========================================================================================================
CORPUS tfil_ab2    70 battles   490 rounds   54939 usable shots by US (ModularBot)
  attribution: owner id -> {e=DrussGT, s=us} recovered per battle from fire geometry+energy;
               cross-checked on the death events: 496/496 deaths have the mapped victim at ~0 energy
  (attribution is per-battle because the Tank Royale owner id is not stable across runs)

  >> THE CONFOUNDER IS REAL: our fired power is a range + energy cap
  band      power         shots   firePx      ourE    enemyE    flight
  0-100     0.50-0.75         6     82.7      15.5      16.8      6.50
  0-100     >=1.50           19     80.3      63.7      57.0     10.89
  100-200   <0.50             5    160.9       8.6       0.6     10.00
  100-200   0.50-0.75        53    165.8      13.2      18.8     10.42
  100-200   0.75-1.00         5    177.3      29.0      33.7     11.00
  100-200   1.00-1.50        23    168.4      85.0      83.1     11.87
  100-200   >=1.50          191    158.7      75.8      71.0     14.86
  200-300   <0.50             6    257.0      99.7      99.8     15.33
  200-300   0.50-0.75       130    266.8      12.7      20.0     15.28
  200-300   0.75-1.00        21    262.7      28.8      26.7     16.14
  200-300   1.00-1.50       780    261.2      83.6      81.5     16.86
  200-300   >=1.50           56    248.4      32.0      15.7     21.95
  300-450   <0.50           333    409.1      14.5       1.9     20.96
  300-450   0.50-0.75      5272    411.3      13.8      19.2     22.36
  300-450   0.75-1.00       880    407.7      29.0      28.5     23.49
  300-450   1.00-1.50     10696    402.0      69.2      62.6     23.70
  450+      <0.50           950    537.0      14.2       1.1     27.03
  450+      0.50-0.75     12960    536.1      13.7      18.6     28.38
  450+      0.75-1.00      2424    540.4      28.8      26.4     30.18
  450+      1.00-1.50     20126    534.2      63.0      53.8     30.52

  (a) MISS AT ARRIVAL px - perpendicular offset of DrussGT from our aim line
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                 23.96                     -                 32.97                 37.21
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                   46.00                 43.03                 33.87                 47.92                 59.00
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                   53.19                 74.31                 79.82                 74.72                113.81
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                  112.84                104.67                109.32                110.55                177.09
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                     130.86                124.01                132.35                132.26                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  (a') MISS AT ARRIVAL / flight ticks (px per tick - power-neutral)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  3.72                     -                  4.85                  3.61
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                    4.77                  4.45                  3.32                  4.05                  4.37
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                    3.41                  5.01                  5.18                  4.67                  5.47
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                    5.52                  4.85                  4.85                  4.88                  9.84
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                       4.97                  4.52                  4.55                  4.51                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  (b) LATERAL DISPLACEMENT px over the flight window
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                 30.64                     -                 42.81                 47.99
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                   46.73                 37.57                 45.85                 56.50                 64.60
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                   79.80                 59.91                 58.51                 71.56                103.43
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                   62.79                 88.47                 94.34                 91.94                 57.29
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                      78.40                 97.42                102.03                103.30                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  (b/ ) LATERAL DISPLACEMENT / flight ticks (px per tick - power-neutral)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  4.66                     -                  6.54                  4.54
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                    4.38                  3.44                  3.77                  4.76                  4.22
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                    5.13                  3.79                  3.45                  4.12                  4.75
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                    2.96                  3.94                  4.00                  3.86                  3.18
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                       2.90                  3.47                  3.41                  3.42                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  (b') LATERAL DISPLACEMENT px over a FIXED 12-tick window (power-neutral)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                 59.58                     -                 85.08                 55.36
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                   56.15                 43.26                 46.77                 59.47                 51.69
                              n=5                  n=52                   n=5                  n=23                 n=188
  200-300                   64.29                 47.20                 40.99                 50.09                 54.53
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                   42.81                 54.20                 54.14                 52.75                 38.69
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                      45.56                 55.63                 54.97                 55.47                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  (b'') CONTROL: lateral displacement px, SAME shot, 40 ticks later (bullet gone)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                 47.22                     -                 59.18                 54.33
                              n=0                   n=5                   n=0                   n=2                  n=15
  100-200                   46.20                 46.92                 12.30                 50.59                 45.10
                              n=2                  n=41                   n=5                  n=23                 n=170
  200-300                   56.80                 43.68                 49.06                 49.21                 41.62
                              n=6                 n=127                  n=21                 n=780                  n=32
  300-450                   37.42                 52.80                 53.83                 51.95                 61.95
                            n=265                n=5155                 n=877               n=10695                   n=1
  450+                      42.34                 52.03                 52.53                 52.64                     -
                            n=821               n=12828                n=2421               n=20120                   n=0

  (f) FLIGHT WINDOW LENGTH ticks (low power = FASTER bullet = shorter)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  6.50                     -                  6.50                 10.89
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                   10.00                 10.42                 11.00                 11.87                 14.86
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                   15.33                 15.28                 16.14                 16.86                 21.95
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                   20.96                 22.36                 23.49                 23.70                 18.00
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                      27.03                 28.38                 30.18                 30.52                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  (c) RESPONSE LATENCY ticks to a >15 deg heading turn
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  4.20                     -                  4.00                  5.67
                              n=0                   n=5                   n=0                   n=2                  n=15
  100-200                    6.25                  6.34                  5.50                  6.44                  7.00
                              n=4                  n=29                   n=2                  n=16                 n=148
  200-300                    8.33                  9.03                 10.00                  7.68                  9.27
                              n=6                  n=78                  n=11                 n=566                  n=49
  300-450                   10.99                 11.55                 11.84                 11.46                  2.00
                            n=149                n=2968                 n=525                n=6860                   n=1
  450+                      13.37                 13.60                 14.57                 14.27                     -
                            n=559                n=8682                n=1745               n=13884                   n=0

