Optimal Force-Velocity Profile for Sprinting: Is It All Bollocks? – Part 6

Håkan Andresson is an absolute legend

Håkan Andresson was kind enough to listen to my proposal and immediately collect data using very similar conditions to the simulation in fig-model-predictions. Håkan used single athlete (82 kg body weight, 186 cm height) who sprinted over cca 50m in normal condition, with 6.6 kg weight vest, and with horizontal resistance of 6.6 kg (or 65.75N) provided by the Dynaspeed. Sprint performance was measured using the LaserSpeed device. The velocity time trace of these three sprints can be seen in Figure 3.

athlete_BW <- 82
athlete_BH <- 1.86
vest_weight <- 6.6
resistance <- 6.6 * 9.81

hakan <- read_csv("data/hakan.csv") %>%
  mutate(time = time / 1000)

ggplot(hakan, aes(x = time, color = type)) +
  theme_linedraw(8) +
  geom_line(aes(y = `velocity-raw`), alpha = 0.5) + 
  geom_line(aes(y = `velocity-smooth`), alpha = 0.9) +
  geom_dl(
    aes(y = `velocity-smooth`, label = paste("  ", type)),
    method = list("last.bumpup", cex = 0.5)
  ) +
  xlim(-0.5, 8) +
  xlab("Time (s)") +
  ylab("Velocity (m/s)") +
  theme(legend.position = "none")

Figure 3: Laser gun data for a single individual. “Jumpy” lines represent the raw laser velocity, while the “smooth” line represent the smoothed velocity provided by the LaserSpeed device. Courtesy of Håkan Andresson

To avoid deceleration phase in the analysis, all three sprint traced are trimmed at 6s point. Mono-exponential model is fitted to each sprint using the {shorts} package (Jovanović and Vescovi 2022; Jovanović 2022) package (Figure 4).

hakan <- hakan %>%
  filter(time <= 6) 

# Get predictions
hakan <- hakan %>%
  group_by(type) %>%
  mutate(`velocity-predicted` = predict(model_radar_gun(time, `velocity-raw`))) %>%
  ungroup()

# Plot
ggplot(hakan, aes(x = time, color = type)) +
  theme_linedraw(8) +
  geom_line(aes(y = `velocity-raw`), alpha = 0.5) + 
  geom_line(aes(y = `velocity-predicted`), alpha = 0.9) +
  geom_dl(
    aes(y = `velocity-predicted`, label = paste("  ", type)),
    method = list("last.bumpup", cex = 0.5)
  ) +
  xlim(-0.5, 6.5) +
  xlab("Time (s)") +
  ylab("Velocity (m/s)") +
  theme(legend.position = "none")

Figure 4: Predicted velocity using the models fitted with mono-exponential equation ({shorts} package (Jovanović and Vescovi 2022; Jovanović 2022) package)

The next step is to estimate the FVP using each individual sprint and the load conditions, as well as to estimate MSS and MAC for each condition assuming that the $F_0$ and $V_0$ from the normal sprint are mechanical determinants. In addition to this, I will provide estimated $F_0$ and $V_0$ disregarding the information about the load. Results are in Table 1.

# Model
avp <- hakan %>%
  group_by(type) %>%
  summarise(data.frame(model_radar_gun(time, `velocity-raw`)$parameters)) %>%
  ungroup() %>%
  mutate(
    BW = athlete_BW,
    BH = athlete_BH,
    load = ifelse(type == "vest", vest_weight, 0),
    resistance = ifelse(type == "resisted", resistance, 0)) 

fvp <- avp %>%
  group_by(type) %>%
  mutate(find_FV(MSS, MAC, BW, BH, load, resistance)) %>%
  ungroup() %>%
  relocate(type, BW, BH) %>%
  select(-TC, -PMAX, -TAU)

# Created predicted sprint perf assuming normal F0 and V0 are "causal"
normal_fvp <- fvp %>%
  filter(type == "normal")

pred_avp <- function(df) {
  res <- find_AVP(normal_fvp$F0, normal_fvp$V0, df$BW, df$BH, df$load, df$resistance)
  
  data.frame(
    df,
    `predMSS` = res$MSS,
    `predMAC` = res$MAC)
}

disregard_cond <- function(df) {
  res <- find_FV(df$MSS, df$MAC, df$BW, df$BH, inertia = 0, resistance = 0)
  
  data.frame(
    df,
    `disregF0` = res$F0,
    `disregV0` = res$V0)
}

fvp <- fvp %>%
  rowwise() %>%
  do(pred_avp(.)) %>%
  do(disregard_cond(.))

kbl(fvp, digits = 2) %>%
  kable_classic(full_width = FALSE)

Table 1: Estimated sprint performance parameters (MSS and MAC) and FVP parameters (F0 and V0) for each sprint condition. predMSS and predMAC represent estimated sprint performance parameters assuming estimated $F_0$ and $V_0$ from a normal condition to be causal individual mechanical traits. disregF0 and disregV0 represent estimated FVP parameters disregarding information about additional load/resistance.

