FA-62871 / Insurance premium rating / Open access

Workers compensation experience modification: Primary losses are split on the aggregate instead of per claim · case 01

Several moderate claims are treated as mostly excess, understating the mod.

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ROOT CAUSE

The split point is applied once to total losses rather than to each claim.

VERIFIED REPAIR

Split every claim at the split point and sum the primary parts.

Unsuccessful approach: Scaling the aggregate cap by claim count still lets large claims borrow unused primary room from small ones.

Case contract

Input expected (cents, >0 else 'invalid expected'), split, weight W (per mille), primary_ratio (per mille of expected that is primary), ballast B, claims [[amount, 'ind'|'med']]. Medical-only claims count at 30%. Each claim splits into primary min(v,split) and excess. mod=(Ap+W*Ae+(1-W)*Ee+B)/(E+B), returned in hundredths rounded half-up.

Why this case matters

Experience rating multiplies manual premium, so a wrong split, weight or reduction shifts an employer's premium.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    E=x['expected']
    if E<=0: return 'invalid expected'
    S=x['split']; W=Fraction(x['weight'],1000)
    vals=[Fraction(amt)*Fraction(30,100) if kind=='med' else Fraction(amt) for amt,kind in x['claims']]
    ap=min(sum(vals),S)
    ae=sum(vals)-ap
    ep=Fraction(E*x['primary_ratio'],1000); ee=E-ep
    B=x['ballast']
    mod=(ap+W*ae+(1-W)*ee+B)/(E+B)
    return int(mod*100+Fraction(1,2))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mixed claim history 0', {'expected': 311400, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[33740, 'ind'], [37448, 'ind'], [55230, 'ind'], [10817, 'med']]}, 78], ['mixed claim history 1', {'expected': 767200, 'split': 17000, 'weight': 150, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[42590, 'med'], [38435, 'med'], [27276, 'ind'], [26563, 'med'], [15138, 'ind'], [4744, 'ind'], [87257, 'ind'], [10244, 'med']]}, 75], ['mixed claim history 2', {'expected': 858400, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[54743, 'med'], [57687, 'ind'], [5771, 'med'], [32069, 'ind'], [9463, 'med']]}, 62], ['mixed claim history 3', {'expected': 677800, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[20283, 'ind'], [10778, 'ind'], [6643, 'med'], [45395, 'med'], [59048, 'ind'], [5648, 'med']]}, 64], ['mixed claim history 4', {'expected': 650900, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[37467, 'ind'], [13425, 'med'], [17798, 'ind'], [25433, 'ind'], [13608, 'med']]}, 63], ['mixed claim history 5', {'expected': 447400, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[41535, 'ind'], [48038, 'ind'], [32890, 'ind'], [5200, 'med']]}, 75], ['large medical-only claim', {'expected': 323600, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[101990, 'med'], [5314, 'ind']]}, 62], ['claim free risk', {'expected': 867900, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 50000, 'claims': []}, 48], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 797000, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[11195, 'ind'], [36197, 'ind']]}, 63]], [['mixed claim history 0', {'expected': 316700, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[10286, 'med'], [40310, 'med'], [26393, 'ind'], [5424, 'med']]}, 65], ['mixed claim history 1', {'expected': 859500, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[23316, 'med'], [15025, 'ind'], [57735, 'ind'], [16008, 'ind'], [45146, 'ind'], [11487, 'med'], [60418, 'ind'], [6233, 'med']]}, 72], ['mixed claim history 2', {'expected': 896000, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[21038, 'ind'], [5062, 'ind'], [14527, 'med'], [1264, 'med'], [4935, 'med'], [56017, 'ind'], [59572, 'ind'], [6562, 'med']]}, 67], ['mixed claim history 3', {'expected': 779700, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[57322, 'ind'], [16107, 'med'], [20840, 'med'], [82520, 'ind'], [5448, 'med']]}, 59], ['mixed claim history 4', {'expected': 827000, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[31790, 'ind'], [13488, 'ind'], [71208, 'ind'], [13222, 'med']]}, 67], ['mixed claim history 5', {'expected': 464000, 'split': 17000, 'weight': 150, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[17834, 'ind'], [18093, 'med'], [30643, 'med'], [29993, 'med'], [55402, 'med'], [31809, 'ind'], [13749, 'med']]}, 80], ['large medical-only claim', {'expected': 469100, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[101036, 'med'], [5613, 'ind']]}, 65], ['claim free risk', {'expected': 687800, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': []}, 53], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 721000, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[15423, 'ind'], [31956, 'ind']]}, 57]], [['mixed claim history 0', {'expected': 610400, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[53344, 'ind'], [48923, 'ind'], [52350, 'ind'], [50819, 'ind'], [10135, 'ind'], [12464, 'ind'], [67060, 'ind'], [12311, 'med']]}, 77], ['mixed claim history 1', {'expected': 