# Expected values for the two essays.  Format:  key = value  tol
# Calibration: strong archer anchored at 692/720.

sigma_692_cm        = 4.33   0.03
sigma_700_cm        = 3.78   0.03
sigma_630_cm        = 8.52   0.03

picco_costo_pp      = 2.32   0.02
picco_avversario    = 675    1.0

costo_700_pp        = 1.99   0.05
costo_690_pp        = 2.38   0.05
costo_680_pp        = 2.63   0.05
costo_670_pp        = 2.82   0.05
costo_660_pp        = 2.97   0.05

scomp_totale_pp     = 2.32   0.02
scomp_regola_pp     = 0.50   0.05
scomp_frecce_extra_pp = 1.82   0.05
durata_frecce       = 12.8   0.1
durata_set          = 4.27   0.03

paradosso_actual_pc = 7.1    0.15
paradosso_15_pc     = 7.6    0.15

# table of the shapes at the stated pairing 692 vs 675 (not at the symmetric peak):
# the isotropic shape coincides with the peak of the cost (2.32), a single pairing, no inconsistency.
forma_isotropo_pp   = 2.32   0.05
forma_hoyt_pp       = 2.34   0.05
forma_rice_pp       = 2.36   0.05
forma_mistura_pp    = 0.68   0.05

spareggio_050_pp    = 2.96   0.05
spareggio_055_pp    = 2.67   0.05
spareggio_060_pp    = 2.39   0.05
spareggio_065_pp    = 2.14   0.05

# central density AT THE PAIRING 692 vs 675, from the pure circular model (X = strong archer).
# STATED convention: equal-increment (both archers densified by the same Δ above
# their natural X-rate), w=0.5, iso-equivalent shoot-off. Version v2 of the
# essay adopts this same convention and these same values.
densita_X22_pp      = 2.320  0.02   # = peak of the cost (pure circular), consistent
densita_X24_pp      = 2.532  0.02
densita_X26_pp      = 2.743  0.02
densita_X28_pp      = 2.943  0.02
densita_X30_pp      = 3.127  0.02

sd_differenza_pt    = 6.30   0.05
distacco_95_pt      = 10.4   0.1

campo_concavo_set   = 30.9   0.2
campo_lineare_set   = 42.5   0.2
campo_convesso_set  = 58.4   0.2
campo_sigmoide_set  = 31.1   0.2
campo_concavo_cum   = 34.5   0.2
campo_lineare_cum   = 46.7   0.2
campo_convesso_cum  = 62.7   0.2
campo_sigmoide_cum  = 34.4   0.2

# --- general-readership numbers from the "Theory" essay (same calibration, same engine) ---
# composition of the group: σ and expected tens at two reference levels
sigma_690_cm        = 4.46   0.05   # essay "four and a half centimetres"
dieci_690           = 43.5   1.0    # essay "about six arrows in ten" -> ~0.60·72
sigma_650_cm        = 7.17   0.05   # essay "just over seven centimetres"
dieci_650           = 21.5   1.5    # essay "three in ten" -> ~0.30·72
# shoot-off 690 vs 665
spareggio_690_665   = 0.655  0.01   # essay "just over 65 in 100"
# paradox between equals, moving down in level
paradosso_670_pc    = 9.2    0.2    # essay "already 9.2 per cent"
paradosso_650_pc    = 10.3   0.3    # essay "from 650 on it goes above ten"
# paradox AT THE PEAK (692 vs 675): the only case with an asymmetric shoot-off (p_so=0.6157).
# With the closed form: 4.746/5.164 (essay). With the p_so=0.5 bug it would give 5.25/5.66.
paradosso_picco_actual_pc = 4.746  0.02   # essay 4.746
paradosso_picco_15_pc     = 5.164  0.02   # essay 5.164
# average margin of a set won (pairing 692 vs 675)
margine_set_pt      = 1.76   0.03   # essay "by 1.76 points on average"
# sweep over the number of sets (5 sets = peak 2.32, already above)
sweep_3set_pp       = 1.84   0.05   # essay "three sets against nine arrows: 1.84"
sweep_7set_pp       = 2.38   0.05   # essay "seven sets against twenty-one: 2.38"
# consistency: regular (iso) vs irregular (mixture) at equal mean
costanza_cum_pc     = 48.5   0.3    # essay "under the cumulative format the regular archer wins 48.5%"
costanza_set_pc     = 45.4   0.3    # essay "under the set system it drops to 45.4%"
# confidence in the true ordering = Φ(gap / sd), sd = 6.30
conf_1pt_pc         = 56.0   0.7    # essay 56%
conf_3pt_pc         = 68.0   0.7    # essay 68%
conf_5pt_pc         = 79.0   0.7    # essay 79%
conf_8pt_pc         = 90.0   0.7    # essay 90%
conf_12pt_pc        = 97.0   0.7    # essay 97%
conf_16pt_pc        = 99.0   0.7    # essay 99%
# diagnostic quantities cited in the essay (not printed before)
pendenza_cm_punto   = 0.0677 0.002  # essay 0.0676 cm/point (mean 700..630)
delta_mu_picco      = 0.236  0.002  # essay Δμ 0.236
distacco_medio_pt   = 5.03   0.03   # essay 5.03 points (= sd·√(2/π))
ellisse_non_rical_pt= 675.2  1.0    # essay "a 692 stretched 1.5:1 is worth 675"