Let us discuss results from Table 1. When using only horizontal force resistance, theoretical model (Figure 2) predicts that both MSS and MAC will be affected. This is actually the case, as expected. But, the estimated $F_0$ and $V_0$ are not the same as those estimated with the normal sprint. If they are mechanical determinants, they should be equal (assuming there is no measurement error nor biological variation or fatigue/facilitation between sprints; that’s why we need more individuals). Estimated $F_0$ is actually larger than the $F_0$ estimated in the normal condition, which indicates that somehow, the individual is able to generate more initial horizontal force when using additional resistance. If $F_0$ is some type of the mechanical determinant, individual will show the same $F_0$, yielding smaller MAC, since part of it is spent on overcoming fixed horizontal resistance.

If we assume sprint FVP parameters estimated from the normal sprint condition to be mechanical determinants or traits, predicted MSS is larger than the observed, and predicted MAC is smaller than the observed (see Figure 5 for visual representation).

For the weighted vest condition, theoretical model (Figure 2) predicts that MAC will be affected, while MSS will stay the same. This is not the case (see Figure 5 for visual representation). Also, estimated $F_0$ is actually larger than the $F_0$ estimated in the normal condition, which indicates that somehow, the individual is able to generate more initial horizontal force when using additional inertia.

pre_df <- fvp %>%
  filter(type == "normal") %>%
  select(MSS, MAC) %>%
  mutate(predMSS = MSS, predMAC = MAC, load = "norm") %>%
  expand_grid(type = c("resisted", "vest"))

post_df <- fvp %>%
  filter(type != "normal") %>%
  select(type, MSS, MAC, predMSS, predMAC) %>%
  mutate(load = "load")

df <- full_join(pre_df, post_df) %>%
  mutate(load = factor(load, levels = c("norm", "load")))

df_observed <- df %>%
  select(load, type, MSS, MAC) %>%
  pivot_longer(cols = c(MSS, MAC), names_to = "parameter") %>%
  mutate(model = "observed")

df_predicted <- df %>%
  select(load, type, predMSS, predMAC) %>%
  rename(MSS = predMSS,  MAC = predMAC) %>%
  pivot_longer(cols = c(MSS, MAC), names_to = "parameter") %>%
  mutate(model = "predicted")

plot_df <- rbind(df_observed, df_predicted) %>%
  mutate(parameter = factor(parameter, levels = c("MSS", "MAC")))

ggplot(plot_df, aes(x = load, y = value, color = model, group = model)) +
  theme_linedraw(8) +
  geom_line() +
  geom_point(fill = "white", shape = 21) +
  facet_grid(parameter~type, scales = "free") +
  geom_dl(
    aes(label = paste("  ", model)),
    method = list("last.bumpup", cex = 0.5)
  ) +
  xlab(NULL) +
  ylab(NULL) +
  theme(legend.position = "none")

Figure 5: Comparisson between theoretical model sprint performance parameters predictions (i.e., assuming normal sprint estimated FVP parameters represent mechanical determinants or traits of the individual) and estimated sprint performance parameters

Although we need more samples, I do not think that this simple N=1 experiment support the realist model, which is implicit in viewing FVP as mechanical determinant of performance. Rather, I see FVP as additional performance summary (Figure 6) or indicators of performance that can pretty much be unnecessary if one knows MSS and MAC. Yeah, maybe one would like to know $F_0$ changes over time when individual also demonstrates changes in body weight, or if the ambient conditions change (e.g., air pressure, wind, or temperature) to check is someone “improved their force capabilities”, but this viewpoint actually takes the realist stance (with one being aware of it or not ¹), that we have just disproved (assuming N=1 is enough to disprove it).

Figure 6: Instrumentalist viewpoint in which the $F_0$ and $V_0$ are simply indicators of performance

All in all, I still think that FVP is generally bollocks that seems to caught momentum and fame in the sports science community. It does looks like “science”, it does look like we are uncovering individual traits or qualities, especially will statements like “oh, your FVP profile is imbalanced – you need to work more on your ability to develop force” it is more pseudoscience maskarading as “evidence-based” scientific method. Am I against it? Yeah. I think summarizing sprint performance using MSS and MAC is enough. FVP will not give you anything more insightful or useful, except maybe to look and sound smart when presenting the data. Will you be able to pinpoint to performance limiter by looking at the FVP analysis? Nope. I still think that watching the sprint itself and motion-analysis will give you more information you might find actionable. For example, feet collapsing, or backside mechanics will not be seen in FVP profile. FVP profile will thus not determine sprint performance, but it will reflect sprint performance. If your fixing of someone’s feet collapsing or fixing someones back-side mechanics to be more front side improves sprint performance and thus FVP, then how can we state that FVP parameters represent mechanical determinants? Bollock, I tell you. Bollocks.

References

1. Jovanović, Mladen. 2022. Shorts: Short Sprints. https://cran.r-project.org/package=shorts.
2. Jovanović, Mladen, and Jason Vescovi. 2022. “Shorts: An r Package for Modeling Short Sprints.” International Journal of Strength and Conditioning 2 (1). https://doi.org/10.47206/ijsc.v2i1.74.

Footnotes

1. Like it or not, or accept it or not, every our measurement, inference, or prediction assumes certain theoretical model. You just need to transparently state it, or if you are not aware of it, elucidate it. Eventually one can test predictions of such a model against the “real world” like we did in this installment. Yes we do need more samples to be conclusive, but this is a good start↩︎