  (d) MEAN TURN RATE deg/tick, flight window
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  2.83                     -                  3.89                  3.48
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                    3.77                  2.01                  3.39                  2.86                  2.78
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                    3.55                  2.08                  1.72                  2.49                  2.07
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                    1.30                  1.48                  1.48                  1.61                  3.30
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                       1.37                  1.49                  1.51                  1.46                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  (d') MEAN TURN RATE deg/tick, fixed 12-tick window
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  2.54                     -                  2.91                  3.43
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                    3.64                  2.09                  3.37                  2.66                  2.64
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                    3.22                  1.91                  1.45                  2.22                  2.03
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                    1.33                  1.46                  1.45                  1.50                  2.78
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                       1.36                  1.43                  1.46                  1.28                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  (d'') CONTROL: mean turn rate deg/tick, 40 ticks later
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  3.07                     -                  2.91                  3.18
                              n=0                   n=5                   n=0                   n=2                  n=15
  100-200                    2.93                  2.20                  2.61                  3.04                  2.61
                              n=3                  n=44                   n=5                  n=23                 n=174
  200-300                    2.80                  1.78                  1.35                  2.19                  3.17
                              n=6                 n=127                  n=21                 n=780                  n=37
  300-450                    1.31                  1.44                  1.38                  1.57                  2.99
                            n=295                n=5211                 n=878               n=10696                   n=1
  450+                       1.30                  1.52                  1.54                  1.58                     -
                            n=886               n=12902                n=2423               n=20126                   n=0

  (d) MEAN SPEED px/tick, flight window
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  7.39                     -                  8.00                  7.45
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                    5.73                  6.05                  4.83                  6.05                  5.87
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                    6.18                  5.39                  5.64                  5.44                  6.20
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                    5.41                  5.49                  5.53                  5.49                  3.94
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                       5.37                  5.46                  5.44                  5.48                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  (d'') CONTROL: mean speed px/tick, 40 ticks later
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  6.07                     -                  6.23                  6.33
                              n=0                   n=5                   n=0                   n=2                  n=15
  100-200                    5.23                  5.84                  3.45                  5.86                  5.73
                              n=3                  n=44                   n=5                  n=23                 n=174
  200-300                    6.32                  5.63                  6.45                  5.48                  6.53
                              n=6                 n=127                  n=21                 n=780                  n=37
  300-450                    5.48                  5.50                  5.56                  5.45                  5.37
                            n=295                n=5211                 n=878               n=10696                   n=1
  450+                       5.37                  5.46                  5.46                  5.47                     -
                            n=886               n=12902                n=2423               n=20126                   n=0

  (e) fraction where |perp| GREW (moved further off the line)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  0.50                     -                  0.50                  0.63
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                    0.40                  0.40                  0.60                  0.52                  0.60
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                    0.50                  0.54                  0.52                  0.59                  0.77
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                    0.54                  0.57                  0.59                  0.60                  1.00
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                       0.56                  0.59                  0.60                  0.61                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

  OUTCOME hit rate (real server events)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                  0.67                     -                  0.50                  0.32
                              n=0                   n=6                   n=0                   n=2                  n=19
  100-200                    0.20                  0.30                  0.40                  0.39                  0.20
                              n=5                  n=53                   n=5                  n=23                 n=191
  200-300                    0.50                  0.18                  0.10                  0.16                  0.07
                              n=6                 n=130                  n=21                 n=780                  n=56
  300-450                    0.03                  0.11                  0.13                  0.12                  0.00
                            n=333                n=5272                 n=880               n=10696                   n=1
  450+                       0.01                  0.10                  0.09                  0.09                     -
                            n=950               n=12960                n=2424               n=20126                   n=0

--------------------------------------------------------------------------------------------------------
SHUFFLED-LABEL NULL  (labels permuted WITHIN each range band, 400 reps)
  For the arrival-dependent metrics the arrival tick is RE-DERIVED from the permuted power,
  so the null keeps the kinematic channel (a slower bullet really does arrive later) and destroys
  only the response.  p is the two-sided permutation p on delta = mean(HIGH) - mean(LOW) inside that band.
  miss              0-100 n/a  100-200 d=+5.354(null sd=7.077,p=0.893)  200-300 d=+0.348(null sd=4.611,p=0.389)  300-450 d=+5.913(null sd=1.285,p=0.274)  450+ d=+8.238(null sd=1.040,p=0.005)
  miss_per_tick     0-100 n/a  100-200 d=-0.354(null sd=0.692,p=0.623)  200-300 d=-0.342(null sd=0.332,p=0.524)  300-450 d=+0.026(null sd=0.064,p=0.010)  450+ d=-0.008(null sd=0.040,p=0.005)
  lat_disp_abs      0-100 n/a  100-200 d=+19.401(null sd=7.561,p=0.075)  200-300 d=+11.592(null sd=3.772,p=0.075)  300-450 d=+3.497(null sd=0.895,p=0.444)  450+ d=+5.865(null sd=0.679,p=0.005)
  flight            0-100 n/a  100-200 d=+1.473(null sd=0.557,p=0.584)  200-300 d=+1.553(null sd=0.209,p=0.319)  300-450 d=+1.349(null sd=0.044,p=0.005)  450+ d=+2.131(null sd=0.039,p=0.015)
  lat_fixed_abs     0-100 n/a  100-200 d=+16.205(null sd=6.822,p=0.020)  200-300 d=+2.890(null sd=2.739,p=0.269)  300-450 d=-1.453(null sd=0.521,p=0.005)  450+ d=-0.154(null sd=0.340,p=0.663)
  lat_ctrl_abs      0-100 n/a  100-200 d=+3.671(null sd=7.943,p=0.683)  200-300 d=+5.532(null sd=2.951,p=0.095)  300-450 d=-0.846(null sd=0.492,p=0.095)  450+ d=+0.610(null sd=0.339,p=0.080)
  latency           0-100 n/a  100-200 d=+0.093(null sd=1.210,p=0.898)  200-300 d=-1.349(null sd=0.628,p=0.035)  300-450 d=-0.094(null sd=0.145,p=0.484)  450+ d=+0.677(null sd=0.117,p=0.005)
  turn_fixed        0-100 n/a  100-200 d=+0.574(null sd=0.406,p=0.150)  200-300 d=+0.316(null sd=0.147,p=0.040)  300-450 d=+0.034(null sd=0.021,p=0.125)  450+ d=-0.148(null sd=0.012,p=0.005)
  turn_ctrl         0-100 n/a  100-200 d=+0.839(null sd=0.442,p=0.060)  200-300 d=+0.407(null sd=0.154,p=0.005)  300-450 d=+0.135(null sd=0.021,p=0.005)  450+ d=+0.064(null sd=0.014,p=0.005)
  speed_fixed       0-100 n/a  100-200 d=+0.086(null sd=0.533,p=0.913)  200-300 d=+0.021(null sd=0.177,p=0.853)  300-450 d=-0.050(null sd=0.033,p=0.135)  450+ d=-0.007(null sd=0.022,p=0.758)
  hit               0-100 n/a  100-200 d=+0.089(null sd=0.115,p=0.574)  200-300 d=-0.022(null sd=0.034,p=0.668)  300-450 d=+0.004(null sd=0.005,p=0.429)  450+ d=-0.013(null sd=0.003,p=0.005)

