actual slope relative to this optimum is the diagnostic target.

How to Build Your F-V Profile

A field-based F-V profile requires jump testing at three to five load conditions. The following protocol is adapted from Samozino et al. (2016) and validated for use with wearable IMU sensors:

Equipment Needed

• Barbell or hex bar (or a loaded vest for unloaded-biased athletes)
• IMU sensor or jump mat capable of measuring peak vertical velocity or jump height
• Stopwatch for rest intervals

Protocol

1. Warm-up: 10 min dynamic lower-body warm-up + 3 submaximal CMJs to prime the stretch-shortening cycle.
2. Condition 1 — Unloaded CMJ: Three maximal CMJs from a slightly wider than shoulder-width stance. Record mean peak velocity (m/s) or mean jump height (cm) across the three trials. Rest 2 min between jumps, 5 min before next condition.
3. Condition 2 — Light loaded jump squat (20–30% 1RM): Three maximal jump squats with the bar on the back (or hex bar). Record mean velocity. Rest as above.
4. Condition 3 — Moderate loaded (50–60% 1RM): Three trials. Record mean velocity.
5. Condition 4 — Heavy loaded (70–80% 1RM, optional): Three trials for athletes with good barbell proficiency. This condition better defines the force end of the spectrum. Novice athletes may skip this to avoid fatigue contamination.

The load sequence should always progress from lightest to heaviest to prevent fatigue-induced underperformance at the lighter loads. Discard any trial where foot contact is lost or where the athlete visibly decelerates before bar liftoff.

Reading the Profile: Slope and Optimal F-V

Once you have three to four (force, velocity) data pairs, plot them in a spreadsheet and fit a linear trendline. The slope of that line is your SFV. The intercepts give you estimates of F0 (where the line crosses the x-axis) and V0 (where the line crosses the y-axis).

The optimal slope (SFV_opt) can be estimated using Samozino's equation: SFV_opt = –4 × g × h_opt ÷ V0², where g = 9.81 m/s² and h_opt is the athlete's targeted optimal jump height (typically set to their actual best CMJ height as a baseline). In practice, many practitioners use published normative slopes as a benchmark:

• SFV_opt for team-sport athletes: approximately –1.0 to –1.2 (N/kg)/(m/s)
• SFV_opt for sprint/jump-dominant athletes: approximately –0.8 to –1.0 (N/kg)/(m/s)
• SFV_opt for strength-sport athletes: approximately –1.3 to –1.6 (N/kg)/(m/s)

If your measured SFV is more negative than SFV_opt, your profile is too force-dominant relative to your power-output potential. If it is less negative (shallower slope), you are velocity-dominant.

Diagnosing Force vs. Velocity Deficit

The F-V imbalance ratio (FVimb) proposed by Samozino et al. (2012) provides a single number: FVimb = SFV ÷ SFV_opt. Interpretation:

• FVimb = 1.0: Perfectly balanced profile — training emphasis should maintain both qualities simultaneously.
• FVimb > 1.0 (e.g., 1.3): Force-dominant profile — the athlete has relatively too much force and not enough velocity capacity. Train for speed-strength.
• FVimb < 1.0 (e.g., 0.7): Velocity-dominant profile — the athlete has relatively too much velocity capacity and insufficient force foundation. Train for strength-speed and heavy loaded power.

Population data from Jiménez-Reyes et al. (2017) showed that 79% of a mixed recreational-to-elite athlete cohort had an FVimb deviating >15% from optimal, with roughly even distribution between force-dominant and velocity-dominant profiles depending on sport background. Strength-sport athletes (powerlifters, weightlifters) almost always present as force-dominant; sprint and jump athletes more often present as velocity-dominant due to years of light-load explosive training without adequate heavy loading.

Training Interventions by Deficit Type

For Force-Dominant Athletes (FVimb > 1.15)

The goal is to shift the F-V line's velocity intercept (V0) upward while maintaining F0. This requires high-velocity, low-to-moderate load training with explicit intent to move at maximum speed:

• Jump squats at 15–35% 1RM: Target mean concentric velocity >1.2 m/s. Any rep below 1.0 m/s terminates the set — velocity quality is the stimulus, not volume completion.
• Unloaded CMJ supersets with sprint starts: 3 × (5 CMJs + 2 × 20 m sprint). The sprint provides maximum velocity expression after jump-primed motor patterns.
• Medicine ball throws (overhead, rotational, chest): Provide ballistic upper-body velocity stimulus to complement lower-body work.
• VBT bench press at 30–45% 1RM: Mean velocity target >0.90 m/s per rep. González-Badillo et al. (2014) found that velocity loss of >20% within a set at these loads produces disproportionate fatigue without additional power adaptation benefit — keep sets to 4–5 reps maximum.

For Velocity-Dominant Athletes (FVimb < 0.85)

The goal is to shift F0 rightward by building force capacity at moderate-to-high loads while maintaining explosive intent:

• Back squat or hex-bar deadlift at 75–87% 1RM: 4 × 3–5 reps with maximal concentric intent. Even at these loads, the athlete should attempt to move the bar as fast as possible — this maintains RFD stimulus alongside force development.
• Loaded jump squat at 50–65% 1RM: 3 × 4 reps. This load zone specifically trains the moderate-load region where velocity-dominant athletes are weakest relative to their V0.
• Isometric mid-thigh pull (IMTP): 3 × 3 s maximal isometric contraction. IMTP peak force correlates strongly with F0, and isometric training at long muscle lengths provides a unique stimulus that ballistic training cannot replicate.

Reassessment and Progress Benchmarks

F-V profiles should be reassessed every 4–6 weeks during an active training block. Given the measurement variability of field-based jump testing (coefficient of variation ≈ 3–5% for CMJ height), meaningful changes in SFV require shifts of at least 0.15 (N/kg)/(m/s) to exceed typical noise.

Jiménez-Reyes et al. (2017) demonstrated that an 8-week individualized F-V training program (matching training emphasis to diagnosed deficit) produced 7.5% greater jump height improvement than a non-individualized program prescribing the same total training volume. The FVimb in the individualized group moved from 0.71 or 1.34 (depending on initial deficit type) toward 0.95–1.05. These benchmarks help set realistic expectations: a single 8-week block targeting a specific deficit can realistically correct FVimb by 25–35% of the initial deviation from optimal.

Practical monitoring checklist between full F-V assessments:

1. Weekly unloaded CMJ (3 jumps before the first session of each week). Provides V0 trend without additional testing burden.
2. Monthly loaded jump squat at a fixed reference load (e.g., 40% 1RM). Provides F-V slope trend with two data points (CMJ + loaded).
3. Quarterly full four-condition protocol. Provides complete slope re-diagnosis to detect which deficit, if any, has re-emerged.