---
title: 'Overtake Score: Definitions and Applications'
url: https://www.emergentmind.com/topics/overtake-score
type: topic
---

# Overtake Score: Definitions and Applications

Searching arXiv for the cited papers and closely related work on Overtake Score.
“Overtake Score” denotes different but related quantities in recent driving research. In truck overtake prediction from Controller Area Network (CAN) data, it is the calibrated posterior probability that a sliding-window feature vector corresponds to an overtaking event, or an aggregate of such probabilities over a file [2404.05723; 2507.00593]. In desired-speed conditioned autonomous driving, the same term refers instead to a route-level command-compliance metric: the percentage of overtake/follow scenarios in which the policy executes the commanded interaction outcome [2603.25672]. A plausible implication is that the term is not yet standardized across the literature; its meaning depends on whether the task is maneuver detection from logged signals or instruction-following evaluation in closed-loop driving.

## 1. Terminological scope

The recent literature uses “Overtake Score” in at least three task-specific senses.

| Context | Object being scored | Definition |
|---|---|---|
| Truck CAN-window classification | Window \(X_t\) | \(S_C(t)\equiv P_C(\text{class}=1\mid X_t)\in[0,1]\) |
| Truck file-level classification | File with \(K\) windows | \(S=\frac{1}{K}\sum_{k=1}^K \hat p_k\) |
| Desired-speed conditioned autonomous driving | Set of routes \(R\) | \(100\times \frac{1}{|R|}\sum_{r\in R}s_r\) |

In “Predicting Overtakes in Trucks Using CAN Data,” each classifier \(C\in\{\text{ANN},\text{RF},\text{SVML},\text{SVM}^{\text{rbf}}\}\) outputs a score
\[
S_C(t)\equiv P_C(\text{class}=1\mid X_t)\in[0,1],
\]
described as the “Overtake Score” for window \(t\) [2404.05723]. In the 2025 comparative study, the same basic quantity is produced per sample, but the score reported for a file is the arithmetic mean over all sliding-window samples in that file [2507.00593]. In Bench2Drive-Speed, by contrast, Overtake-Score is a benchmark metric computed from binary route-level success indicators rather than from classifier posteriors [2603.25672].

This distinction is consequential. In the truck papers, the score is a calibrated confidence signal that can be thresholded for detection. In Bench2Drive-Speed, it is already an aggregated evaluation statistic in percent. Confusing these two usages would conflate posterior estimation with benchmark-level task success.

## 2. CAN-based overtake score as a posterior probability

In the 2024 truck study, the score is defined over feature vectors extracted from 1 s windows of CAN data ending at time \(t\). Let \(X_t\in\mathbb{R}^d\) be the \(d\)-dimensional feature vector extracted from the CAN bus over the 1 s window ending at time \(t\). The logger records 10 Hz signals, so a 1 s window has \(N=10\) samples, and windows advance every 0.5 s, yielding 21 windows per file [2404.05723].

For each continuous signal \(j\in\{1\ldots 7\}\) within window \(W_t=\{t_1\ldots t_N\}\), the paper computes
\[
\mu_j(t)=\frac{1}{N}\sum_{k=1}^N s_j(t_k),
\qquad
\sigma_j(t)=\sqrt{\frac{1}{N}\sum_{k=1}^N [s_j(t_k)-\mu_j(t)]^2 }.
\]
For each categorical signal \(k\in\{8,9,10\}\), the modal value is taken:
\[
m_k(t)=\operatorname{mode}\{s_k(t_1),\ldots,s_k(t_N)\}.
\]
This yields \(2\times 7+3=17\) features per window [2404.05723].

The paper configures all four classifiers to output calibrated probabilities. For the ANN, the output layer is a 2-neuron softmax, so
\[
S_{\text{ANN}}(t)=\frac{\exp(z_1)}{\exp(z_0)+\exp(z_1)},
\]
where
\[
z=W_2\cdot \sigma(W_1\cdot X_t+b_1)+b_2.
\]
The architecture is input \(=17\), hidden \(=10\), output \(=2\) [2404.05723].

For Random Forest,
\[
S_{\text{RF}}(t)=\frac{1}{M}\sum_{m=1}^M I_m(X_t),
\]
where \(I_m(X_t)\in\{0,1\}\) is the vote of tree \(m\) for class \(=1\), with \(M=100\) trees, bootstrap samples, and default splits [2404.05723].