--------------------------------------------------------------------------------------------------------
FIXED-HORIZON TEST  (no arrival tick, no flight-window confound)
  |perpendicular offset of DrussGT from our aim line| at k ticks after the fire (flight window),
  and the same quantity in the CONTROL window at k+40 ticks, when the bullet is long gone.
  A response to our shot would be ~0 at k=5 and grow with k; a phase/geometry difference is
  present at k=5 and identical in the control.
  band 200-300   (nLOW=130 nHIGH=780 per k)
    k= 5  flight: LOW=   55.5 HIGH=   54.0 d= -1.50 | control(+40): LOW=  132.6 HIGH=  136.8 d= +4.11
    k=10  flight: LOW=   60.1 HIGH=   57.4 d= -2.76 | control(+40): LOW=  141.8 HIGH=  144.8 d= +3.00
    k=15  flight: LOW=   72.4 HIGH=   69.1 d= -3.28 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=20  flight: LOW=   83.8 HIGH=   82.5 d= -1.29 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=25  flight: LOW=   94.5 HIGH=   93.8 d= -0.69 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=30  flight: LOW=  104.2 HIGH=  105.2 d= +1.05 | control(+40): LOW=    nan HIGH=    nan d=  +nan
  band 300-450   (nLOW=5272 nHIGH=10696 per k)
    k= 5  flight: LOW=   80.1 HIGH=   82.8 d= +2.67 | control(+40): LOW=  140.1 HIGH=  141.5 d= +1.35
    k=10  flight: LOW=   80.3 HIGH=   83.4 d= +3.17 | control(+40): LOW=  145.8 HIGH=  146.7 d= +0.91
    k=15  flight: LOW=   87.9 HIGH=   91.4 d= +3.46 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=20  flight: LOW=   99.5 HIGH=  102.4 d= +2.95 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=25  flight: LOW=  111.0 HIGH=  113.5 d= +2.46 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=30  flight: LOW=  120.3 HIGH=  122.5 d= +2.20 | control(+40): LOW=    nan HIGH=    nan d=  +nan
  band 450+   (nLOW=12960 nHIGH=20126 per k)
    k= 5  flight: LOW=   94.9 HIGH=   99.1 d= +4.21 | control(+40): LOW=  144.2 HIGH=  149.7 d= +5.57
    k=10  flight: LOW=   95.0 HIGH=   98.9 d= +3.86 | control(+40): LOW=  147.8 HIGH=  153.1 d= +5.23
    k=15  flight: LOW=  100.7 HIGH=  104.3 d= +3.53 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=20  flight: LOW=  109.0 HIGH=  112.5 d= +3.50 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=25  flight: LOW=  118.7 HIGH=  122.6 d= +3.83 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=30  flight: LOW=  127.7 HIGH=  132.5 d= +4.74 | control(+40): LOW=    nan HIGH=    nan d=  +nan

--------------------------------------------------------------------------------------------------------
FLIGHT- *AND* RANGE-MATCHED CONTRAST  (kinematics and range both removed)
  Within each range band we compare LOW vs HIGH power only inside the SAME cell = (integer
  flight window, 50 px range sub-bin), pooling the per-cell differences with n weights.  A longer
  window lets DrussGT drift further off the line; at a fixed window a slower bullet implies a
  shorter range and the gun's aim error grows with range.  Anything left here is neither.
  band         obs d   n used     bins |    null sd    p_two         
  200-300     +19.25      480        7 |       5.28    0.005
  300-450     +38.59    15455       28 |       1.17    0.005
  450+        +59.05    29975       46 |       1.09    0.005

--------------------------------------------------------------------------------------------------------
HEADLINE WITHIN-BAND CONTRAST  LOW p in [0.50,0.75)  vs  HIGH p in [1.00,1.50)
  (HELD fixed inside each range band; 95%% CI from a ROUND-cluster bootstrap)