# --- uncertainty of the inversion from a single observed round (essay, section "From a
# score to a spread": "leaves the spread undetermined to within more than a centimetre") ---
sd_round_690_pt     = 4.58   0.05
sigma_690_lo_cm     = 3.85   0.03
sigma_690_hi_cm     = 5.07   0.03

# --- values cited in the essay and in the appendix (addition) ---
cinque_pari_pari_pc     = 20.5036    0.4101 
costo_gap25_pp          = 1.9680     0.0394 
costo_gap2_pp           = 0.4729     0.0095 
costo_gap35_pp          = 1.1917     0.0238 
costo_gap45_pp          = 0.5968     0.0119 
costo_gap5_pp           = 1.1323     0.0226 
dieci_692_su72          = 45.3590    0.9072 
ellisse_perdita_690_pt  = 17.3233    0.3465 
fuori_dieci_690         = 0.3927     0.0079 
margine_set_pari_pt     = 1.4099     0.0282 
mu_650                  = 9.0278     0.1806 
mu_690                  = 9.5833     0.1917 
p10_690_pc              = 60.7330    1.2147 
p8_690_pc               = 2.3553     0.0471 
p9_690_pc               = 36.8895    0.7378 
paradosso_gap25_pc      = 2.9936     0.0599 
paradosso_gap35_pc      = 1.4567     0.0291 
pi_cum15_picco          = 0.8700     0.0174 
pi_set_picco            = 0.8468     0.0169 
raggio_95_690_cm        = 10.9201    0.2184 
raggio_mediano_690_cm   = 5.2527     0.1051 
raggio_medio_690_cm     = 5.5914     0.1118 
scomp_media_durate_pp   = 0.3181     0.0064 
spareggio_picco_pc      = 61.5698    1.2314 
sweep_13set_pp          = 1.8498     0.0370 
sweep_1set_pp           = 0.0000     0.0050 
sweep_21set_cum_pc      = 98.8489    1.9770 
sweep_21set_pp          = 1.0354     0.0207 
sweep_21set_set_pc      = 97.8135    1.9563 
sweep_9set_pp           = 2.2678     0.0454 
volee_30_forte_pc       = 25.0030    0.5001 
volee_30_sfid_pc        = 9.8840     0.1977 
volee_pari_pc           = 24.6514    0.4930 
volee_persa_pc          = 19.8113    0.3962 
volee_vinta_pc          = 55.5374    1.1107 
x_692_su72              = 15.8452    0.3169 
rapporto_modulo_sd_pc   = 79.7885    0.0500 
taglio_linea_690_pt     = 691.2399   0.1500 

# --- derived values cited in prose in the essay (addition) ---
densita_incremento_pp   = 0.8072     0.0161 
frecce_extra            = 2.1964     0.0439 
varianza_freccia_692    = 0.2757     0.0055 
x_rate_692_pc           = 22.0072    0.4401 
sd_round_692_pt         = 4.4551     0.0891 

# --- how many rounds it takes to demonstrate an improvement (addition) ---
round_650_delta10       = 3.0000     0.0010 
round_650_delta15       = 2.0000     0.0010 
round_650_delta3        = 29.0000    0.0010 
round_650_delta5        = 11.0000    0.0010 
round_650_delta8        = 5.0000     0.0010 
round_690_delta10       = 2.0000     0.0010 
round_690_delta15       = 1.0000     0.0010 
round_690_delta3        = 13.0000    0.0010 
round_690_delta5        = 5.0000     0.0010 
round_690_delta8        = 2.0000     0.0010 
soglia_medie_12round_pt = 4.6606     0.0932 
soglia_medie_1round_pt  = 16.1449    0.3229 
soglia_medie_4round_pt  = 8.0724     0.1614 
soglia_medie_9round_pt  = 5.3816     0.1076 

# --- redistribution of the gold medal across the seeds (addition) ---
oro_concavo_seed2_8_cum = 43.4007    0.8680 
oro_concavo_seed2_8_set = 43.7650    0.8753 
oro_concavo_seed9_32_cum= 22.1308    0.4426 
oro_concavo_seed9_32_set= 25.2760    0.5055 
oro_convesso_seed2_8_cum= 36.3307    0.7266 
oro_convesso_seed2_8_set= 39.7580    0.7952 
oro_convesso_seed9_32_cum= 1.0049     0.0201 
oro_convesso_seed9_32_set= 1.8507     0.0370 
oro_lineare_seed2_8_cum = 46.5462    0.9309 
oro_lineare_seed2_8_set = 48.4603    0.9692 
oro_lineare_seed9_32_cum= 6.7336     0.1347 
oro_lineare_seed9_32_set= 8.9907     0.1798 
oro_sigmoide_seed2_8_cum= 43.6625    0.8732 
oro_sigmoide_seed2_8_set= 44.1467    0.8829 
oro_sigmoide_seed9_32_cum= 21.8967    0.4379 
oro_sigmoide_seed9_32_set= 24.7420    0.4948 
redistr_lineare_seed1_pp  = -4.1729    0.0835 
redistr_lineare_seed2_8_pp= 1.9141     0.0383 
redistr_lineare_seed9_32_pp= 2.2571     0.0451 
