## Scatter Plot: Accuracy vs Deep-Thinking Ratio by Threshold ### Overview The image shows a scatter plot comparing accuracy (Pass@1) against deep-thinking ratio for three different threshold values (g=2.5e-01, g=5.0e-01, g=7.5e-01). Each threshold is represented by a distinct color-coded data series with connecting lines and shaded confidence intervals. The plot includes correlation coefficients (r-values) for each series. ### Components/Axes - **X-axis**: Deep-Thinking Ratio (0.24 to 0.48) - **Y-axis**: Accuracy (Pass@1) (0.600 to 0.700) - **Legend**: - Blue circles: threshold g=2.5e-01 - Brown circles: threshold g=5.0e-01 - Cyan circles: threshold g=7.5e-01 - **Annotations**: - r = 0.820 (blue series) - r = 0.962 (brown series) - r = 0.012 (cyan series) ### Detailed Analysis 1. **Blue Series (g=2.5e-01)**: - Positioned at x ≈ 0.48 - Accuracy range: 0.635–0.650 - Correlation: r = 0.820 (strong positive trend) - Data points show moderate clustering with slight upward trend 2. **Brown Series (g=5.0e-01)**: - Positioned at x ≈ 0.32 - Accuracy range: 0.625–0.660 - Correlation: r = 0.962 (very strong positive trend) - Tight clustering with clear upward trajectory 3. **Cyan Series (g=7.5e-01)**: - Positioned at x ≈ 0.24 - Accuracy range: 0.620–0.665 - Correlation: r = 0.012 (negligible correlation) - Widely scattered points with no discernible pattern ### Key Observations - The brown series (g=5.0e-01) demonstrates the strongest linear relationship (r=0.962) between deep-thinking ratio and accuracy - The cyan series (g=7.5e-01) shows essentially no correlation (r=0.012) despite having the highest deep-thinking ratio - All series exhibit similar accuracy ranges (0.620–0.665), but with varying distributions - Confidence intervals (shaded areas) are widest for the cyan series, indicating greater uncertainty ### Interpretation The data suggests that threshold g=5.0e-01 optimally balances deep-thinking ratio and accuracy, with the strongest predictive relationship (r=0.962). The threshold g=7.5e-01 appears ineffective at correlating these metrics, while g=2.5e-01 shows moderate effectiveness. The similar accuracy ranges across thresholds imply that performance differences stem primarily from deep-thinking ratio distribution rather than absolute accuracy levels. The strong correlation in the brown series indicates a potential causal relationship worth investigating further, possibly representing an optimal operational threshold for the system being measured.