For SVM, both a linear kernel and a Gaussian RBF variant are used. Their decision function \(f(X_t)\) is mapped to a probability by Platt scaling or built-in MATLAB probability estimates:
\[
S_{\text{SVM}}(t)=\operatorname{sigmoid}(f(X_t))=\frac{1}{1+\exp(-f(X_t))}.
\]
For the linear case, \(f(X_t)=w^\top X_t+b\); for the RBF case, it is the kernel decision function [2404.05723].

Preprocessing is classifier-dependent. For ANN and both SVMs, the per-feature normalization is
\[
x'_i=\frac{x_i-\mu^{\text{trainer}}}{\sigma^{\text{trainer}}},
\]
with per-feature mean and standard deviation computed on the training set. RF operates on the unscaled features [2404.05723].

## 3. Temporal evolution, thresholding, and fusion in early overtake prediction

The 2024 study investigates the score up to 10 s before the overtaking event. Figure 1 shows that for class \(=1\) samples, the median \(S_C(t)\) rises from approximately \(0.2\) at \(t=-10\) s to approximately \(0.9\) at \(t=0\) s for ANN, RF, and SVML. For RF specifically, the median \(S_{\text{RF}}\) for class \(=1\) is reported as \(0.22\) at \(t=-10\) s, \(0.53\) at \(t=-5\) s, \(0.78\) at \(t=-1\) s, and \(0.92\) at \(t=0\) s. By contrast, the no-overtake scores remain near \(0.1\)–\(0.3\) for RF and ANN and oscillate for \(\text{SVM}^{\text{rbf}}\) [2404.05723].

This temporal behavior underlies the paper’s main finding: the prediction scores of the overtake class tend to increase as the trigger approaches, while the no-overtake class remains stable or oscillatory depending on the classifier. The best accuracy is therefore achieved when approaching the trigger, and early overtaking prediction is characterized as challenging [2404.05723].

The paper also defines a score-level fusion of RF and linear SVM:
\[
S_{\text{fusion}}(t)=\frac{1}{2}\left[S_{\text{RF}}(t)+S_{\text{SVML}}(t)\right].
\]
A single threshold \(\theta\) yields the final decision,
\[
\hat y(t)=1 \text{ if } S_{\text{fusion}}(t)\ge \theta,\ \text{else } 0.
\]
In practice, \(\theta\) is chosen to maximize \(F_1\), with typical values in \([0.5\ldots 0.6]\); early (\(t\le -3\) s) the optimum \(\theta\) is approximately \(0.47\)–\(0.59\), and closer to the trigger it shifts upward slightly [2404.05723].

The paper defines
\[
P=\frac{TP}{TP+FP},\qquad
R=\frac{TP}{TP+FN},\qquad
F_1=2\cdot \frac{P\cdot R}{P+R},
\]
and
\[
TPR=\frac{TP}{TP+FN},\qquad
TNR=\frac{TN}{TN+FP}.
\]
At \(t=0\) s, RF alone at \(\theta\approx 0.56\) achieves \(TPR=92.5\%\) and \(TNR=89.2\%\), whereas the fusion at \(\theta\approx 0.59\) gives \(TPR=91.3\%\) and \(TNR=93.9\%\) [2404.05723]. The classifiers show good accuracy in classifying overtakes, with Recall/TPR \(>93\%\), but no-overtake classification is weaker, with TNR typically \(80\)–\(90\%\) and below \(60\%\) for one SVM variant; fusion improves no-overtake classification at the expense of reducing overtake accuracy, while keeping the latter above \(91\%\) near the trigger [2404.05723].

AUC-PR results at \(\Delta t=\{0,-1,-2,-3\}\) s further quantify this trade-off:

| Classifier | \(t\) | \(t-1\) | \(t-2\) |
|---|---:|---:|---:|
| ANN | 0.931 | 0.914 | 0.907 |
| RF | 0.896 | 0.885 | 0.890 |
| SVML | 0.952 | 0.950 | 0.946 |
| RF+SVML | 0.981 | 0.981 | 0.975 |

The full table also reports \(t-3\) values of \(0.890\) for ANN, \(0.900\) for RF, \(0.949\) for SVML, \(0.906\) for \(\text{SVM}^{\text{rbf}}\), and \(0.974\) for RF+SVML [2404.05723].

## 4. File-level aggregation and comparative methodology across trucks

The 2025 comparative study reformulates the score at file level. The classifier produces per-sample scores \(\hat p_k\in[0,1]\), \(k=1\ldots K\), for the \(K\) sliding-window feature vectors extracted from one file, and the file-level score is
\[
S=\frac{1}{K}\sum_{k=1}^K \hat p_k.
\]
A final binary decision is then obtained by thresholding the file score, for example \(S\ge 0.5\Rightarrow\) overtake and \(S<0.5\Rightarrow\) no-overtake [2507.00593].