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  miss           0-100           6       2 |   (too few for a contrast)
  miss           100-200        53      23 |    43.03    47.92    +4.89 [-18.33,+31.08]
  miss           200-300       130     780 |    74.31    74.72    +0.40 [-11.42,+11.93]
  miss           300-450      5272   10696 |   104.67   110.55    +5.88 [+2.64,+9.07]
  miss           450+        12960   20126 |   124.01   132.26    +8.25 [+5.39,+11.25]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  miss_per_tick  0-100           6       2 |   (too few for a contrast)
  miss_per_tick  100-200        53      23 |     4.45     4.05    -0.40 [-2.84,+2.26]
  miss_per_tick  200-300       130     780 |     5.01     4.67    -0.34 [-1.16,+0.46]
  miss_per_tick  300-450      5272   10696 |     4.85     4.88    +0.03 [-0.13,+0.17]
  miss_per_tick  450+        12960   20126 |     4.52     4.51    -0.01 [-0.12,+0.10]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  lat_disp_abs   0-100           6       2 |   (too few for a contrast)
  lat_disp_abs   100-200        53      23 |    37.57    56.50   +18.93 [-3.78,+41.06]
  lat_disp_abs   200-300       130     780 |    59.91    71.56   +11.64 [-0.85,+25.19]
  lat_disp_abs   300-450      5272   10696 |    88.47    91.94    +3.47 [+0.78,+6.28]
  lat_disp_abs   450+        12960   20126 |    97.42   103.30    +5.88 [+3.44,+8.31]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  lat_disp_per_tick 0-100           6       2 |   (too few for a contrast)
  lat_disp_per_tick 100-200        53      23 |     3.44     4.76    +1.33 [-0.48,+3.23]
  lat_disp_per_tick 200-300       130     780 |     3.79     4.12    +0.33 [-0.39,+1.14]
  lat_disp_per_tick 300-450      5272   10696 |     3.94     3.86    -0.08 [-0.19,+0.03]
  lat_disp_per_tick 450+        12960   20126 |     3.47     3.42    -0.04 [-0.12,+0.03]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  lat_fixed_abs  0-100           6       2 |   (too few for a contrast)
  lat_fixed_abs  100-200        52      23 |    43.26    59.47   +16.21 [-4.15,+37.80]
  lat_fixed_abs  200-300       130     780 |    47.20    50.09    +2.89 [-5.91,+12.89]
  lat_fixed_abs  300-450      5272   10696 |    54.20    52.75    -1.45 [-2.96,+0.08]
  lat_fixed_abs  450+        12960   20126 |    55.63    55.47    -0.15 [-1.15,+0.84]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  lat_ctrl_abs   0-100           5       2 |   (too few for a contrast)
  lat_ctrl_abs   100-200        41      23 |    46.92    50.59    +3.67 [-19.55,+27.70]
  lat_ctrl_abs   200-300       127     780 |    43.68    49.21    +5.53 [-3.87,+15.33]
  lat_ctrl_abs   300-450      5155   10695 |    52.80    51.95    -0.85 [-2.20,+0.67]
  lat_ctrl_abs   450+        12828   20120 |    52.03    52.64    +0.61 [-0.38,+1.58]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  flight         0-100           6       2 |   (too few for a contrast)
  flight         100-200        53      23 |    10.42    11.87    +1.45 [-0.38,+3.14]
  flight         200-300       130     780 |    15.28    16.86    +1.58 [+0.96,+2.18]
  flight         300-450      5272   10696 |    22.36    23.70    +1.35 [+1.18,+1.52]
  flight         450+        12960   20126 |    28.38    30.52    +2.13 [+1.81,+2.44]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  latency        0-100           5       2 |   (too few for a contrast)
  latency        100-200        29      16 |     6.34     6.44    +0.09 [-4.23,+3.45]
  latency        200-300        78     566 |     9.03     7.68    -1.35 [-2.92,+0.21]
  latency        300-450      2968    6860 |    11.55    11.46    -0.09 [-0.47,+0.30]
  latency        450+         8682   13884 |    13.60    14.27    +0.68 [+0.36,+0.99]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  turn_flight    0-100           6       2 |   (too few for a contrast)
  turn_flight    100-200        53      23 |     2.01     2.86    +0.85 [-0.33,+2.21]
  turn_flight    200-300       130     780 |     2.08     2.49    +0.40 [-0.08,+0.92]
  turn_flight    300-450      5272   10696 |     1.48     1.61    +0.13 [+0.05,+0.21]
  turn_flight    450+        12960   20126 |     1.49     1.46    -0.03 [-0.09,+0.02]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  turn_fixed     0-100           6       2 |   (too few for a contrast)
  turn_fixed     100-200        53      23 |     2.09     2.66    +0.57 [-0.54,+1.89]
  turn_fixed     200-300       130     780 |     1.91     2.22    +0.32 [-0.15,+0.79]
  turn_fixed     300-450      5272   10696 |     1.46     1.50    +0.03 [-0.04,+0.11]
  turn_fixed     450+        12960   20126 |     1.43     1.28    -0.15 [-0.20,-0.10]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  turn_ctrl      0-100           5       2 |   (too few for a contrast)
  turn_ctrl      100-200        44      23 |     2.20     3.04    +0.84 [-0.35,+2.28]
  turn_ctrl      200-300       127     780 |     1.78     2.19    +0.41 [-0.04,+0.88]
  turn_ctrl      300-450      5211   10696 |     1.44     1.57    +0.13 [+0.05,+0.21]
  turn_ctrl      450+        12902   20126 |     1.52     1.58    +0.06 [+0.01,+0.12]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  speed_flight   0-100           6       2 |   (too few for a contrast)
  speed_flight   100-200        53      23 |     6.05     6.05    +0.00 [-1.80,+1.55]
  speed_flight   200-300       130     780 |     5.39     5.44    +0.05 [-0.51,+0.59]
  speed_flight   300-450      5272   10696 |     5.49     5.49    +0.01 [-0.08,+0.10]
  speed_flight   450+        12960   20126 |     5.46     5.48    +0.01 [-0.06,+0.08]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  speed_ctrl     0-100           5       2 |   (too few for a contrast)
  speed_ctrl     100-200        44      23 |     5.84     5.86    +0.01 [-1.55,+1.45]
  speed_ctrl     200-300       127     780 |     5.63     5.48    -0.16 [-0.82,+0.43]
  speed_ctrl     300-450      5211   10696 |     5.50     5.45    -0.05 [-0.14,+0.05]
  speed_ctrl     450+        12902   20126 |     5.46     5.47    +0.01 [-0.06,+0.09]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  hit            0-100           6       2 |   (too few for a contrast)
  hit            100-200        53      23 |     0.30     0.39    +0.09 [-0.33,+0.44]
  hit            200-300       130     780 |     0.18     0.16    -0.02 [-0.10,+0.05]
  hit            300-450      5272   10696 |     0.11     0.12    +0.00 [-0.01,+0.02]
  hit            450+        12960   20126 |     0.10     0.09    -0.01 [-0.02,-0.00]