402300, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[17334, 'ind'], [22438, 'ind'], [22151, 'med'], [26026, 'ind'], [7894, 'med']]}, 65], ['mixed claim history 2', {'expected': 498400, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[48132, 'ind'], [8715, 'ind'], [59441, 'ind'], [20248, 'med'], [17905, 'ind'], [58937, 'med'], [80627, 'ind'], [7990, 'med']]}, 82], ['mixed claim history 3', {'expected': 464700, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[13610, 'ind'], [3088, 'ind'], [43730, 'ind'], [8434, 'med']]}, 65], ['mixed claim history 4', {'expected': 879300, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[13389, 'ind'], [32420, 'med'], [20542, 'ind'], [47517, 'ind'], [16287, 'ind'], [82017, 'ind'], [9410, 'med']]}, 67], ['mixed claim history 5', {'expected': 652900, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[22810, 'ind'], [40463, 'ind'], [74251, 'ind'], [9218, 'med']]}, 67], ['large medical-only claim', {'expected': 703800, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[84297, 'med'], [2962, 'ind']]}, 62], ['claim free risk', {'expected': 479000, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 80000, 'claims': []}, 59], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 447500, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[11462, 'ind'], [38751, 'ind']]}, 66]], [['mixed claim history 0', {'expected': 688800, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[56711, 'ind'], [12536, 'med'], [30221, 'ind'], [51849, 'ind'], [13637, 'med']]}, 62], ['mixed claim history 1', {'expected': 402400, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[14109, 'med'], [42085, 'ind'], [59677, 'ind'], [55680, 'ind'], [6934, 'med']]}, 78], ['mixed claim history 2', {'expected': 773600, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[11209, 'med'], [26799, 'ind'], [10934, 'med'], [16129, 'ind'], [11873, 'ind'], [52155, 'ind'], [10727, 'med']]}, 70], ['mixed claim history 3', {'expected': 741200, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[53124, 'ind'], [16325, 'ind'], [4833, 'ind'], [21033, 'ind'], [6837, 'ind'], [38580, 'ind'], [55554, 'ind'], [13784, 'med']]}, 71], ['mixed claim history 4', {'expected': 331500, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[10786, 'ind'], [17213, 'med'], [39824, 'med'], [24282, 'ind'], [51513, 'ind'], [63075, 'ind'], [10156, 'med']]}, 86], ['mixed claim history 5', {'expected': 409600, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[54286, 'ind'], [35703, 'ind'], [30503, 'med'], [59058, 'ind'], [56149, 'med'], [41950, 'ind'], [41088, 'ind'], [8047, 'med']]}, 92], ['large medical-only claim', {'expected': 831400, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[107249, 'med'], [3434, 'ind']]}, 54], ['claim free risk', {'expected': 597500, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 80000, 'claims': []}, 55], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 770300, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[13951, 'ind'], [35547, 'ind']]}, 55]], [['mixed claim history 0', {'expected': 303600, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[20599, 'ind'], [56506, 'ind'], [28670, 'ind'], [70657, 'ind'], [13633, 'med']]}, 88], ['mixed claim history 1', {'expected': 729600, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[14990, 'med'], [18865, 'ind'], [35152, 'ind'], [37220, 'med'], [45354, 'ind'], [6673, 'med']]}, 59], ['mixed claim history 2', {'expected': 697600, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[36216, 'ind'], [18993, 'ind'], [14909, 'ind'], [50234, 'med'], [88465, 'ind'], [7853, 'med']]}, 70], ['mixed claim history 3', {'expected': 334500, 'split': 17000, 'weight': 150, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[8211, 'ind'], [19267, 'med'], [4256, 'med'], [47071, 'ind'], [74176, 'ind'], [8958, 'med']]}, 83], ['mixed claim history 4', {'expected': 758400, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[24450, 'med'], [45271, 'ind'], [32248, 'med'], [53086, 'ind'], [11516, 'med']]}, 67], ['mixed claim history 5', {'expected': 883600, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[42495, 'ind'], [9679, 'ind'], [36464, 'ind'], [26823, 'ind'], [63484, 'ind'], [12267, 'med']]}, 63], ['large medical-only claim', {'expected': 318100, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[102133, 'med'], [5058, 'ind']]}, 68], ['claim free risk', {'expected': 634700, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': []}, 60], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 457400, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[12750, 'ind'], [32633, 'ind']]}, 65]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
mixed claim history 0	`70`	`78`	Failed
mixed claim history 1	`68`	`75`	Failed
mixed claim history 2	`58`	`62`	Failed
mixed claim history 3	`59`	`64`	Failed
mixed claim history 4	`58`	`63`	Failed
mixed claim history 5	`70`	`75`	Failed
large medical-only claim	`61`	`62`	Failed
claim free risk	`48`	`48`	Passed
invalid expected losses	`invalid expected`	`invalid expected`	Passed
mod rounding near half point	`62`	`63`	Failed