The data are cropped around a trigger. Let \(t=0\) be the moment the trigger fires; each file is cropped from \(t\in[-5\ \mathrm{s},+1\ \mathrm{s}]\), and since samples are recorded at 10 Hz, each file yields 60 raw timesteps [2507.00593]. The trigger is defined by
\[
(\text{lane-change flag}=1)\wedge (\text{ego-speed}>50\ \text{km/h})\wedge (\text{lead-distance}<200\ \text{m})\wedge (\text{wheel-speed difference}>0.1\ \text{km/h}).
\]

Preprocessing differs by classifier. A sliding window of length \(w\) seconds with 50% overlap is run over the crop, with \(w=0\) s for ANN and SVM, and \(w=2\) s for RF. For the seven continuous channels—accelerator pedal position, distance to lead vehicle, lead-vehicle speed, relative wheel speed, ego-speed, lateral acceleration, and longitudinal acceleration—the mean and standard deviation are computed within each window; for the three discrete channels—lane-change flag, left indicator, right indicator—the majority value is taken. This yields \(17\) features for \(w>0\), or \(10\) features if no windowing is used. For ANN and both SVM variants, the continuous signals or window-features are standardized using training-set mean and standard deviation, whereas RF sees the unscaled window statistics [2507.00593].

The score-level fusion strategy is again an unweighted average of RF and linear SVM. If \(\hat p_k^{(\mathrm{RF})}\) and \(\hat p_k^{(\mathrm{SVM})}\) are the per-sample scores, then
\[
\hat p_k^{(\mathrm{fuse})}
=
\frac{1}{2}\Bigl(\hat p_k^{(\mathrm{RF})}+\hat p_k^{(\mathrm{SVM})}\Bigr),
\]
and the fused file-level score is
\[
S^{(\mathrm{fuse})}
=
\frac{1}{K}\sum_{k=1}^K \hat p_k^{(\mathrm{fuse})}
=
\frac{1}{2K}\sum_{k=1}^K
\Bigl(\hat p_k^{(\mathrm{RF})}+\hat p_k^{(\mathrm{SVM})}\Bigr).
\]
The authors also tried 3-way and 4-way averages, but RF+SVM-lin produced the most consistent per-truck results [2507.00593].

After training on balanced data from five trucks and testing on held-out files, RF+SVM-lin yielded the best overall trade-off, with \(\mathrm{TNR}=93.0\%\), \(\mathrm{TPR}=86.5\%\), and \(\mathrm{AUC}\approx 0.93\) [2507.00593]. The per-truck breakdown reported for the fused method is:

| Truck | TNR (%) | TPR (%) |
|---|---:|---:|
| t1 | 70.3 | 93.7 |
| t2 | 99.2 | 80.0 |
| t3 | 100.0 | 28.6 |
| t4 | 95.5 | 81.3 |
| t5 | 100.0 | 62.5 |

The paper notes that some trucks, specifically t3 and t5, have small numbers of training files, hence lower TPR for those drivers [2507.00593]. It also reports that variability in traffic conditions strongly influences the signal patterns, particularly in the no-overtake class, and that training with data from multiple vehicles improves generalization and reduces condition-specific bias [2507.00593].

## 5. Overtake-Score as a route-level command-compliance metric

Bench2Drive-Speed defines Overtake-Score in a substantially different way. Let \(R\) be the set of all evaluated routes that include an explicit overtake or follow command; let \(c_r\in\{\text{Overtake},\text{Follow}\}\) be the user-specified command for route \(r\); let \(a_r\in\{0,1\}\) indicate whether the scenario actually triggered; and let \(p_r\in\{0,1\}\) indicate whether the ego-vehicle successfully passed the lead vehicle during the scenario window [2603.25672].

If the scenario triggered (\(a_r=1\)), then for an Overtake command, \(s_r=1\) if the ego ever passes the lead (\(p_r=1\)), else \(0\); for a Follow command, \(s_r=1\) if the ego never passes the lead (\(p_r=0\)) for the entire scenario, else \(0\). If the scenario never triggered (\(a_r=0\)), the benchmark sets \(s_r=0\) to prevent score inflation. The Overtake-Score is then
\[
\text{Overtake-Score}
=
100\times \frac{1}{|R|}\sum_{r\in R}s_r.
\]
The pass event is defined by
\[
p_r=
\begin{cases}
1,& \text{if } \exists\, t\in[t_{\text{start}}^r,t_{\text{end}}^r]\ \text{such that } s_{\text{ego}}^r(t)>s_{\text{lead}}^r(t)+\Delta_s\\
0,& \text{otherwise.}
\end{cases}
\]
The route-level success is written as
\[
s_r
=
a_r\times
\begin{cases}
1\cdot p_r,& \text{if } c_r=\text{Overtake}\\
1\cdot (1-p_r),& \text{if } c_r=\text{Follow.}
\end{cases}
\]
This construction makes the metric a direct measure of instruction compliance rather than maneuver probability [2603.25672].

