# Study 000B Results

## Summary

This flagship companion study supports a mixed answer rather than a simple one:

- later specialization coincided with better speed-per-heart-rate efficiency
- background recovery markers moved in a favorable direction as running became a larger share of recent activity
- session heart rate did not simply normalize away
- a small positive late-window unexplained HR burden remained even after simple speed-plus-power adjustment

## Early-to-late adaptive efficiency window

| window_label | run_count | start_date | end_date | speed_mps_mean | pace_min_per_mile_mean | avg_hr_bpm_mean | avg_power_w_mean | cadence_spm_mean | stride_length_m_mean | speed_per_hr_mean | power_per_hr_mean | hr_residual_bpm_mean | running_hours_28d_mean | total_activity_hours_28d_mean | running_share_28d_activity_pct_mean | next_day_resting_hr_mean | next_day_sleep_score_mean | next_day_hrv_mean |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| early_qc_window | 30 | 2025-04-16 | 2025-07-18 | 2.14820 | 13.13 | 137.10 | 262.67 | 141.53 | 0.91 | 0.01559 | 1.89463 | -1.59691 | 7.38 | 49.03 | 15.26 | 50.97 | 51.04 | None |
| late_qc_window | 30 | 2026-04-22 | 2026-06-04 | 2.92387 | 9.19 | 165.93 | 321.97 | 171.47 | 1.02 | 0.01768 | 1.94806 | 3.09257 | 14.36 | 25.47 | 56.40 | 41.20 | 54.37 | 74.67 |

The main pattern is visible immediately:

- speed increased
- heart rate also increased
- speed per heart-rate cost improved
- power per heart-rate cost improved only slightly
- running specialization rose sharply
- next-day resting heart rate improved and next-day sleep score improved

These two windows are matched by run count, not by elapsed time. The early window spans `93` calendar days, while the late window spans `43`, so specialization and rolling-load contrasts should be read as denser-late versus broader-early context rather than as perfectly matched periods.

## Early-to-late change table

| metric | early_value | late_value | change_value | change_units |
|---|---|---|---|---|
| speed_mps_mean | 2.14820 | 2.92387 | 36.11 | pct_change |
| pace_min_per_mile_mean | 13.13 | 9.19 | -29.99 | pct_change |
| avg_hr_bpm_mean | 137.10 | 165.93 | 21.03 | pct_change |
| avg_power_w_mean | 262.67 | 321.97 | 22.58 | pct_change |
| cadence_spm_mean | 141.53 | 171.47 | 21.15 | pct_change |
| stride_length_m_mean | 0.91 | 1.02 | 12.24 | pct_change |
| speed_per_hr_mean | 0.01559 | 0.01768 | 13.41 | pct_change |
| power_per_hr_mean | 1.89463 | 1.94806 | 2.82 | pct_change |
| hr_residual_bpm_mean | -1.59691 | 3.09257 | 4.69 | bpm_shift |
| running_share_28d_activity_pct_mean | 15.26 | 56.40 | 269.52 | pct_change |
| next_day_resting_hr_mean | 50.97 | 41.20 | -19.16 | pct_change |
| next_day_sleep_score_mean | 51.04 | 54.37 | 6.53 | pct_change |

This table shows why the study is not just a "higher HR" story:

- speed improved by more than heart rate did
- `speed_per_hr_mean` improved by double digits
- `power_per_hr_mean` improved only modestly
- `hr_residual_bpm_mean` shifted upward rather than disappearing

That is the core mixed signal: the system became more efficient in one sense, but not cost-free.

## Session HR residual model

| model_name | intercept | speed_coef | power_coef | early_mean_residual_bpm | late_mean_residual_bpm | early_residual_sd_bpm | late_residual_sd_bpm |
|---|---|---|---|---|---|---|---|
| hr_from_speed_power | 66.40 | 26.91 | 0.06 | -1.60 | 3.09 | 11.26 | 9.61 |

The HR model is intentionally simple and descriptive. It uses speed and power to estimate expected session HR. The unexplained HR pattern matters more than the coefficients themselves:

- early-window residual burden was slightly negative on average
- late-window residual burden was slightly positive on average

That means the late window does not look like a pure internal-burden reduction story even though output efficiency improved.