  OUR fired-power histogram (exact values, top 12):
   1.00:31641  0.50:14182  0.10:627  0.51:222  0.55:203  0.53:195  0.60:193  0.58:192  0.59:192  0.62:190  0.54:189  0.57:184
========================================================================================================
CORPUS powtest     35 battles   245 rounds   24280 usable shots by US (ModularBot)
  attribution: owner id -> {e=DrussGT, s=us} recovered per battle from fire geometry+energy;
               cross-checked on the death events: 246/246 deaths have the mapped victim at ~0 energy
  (attribution is per-battle because the Tank Royale owner id is not stable across runs)

  >> THE CONFOUNDER IS REAL: our fired power is a range + energy cap
  band      power         shots   firePx      ourE    enemyE    flight
  100-200   1.00-1.50         8    179.5      77.7      79.5     13.25
  100-200   >=1.50           74    169.5      84.3      82.3     14.72
  200-300   0.50-0.75        16    262.3      21.6      33.5     15.44
  200-300   1.00-1.50       406    260.5      83.1      82.2     16.51
  200-300   >=1.50           17    246.1      37.9      22.0     21.00
  300-450   <0.50            51    410.0      30.7       2.7     21.00
  300-450   0.50-0.75      1388    412.6      14.4      17.9     22.36
  300-450   0.75-1.00       254    412.0      29.0      23.1     23.52
  300-450   1.00-1.50      8151    404.0      59.6      54.1     23.78
  450+      <0.50           115    533.7      18.7       1.7     26.86
  450+      0.50-0.75      2249    524.9      13.6      17.8     27.75
  450+      0.75-1.00       456    526.4      28.8      25.2     29.26
  450+      1.00-1.50     11085    525.3      52.6      46.0     29.93

  (a) MISS AT ARRIVAL px - perpendicular offset of DrussGT from our aim line
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                 28.34                 34.35
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                 58.35                     -                 32.74                 62.45
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                 70.50                 71.07                 73.03                112.28
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                  100.28                106.22                111.86                109.93                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                     131.41                122.00                130.11                131.86                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  (a') MISS AT ARRIVAL / flight ticks (px per tick - power-neutral)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  3.15                  2.89
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  7.29                     -                  2.51                  4.57
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                  4.86                  4.68                  4.68                  5.46
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                    4.93                  4.94                  4.96                  4.83                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                       5.02                  4.56                  4.64                  4.59                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  (b) LATERAL DISPLACEMENT px over the flight window
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                 50.56                 59.97
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  6.28                     -                 71.40                 63.01
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                 58.55                 61.90                 71.26                109.05
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                   68.90                 91.35                 94.37                 93.56                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                     104.97                 96.90                102.50                102.74                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  (b/ ) LATERAL DISPLACEMENT / flight ticks (px per tick - power-neutral)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  5.62                  5.11
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  0.78                     -                  5.34                  4.12
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                  3.70                  3.43                  4.22                  5.04
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                    3.29                  4.07                  4.00                  3.91                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                       3.93                  3.53                  3.54                  3.48                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  (b') LATERAL DISPLACEMENT px over a FIXED 12-tick window (power-neutral)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                 72.08                 63.83
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  3.66                     -                 63.36                 49.33
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                 41.73                 28.58                 50.71                 54.65
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                   46.10                 53.99                 54.21                 53.41                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                      61.58                 55.53                 56.08                 55.85                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  (b'') CONTROL: lateral displacement px, SAME shot, 40 ticks later (bullet gone)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  6.62                 55.92
                              n=0                   n=0                   n=0                   n=1                   n=3
  100-200                       -                 20.12                     -                 53.96                 51.68
                              n=0                   n=1                   n=0                   n=8                  n=69
  200-300                       -                 51.96                 42.95                 50.50                 46.25
                              n=0                  n=15                   n=3                 n=405                   n=9
  300-450                   39.77                 53.98                 53.45                 52.69                     -
                             n=43                n=1362                 n=252                n=8118                   n=0
  450+                      57.71                 52.62                 51.98                 53.00                     -
                             n=95                n=2212                 n=454               n=11037                   n=0

  (f) FLIGHT WINDOW LENGTH ticks (low power = FASTER bullet = shorter)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  9.00                 11.50
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  8.00                     -                 13.25                 14.72
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                 15.44                 16.67                 16.51                 21.00
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                   21.00                 22.36                 23.52                 23.78                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                      26.86                 27.75                 29.26                 29.93                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  (c) RESPONSE LATENCY ticks to a >15 deg heading turn
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  5.50                  4.00
                              n=0                   n=0                   n=0                   n=2                   n=3
  100-200                       -                  2.00                     -                  9.25                  7.40
                              n=0                   n=1                   n=0                   n=4                  n=53
  200-300                       -                  9.29                 10.50                  7.58                  9.21
                              n=0                   n=7                   n=2                 n=303                  n=14
  300-450                   11.86                 12.03                 13.06                 11.75                     -
                             n=22                 n=743                 n=152                n=5004                   n=0
  450+                      13.79                 13.89                 14.27                 14.36                     -
                             n=70                n=1457                 n=313                n=7615                   n=0