The computational pipeline uses a CARLA ScenarioRunner extension. XML configuration specifies route waypoints, trigger region for overtaking, spawn distance \(D_0\), front-vehicle speed \(v_{\text{front}}\), and behavior type. During closed-loop execution, sensor inputs and user commands are collected, the policy outputs control or a planned trajectory, and ego and lead positions are logged along the route centerline. Post-processing then checks whether the ego enters the trigger region, determines whether a pass event occurred between \(t_{\text{trigger}}\) and \(\min(t_{\text{timeout}},t_{\text{route end}})\), sets \(s_r\), and averages over all routes [2603.25672].

The benchmark also specifies representative hyperparameters: \(\Delta_s\) is often zero or a small number such as \(0.5\) m; the trigger region geometry is chosen to be \(\pm 2\) m laterally and \(\pm 5\) m longitudinally around the lead-spawn waypoint; timeout is set to the remaining route length or a fixed time such as \(15\) s; initial spawn distance is \(10\)–\(15\) m; and the lead-vehicle speed is sampled as \(v_{\text{front}}\sim \mathrm{Uniform}[\epsilon,v_{\text{target}}-\delta]\), with \(\epsilon\approx 1\) m/s and \(\delta\approx 1\) m/s [2603.25672].

Experimental values from the benchmark make clear that commanded overtaking remains difficult. The reported Overtake-Score values are \(18.75\) for TCP w/o Speed Cmd, \(21.88\) for TCP-Speed (Expert2.1k), and \(40.63\) for TCP-Speed (Virtual2.1k) on the “All (48)” split; on “Medium (16),” the corresponding values are \(37.50\), \(37.50\), and \(56.25\); on “Hard (16),” they are \(0.00\), \(6.25\), and \(25.00\) [2603.25672].

## 6. Interpretation, limitations, and common points of confusion

A recurring source of confusion is that “Overtake Score” does not refer to a single invariant quantity. In the truck CAN papers, it is a posterior probability estimated by a classifier and then optionally fused and thresholded [2404.05723; 2507.00593]. In Bench2Drive-Speed, it is an average of binary successes over routes and is already expressed as a percentage [2603.25672]. These are mathematically distinct objects.

Another common misconception is to treat the score as a direct proxy for safe overtaking. The truck studies evaluate overtakes versus no-overtakes using \(TPR\), \(TNR\), \(F_1\), ROC, and PR behavior, and explicitly report trade-offs between detecting overtakes and suppressing false alarms [2404.05723; 2507.00593]. Bench2Drive-Speed states more directly that its Overtake-Score is a coarse \(0/1\) measure: it does not capture how smoothly or safely the overtake was executed, does not penalize a successful overtake that results in a collision, and should be reported alongside standard safety metrics such as collision rate [2603.25672].

The literature also identifies important failure modes. In the 2024 study, early overtaking prediction is challenging because the overtake-class scores rise as the trigger approaches; performance improves near the trigger, which implies that informative discriminative structure is concentrated in the last few seconds before the event [2404.05723]. In the 2025 study, no-overtake variability under unconstrained real-world conditions affects classification performance if the training data lack adequate diversity, and per-truck accuracy depends on the amount of training data per vehicle [2507.00593]. In Bench2Drive-Speed, activation failures are counted as failures to prevent score inflation, and a policy could “game” the metric by never attempting to overtake, thereby scoring follow commands perfectly but failing all overtake commands; the benchmark therefore suggests balanced aggregates or separate overtake and follow scores [2603.25672].

Taken together, these studies situate Overtake Score as a useful but task-dependent abstraction. In signal-based maneuver detection, it is a calibrated probabilistic indicator whose temporal evolution can support early-warning ADAS logic. In instruction-conditioned autonomous driving, it is a compliance metric for interactive behavior. A plausible implication is that future work may need more explicit nomenclature—distinguishing posterior overtake probability, aggregated file-level overtake score, and route-level overtake compliance—to avoid ambiguity across subfields.

Source: https://www.emergentmind.com/topics/overtake-score