## Monthly efficiency and specialization summary

| year_month | qc_run_count | speed_mps_norm | avg_hr_bpm | avg_power_w | speed_per_hr | power_per_hr | hr_residual_bpm | running_share_28d_activity_pct | next_day_resting_hr | next_day_sleep_score | next_day_hrv |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2025-04 | 4 | 1.82925 | 127.00 | 198.75 | 0.01466 | 1.58664 | 0.41080 | 21.39 | 53.25 | 54.25 | None |
| 2025-05 | 4 | 2.00500 | 136.25 | 220.00 | 0.01452 | 1.57730 | 3.75943 | 9.17 | 57.50 | 41.67 | None |
| 2025-06 | 11 | 2.10982 | 132.45 | 257.00 | 0.01584 | 1.91874 | -4.89700 | 10.52 | 49.64 | 57.10 | None |
| 2025-07 | 14 | 2.40314 | 146.50 | 316.21 | 0.01633 | 2.15027 | -2.01035 | 20.80 | 48.86 | 49.14 | None |
| 2025-08 | 13 | 2.33777 | 148.77 | 307.23 | 0.01567 | 2.04775 | 2.51351 | 19.61 | 46.62 | 62.15 | None |
| 2025-10 | 6 | 2.45600 | 157.83 | 320.50 | 0.01561 | 2.03600 | 7.66422 | 7.02 | 47.67 | 60.33 | 61.50 |
| 2025-11 | 7 | 2.43714 | 144.57 | 294.86 | 0.01686 | 2.03840 | -3.67625 | 15.76 | 49.00 | 65.50 | 57.17 |
| 2025-12 | 9 | 2.53411 | 149.33 | 327.22 | 0.01698 | 2.19238 | -3.30850 | 20.14 | 47.33 | 62.25 | 61.12 |
| 2026-01 | 25 | 2.43808 | 150.56 | 315.80 | 0.01624 | 2.10112 | 1.13230 | 42.49 | 40.88 | 68.30 | 72.87 |
| 2026-02 | 22 | 2.39555 | 150.09 | 290.95 | 0.01605 | 1.93804 | 3.17786 | 72.57 | 40.77 | 67.76 | 71.38 |
| 2026-03 | 25 | 2.65948 | 148.92 | 324.92 | 0.01799 | 2.20210 | -6.96869 | 65.59 | 40.84 | 64.05 | 75.82 |
| 2026-04 | 24 | 2.86079 | 163.46 | 317.83 | 0.01755 | 1.95039 | 2.54290 | 75.74 | 40.46 | 60.87 | 72.91 |
| 2026-05 | 19 | 2.91453 | 166.32 | 320.05 | 0.01755 | 1.92725 | 3.83193 | 55.73 | 41.26 | 49.95 | 75.32 |
| 2026-06 | 3 | 2.91900 | 154.67 | 326.00 | 0.01924 | 2.15454 | -8.26553 | 51.59 | 40.67 | 78.00 | 79.67 |

At the monthly level:

- running share of recent activity rose markedly into 2026
- speed-per-HR improved into the later months
- HR residual burden remained mixed rather than collapsing monotonically

This supports a specialization-with-mixed-cost reading better than a simple fitness-improvement reading.

## Specialization correlations

| relationship | correlation_r | n_points |
|---|---|---|
| running_share_vs_speed_per_hr | 0.31 | 187 |
| running_share_vs_power_per_hr | 0.02 | 187 |
| running_share_vs_hr_residual | -0.02 | 187 |
| running_share_vs_nextday_resting_hr | -0.81 | 187 |
| running_share_vs_nextday_sleep_score | 0.16 | 176 |
| running_share_vs_nextday_hrv | 0.42 | 131 |

These correlations are descriptive and likely time-confounded, but they still help position the system:

- higher running share tracked better speed-per-HR efficiency
- higher running share tracked lower next-day resting HR
- higher running share tracked higher available HRV in the late window
- specialization did not meaningfully reduce the simple run-level unexplained HR burden by itself

## Partial late-window food context

| subset | n_days | mean_food_calories | mean_net_carbs_g | mean_sleep_score | mean_hrv | mean_running_hours_7d |
|---|---|---|---|---|---|---|
| all_overlap_days | 109 | 437.05 | 4.90 | 61.79 | 75.13 | 3.77 |
| food_item_days_only | 30 | 1587.93 | 17.80 | 63.72 | 75.90 | 4.32 |

| relationship | correlation_r | n_points |
|---|---|---|
| food_calories_vs_running_hours_7d | 0.31 | 109 |
| net_carbs_vs_sleep_score | 0.16 | 100 |
| food_calories_vs_hrv | 0.02 | 100 |

The food layer remains partial and late-window only. It is useful as confound context, but not strong enough to anchor the central claim of this study.

## What this study can and cannot answer

| category | question | answer |
|---|---|---|
| answered | Did adaptive efficiency improve as specialization increased in the later running window? | Yes, at least at the speed-per-heart-rate level. The late window shows better external speed per unit heart-rate cost than the early window. |
| answered | Did background recovery markers move in a favorable direction as specialization increased? | Yes, descriptively for next-day resting heart rate and next-day sleep score. HRV is late-window only and should be treated as contextual rather than symmetric early-late evidence. |
| supported_not_proven | Did unexplained session HR burden disappear as adaptation advanced? | No. Session heart rate remained high, and a simple speed-plus-power HR model shows slightly positive late-window unexplained HR burden rather than a full disappearance of burden. |
| not_answered | Can this study prove causal physiology or exact fatigue mechanism? | No. The study characterizes a mixed pattern of improved efficiency and persistent session-level burden, but it does not prove mechanism. |