  (d) MEAN TURN RATE deg/tick, flight window
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  2.85                  3.72
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  3.76                     -                  1.52                  2.60
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                  1.86                  1.48                  2.49                  2.01
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                    1.28                  1.42                  1.43                  1.55                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                       1.42                  1.45                  1.41                  1.42                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  (d') MEAN TURN RATE deg/tick, fixed 12-tick window
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  2.98                  3.38
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  4.90                     -                  1.32                  2.41
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                  1.68                  1.29                  2.20                  2.38
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                    1.29                  1.39                  1.35                  1.43                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                       1.39                  1.40                  1.37                  1.25                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  (d'') CONTROL: mean turn rate deg/tick, 40 ticks later
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  4.12                  3.24
                              n=0                   n=0                   n=0                   n=1                   n=3
  100-200                       -                  4.93                     -                  2.58                  2.32
                              n=0                   n=1                   n=0                   n=8                  n=70
  200-300                       -                  1.96                  2.13                  2.24                  3.14
                              n=0                  n=15                   n=3                 n=405                  n=11
  300-450                    1.11                  1.39                  1.45                  1.55                     -
                             n=47                n=1377                 n=253                n=8135                   n=0
  450+                       1.34                  1.49                  1.45                  1.54                     -
                            n=105                n=2231                 n=455               n=11069                   n=0

  (d) MEAN SPEED px/tick, flight window
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  8.00                  7.01
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  2.25                     -                  6.77                  5.45
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                  5.16                  5.82                  5.48                  6.04
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                    4.81                  5.50                  5.56                  5.51                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                       5.74                  5.43                  5.54                  5.51                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  (d'') CONTROL: mean speed px/tick, 40 ticks later
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  4.08                  6.49
                              n=0                   n=0                   n=0                   n=1                   n=3
  100-200                       -                  4.08                     -                  5.97                  5.88
                              n=0                   n=1                   n=0                   n=8                  n=70
  200-300                       -                  5.50                  5.18                  5.61                  6.99
                              n=0                  n=15                   n=3                 n=405                  n=11
  300-450                    4.60                  5.54                  5.53                  5.47                     -
                             n=47                n=1377                 n=253                n=8135                   n=0
  450+                       5.66                  5.46                  5.47                  5.51                     -
                            n=105                n=2231                 n=455               n=11069                   n=0

  (e) fraction where |perp| GREW (moved further off the line)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  0.50                  0.50
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  1.00                     -                  0.25                  0.58
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                  0.56                  0.67                  0.58                  0.82
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                    0.55                  0.61                  0.59                  0.59                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                       0.59                  0.58                  0.58                  0.61                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

  OUTCOME hit rate (real server events)
  band                      <0.50             0.50-0.75             0.75-1.00             1.00-1.50                >=1.50
  0-100                         -                     -                     -                  0.50                  0.50
                              n=0                   n=0                   n=0                   n=2                   n=4
  100-200                       -                  0.00                     -                  0.50                  0.20
                              n=0                   n=1                   n=0                   n=8                  n=74
  200-300                       -                  0.19                  0.33                  0.16                  0.00
                              n=0                  n=16                   n=3                 n=406                  n=17
  300-450                    0.00                  0.12                  0.12                  0.12                     -
                             n=51                n=1388                 n=254                n=8151                   n=0
  450+                       0.02                  0.10                  0.10                  0.09                     -
                            n=115                n=2249                 n=456               n=11085                   n=0

--------------------------------------------------------------------------------------------------------
SHUFFLED-LABEL NULL  (labels permuted WITHIN each range band, 400 reps)
  For the arrival-dependent metrics the arrival tick is RE-DERIVED from the permuted power,
  so the null keeps the kinematic channel (a slower bullet really does arrive later) and destroys
  only the response.  p is the two-sided permutation p on delta = mean(HIGH) - mean(LOW) inside that band.
  miss              0-100 n/a  100-200 n/a  200-300 d=+3.592(null sd=12.030,p=0.993)  300-450 d=+3.788(null sd=2.135,p=0.793)  450+ d=+9.865(null sd=1.815,p=0.005)
  miss_per_tick     0-100 n/a  100-200 n/a  200-300 d=-0.124(null sd=0.878,p=0.948)  300-450 d=-0.100(null sd=0.107,p=0.514)  450+ d=+0.031(null sd=0.074,p=0.005)
  lat_disp_abs      0-100 n/a  100-200 n/a  200-300 d=+13.420(null sd=10.885,p=0.439)  300-450 d=+2.201(null sd=1.619,p=0.200)  450+ d=+5.908(null sd=1.474,p=0.160)
  flight            0-100 n/a  100-200 n/a  200-300 d=+1.200(null sd=0.588,p=0.933)  300-450 d=+1.419(null sd=0.071,p=0.005)  450+ d=+2.177(null sd=0.078,p=0.818)
  lat_fixed_abs     0-100 n/a  100-200 n/a  200-300 d=+8.977(null sd=6.784,p=0.195)  300-450 d=-0.580(null sd=0.874,p=0.484)  450+ d=+0.315(null sd=0.672,p=0.603)
  lat_ctrl_abs      0-100 n/a  100-200 n/a  200-300 d=-1.460(null sd=7.562,p=0.783)  300-450 d=-1.285(null sd=0.876,p=0.155)  450+ d=+0.386(null sd=0.653,p=0.519)
  latency           0-100 n/a  100-200 n/a  200-300 n/a  300-450 d=-0.285(null sd=0.258,p=0.279)  450+ d=+0.473(null sd=0.236,p=0.045)
  turn_fixed        0-100 n/a  100-200 n/a  200-300 d=+0.514(null sd=0.383,p=0.195)  300-450 d=+0.040(null sd=0.036,p=0.254)  450+ d=-0.157(null sd=0.027,p=0.005)
  turn_ctrl         0-100 n/a  100-200 n/a  200-300 d=+0.279(null sd=0.395,p=0.494)  300-450 d=+0.156(null sd=0.040,p=0.005)  450+ d=+0.052(null sd=0.027,p=0.055)
  speed_fixed       0-100 n/a  100-200 n/a  200-300 d=+0.331(null sd=0.467,p=0.504)  300-450 d=+0.029(null sd=0.055,p=0.648)  450+ d=+0.053(null sd=0.042,p=0.200)
  hit               0-100 n/a  100-200 n/a  200-300 d=-0.025(null sd=0.094,p=1.000)  300-450 d=-0.002(null sd=0.009,p=0.918)  450+ d=-0.007(null sd=0.006,p=0.344)

--------------------------------------------------------------------------------------------------------
FIXED-HORIZON TEST  (no arrival tick, no flight-window confound)
  |perpendicular offset of DrussGT from our aim line| at k ticks after the fire (flight window),
  and the same quantity in the CONTROL window at k+40 ticks, when the bullet is long gone.
  A response to our shot would be ~0 at k=5 and grow with k; a phase/geometry difference is
  present at k=5 and identical in the control.
  band 200-300   (nLOW=16 nHIGH=406 per k)
    k= 5  flight: LOW=   54.8 HIGH=   54.5 d= -0.24 | control(+40): LOW=  123.5 HIGH=  134.1 d=+10.56
    k=10  flight: LOW=   58.3 HIGH=   57.3 d= -1.02 | control(+40): LOW=  138.4 HIGH=  142.9 d= +4.52
    k=15  flight: LOW=   69.1 HIGH=   69.6 d= +0.52 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=20  flight: LOW=   77.8 HIGH=   83.8 d= +6.03 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=25  flight: LOW=   84.9 HIGH=   96.8 d=+11.83 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=30  flight: LOW=   98.6 HIGH=  108.8 d=+10.24 | control(+40): LOW=    nan HIGH=    nan d=  +nan
  band 300-450   (nLOW=1388 nHIGH=8151 per k)
    k= 5  flight: LOW=   78.4 HIGH=   84.0 d= +5.62 | control(+40): LOW=  143.3 HIGH=  141.4 d= -1.87
    k=10  flight: LOW=   79.1 HIGH=   84.0 d= +4.83 | control(+40): LOW=  149.7 HIGH=  147.2 d= -2.52
    k=15  flight: LOW=   88.3 HIGH=   91.5 d= +3.15 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=20  flight: LOW=  101.0 HIGH=  102.3 d= +1.29 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=25  flight: LOW=  112.2 HIGH=  112.9 d= +0.70 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=30  flight: LOW=  121.1 HIGH=  121.8 d= +0.60 | control(+40): LOW=    nan HIGH=    nan d=  +nan
  band 450+   (nLOW=2249 nHIGH=11085 per k)
    k= 5  flight: LOW=   93.0 HIGH=   99.0 d= +5.97 | control(+40): LOW=  143.7 HIGH=  150.3 d= +6.59
    k=10  flight: LOW=   93.3 HIGH=   99.1 d= +5.83 | control(+40): LOW=  147.7 HIGH=  153.8 d= +6.03
    k=15  flight: LOW=   99.4 HIGH=  104.9 d= +5.50 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=20  flight: LOW=  108.1 HIGH=  113.2 d= +5.12 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=25  flight: LOW=  118.3 HIGH=  123.5 d= +5.13 | control(+40): LOW=    nan HIGH=    nan d=  +nan
    k=30  flight: LOW=  126.7 HIGH=  133.3 d= +6.61 | control(+40): LOW=    nan HIGH=    nan d=  +nan

--------------------------------------------------------------------------------------------------------
FLIGHT- *AND* RANGE-MATCHED CONTRAST  (kinematics and range both removed)
  Within each range band we compare LOW vs HIGH power only inside the SAME cell = (integer
  flight window, 50 px range sub-bin), pooling the per-cell differences with n weights.  A longer
  window lets DrussGT drift further off the line; at a fixed window a slower bullet implies a
  shorter range and the gun's aim error grows with range.  Anything left here is neither.
  band         obs d   n used     bins |    null sd    p_two         
  300-450     +37.84     8588       23 |       2.32    0.005
  450+        +57.39    10809       34 |       2.31    0.005

--------------------------------------------------------------------------------------------------------
HEADLINE WITHIN-BAND CONTRAST  LOW p in [0.50,0.75)  vs  HIGH p in [1.00,1.50)
  (HELD fixed inside each range band; 95%% CI from a ROUND-cluster bootstrap)

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  miss           0-100           0       2 |   (too few for a contrast)
  miss           100-200         1       8 |   (too few for a contrast)
  miss           200-300        16     406 |    70.50    73.03    +2.53 [-12.34,+28.80]
  miss           300-450      1388    8151 |   106.22   109.93    +3.72 [-1.50,+8.65]
  miss           450+         2249   11085 |   122.00   131.86    +9.86 [+4.56,+15.25]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  miss_per_tick  0-100           0       2 |   (too few for a contrast)
  miss_per_tick  100-200         1       8 |   (too few for a contrast)
  miss_per_tick  200-300        16     406 |     4.86     4.68    -0.19 [-1.31,+1.76]
  miss_per_tick  300-450      1388    8151 |     4.94     4.83    -0.10 [-0.37,+0.15]
  miss_per_tick  450+         2249   11085 |     4.56     4.59    +0.03 [-0.19,+0.25]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  lat_disp_abs   0-100           0       2 |   (too few for a contrast)
  lat_disp_abs   100-200         1       8 |   (too few for a contrast)
  lat_disp_abs   200-300        16     406 |    58.55    71.26   +12.71 [-18.26,+36.16]
  lat_disp_abs   300-450      1388    8151 |    91.35    93.56    +2.21 [-2.02,+6.72]
  lat_disp_abs   450+         2249   11085 |    96.90   102.74    +5.84 [+1.65,+9.94]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  lat_disp_per_tick 0-100           0       2 |   (too few for a contrast)
  lat_disp_per_tick 100-200         1       8 |   (too few for a contrast)
  lat_disp_per_tick 200-300        16     406 |     3.70     4.22    +0.52 [-0.90,+1.65]
  lat_disp_per_tick 300-450      1388    8151 |     4.07     3.91    -0.16 [-0.32,+0.02]
  lat_disp_per_tick 450+         2249   11085 |     3.53     3.48    -0.05 [-0.20,+0.11]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  lat_fixed_abs  0-100           0       2 |   (too few for a contrast)
  lat_fixed_abs  100-200         1       8 |   (too few for a contrast)
  lat_fixed_abs  200-300        16     406 |    41.73    50.71    +8.98 [-11.36,+23.25]
  lat_fixed_abs  300-450      1388    8151 |    53.99    53.41    -0.58 [-3.07,+1.89]
  lat_fixed_abs  450+         2249   11085 |    55.53    55.85    +0.31 [-1.24,+1.87]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  lat_ctrl_abs   0-100           0       1 |   (too few for a contrast)
  lat_ctrl_abs   100-200         1       8 |   (too few for a contrast)
  lat_ctrl_abs   200-300        15     405 |    51.96    50.50    -1.46 [-21.67,+14.83]
  lat_ctrl_abs   300-450      1362    8118 |    53.98    52.69    -1.29 [-3.11,+0.47]
  lat_ctrl_abs   450+         2212   11037 |    52.62    53.00    +0.39 [-0.83,+1.57]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  flight         0-100           0       2 |   (too few for a contrast)
  flight         100-200         1       8 |   (too few for a contrast)
  flight         200-300        16     406 |    15.44    16.51    +1.07 [-0.61,+2.99]
  flight         300-450      1388    8151 |    22.36    23.78    +1.42 [+1.15,+1.68]
  flight         450+         2249   11085 |    27.75    29.93    +2.18 [+1.63,+2.73]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  latency        0-100           0       2 |   (too few for a contrast)
  latency        100-200         1       4 |   (too few for a contrast)
  latency        200-300         7     303 |   (too few for a contrast)
  latency        300-450       743    5004 |    12.03    11.75    -0.29 [-0.81,+0.25]
  latency        450+         1457    7615 |    13.89    14.36    +0.47 [-0.15,+1.14]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  turn_flight    0-100           0       2 |   (too few for a contrast)
  turn_flight    100-200         1       8 |   (too few for a contrast)
  turn_flight    200-300        16     406 |     1.86     2.49    +0.62 [+0.33,+1.09]
  turn_flight    300-450      1388    8151 |     1.42     1.55    +0.13 [+0.04,+0.23]
  turn_flight    450+         2249   11085 |     1.45     1.42    -0.03 [-0.13,+0.06]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  turn_fixed     0-100           0       2 |   (too few for a contrast)
  turn_fixed     100-200         1       8 |   (too few for a contrast)
  turn_fixed     200-300        16     406 |     1.68     2.20    +0.51 [+0.11,+1.18]
  turn_fixed     300-450      1388    8151 |     1.39     1.43    +0.04 [-0.06,+0.15]
  turn_fixed     450+         2249   11085 |     1.40     1.25    -0.16 [-0.26,-0.06]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  turn_ctrl      0-100           0       1 |   (too few for a contrast)
  turn_ctrl      100-200         1       8 |   (too few for a contrast)
  turn_ctrl      200-300        15     405 |     1.96     2.24    +0.28 [-0.78,+0.97]
  turn_ctrl      300-450      1377    8135 |     1.39     1.55    +0.16 [+0.04,+0.28]
  turn_ctrl      450+         2231   11069 |     1.49     1.54    +0.05 [-0.06,+0.15]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  speed_flight   0-100           0       2 |   (too few for a contrast)
  speed_flight   100-200         1       8 |   (too few for a contrast)
  speed_flight   200-300        16     406 |     5.16     5.48    +0.31 [-0.96,+1.28]
  speed_flight   300-450      1388    8151 |     5.50     5.51    +0.01 [-0.13,+0.14]
  speed_flight   450+         2249   11085 |     5.43     5.51    +0.08 [-0.02,+0.19]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  speed_ctrl     0-100           0       1 |   (too few for a contrast)
  speed_ctrl     100-200         1       8 |   (too few for a contrast)
  speed_ctrl     200-300        15     405 |     5.50     5.61    +0.11 [-0.78,+1.18]
  speed_ctrl     300-450      1377    8135 |     5.54     5.47    -0.07 [-0.20,+0.07]
  speed_ctrl     450+         2231   11069 |     5.46     5.51    +0.05 [-0.06,+0.15]

  metric         band         nLOW   nHIGH |      LOW     HIGH    delta   95% CI
  hit            0-100           0       2 |   (too few for a contrast)
  hit            100-200         1       8 |   (too few for a contrast)
  hit            200-300        16     406 |     0.19     0.16    -0.02 [-0.17,+0.20]
  hit            300-450      1388    8151 |     0.12     0.12    -0.00 [-0.03,+0.02]
  hit            450+         2249   11085 |     0.10     0.09    -0.01 [-0.02,+0.01]

  OUR fired-power histogram (exact values, top 12):
   1.00:19653  0.50:2760  2.00:64  0.62:61  0.90:56  0.52:56  0.10:56  0.57:54  0.59:53  0.67:49  0.65:47  0.64:44