SHA-256 / 3c2b75d3b040d1c3b6094ceb569feab128d7d2f359abb9bddc48275d0e0914f0

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    E=x['expected']
    if E<=0: return 'invalid expected'
    S=x['split']; W=Fraction(x['weight'],1000)
    vals=[Fraction(amt)*Fraction(30,100) if kind=='med' else Fraction(amt) for amt,kind in x['claims']]
    ap=min(sum(vals),S*len(vals))
    ae=sum(vals)-ap
    ep=Fraction(E*x['primary_ratio'],1000); ee=E-ep
    B=x['ballast']
    mod=(ap+W*ae+(1-W)*ee+B)/(E+B)
    return int(mod*100+Fraction(1,2))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mixed claim history 0', {'expected': 311400, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[33740, 'ind'], [37448, 'ind'], [55230, 'ind'], [10817, 'med']]}, 78], ['mixed claim history 1', {'expected': 767200, 'split': 17000, 'weight': 150, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[42590, 'med'], [38435, 'med'], [27276, 'ind'], [26563, 'med'], [15138, 'ind'], [4744, 'ind'], [87257, 'ind'], [10244, 'med']]}, 75], ['mixed claim history 2', {'expected': 858400, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[54743, 'med'], [57687, 'ind'], [5771, 'med'], [32069, 'ind'], [9463, 'med']]}, 62], ['mixed claim history 3', {'expected': 677800, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[20283, 'ind'], [10778, 'ind'], [6643, 'med'], [45395, 'med'], [59048, 'ind'], [5648, 'med']]}, 64], ['mixed claim history 4', {'expected': 650900, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[37467, 'ind'], [13425, 'med'], [17798, 'ind'], [25433, 'ind'], [13608, 'med']]}, 63], ['mixed claim history 5', {'expected': 447400, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[41535, 'ind'], [48038, 'ind'], [32890, 'ind'], [5200, 'med']]}, 75], ['large medical-only claim', {'expected': 323600, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[101990, 'med'], [5314, 'ind']]}, 62], ['claim free risk', {'expected': 867900, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 50000, 'claims': []}, 48], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 797000, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[11195, 'ind'], [36197, 'ind']]}, 63]], [['mixed claim history 0', {'expected': 316700, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[10286, 'med'], [40310, 'med'], [26393, 'ind'], [5424, 'med']]}, 65], ['mixed claim history 1', {'expected': 859500, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[23316, 'med'], [15025, 'ind'], [57735, 'ind'], [16008, 'ind'], [45146, 'ind'], [11487, 'med'], [60418, 'ind'], [6233, 'med']]}, 72], ['mixed claim history 2', {'expected': 896000, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[21038, 'ind'], [5062, 'ind'], [14527, 'med'], [1264, 'med'], [4935, 'med'], [56017, 'ind'], [59572, 'ind'], [6562, 'med']]}, 67], ['mixed claim history 3', {'expected': 779700, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[57322, 'ind'], [16107, 'med'], [20840, 'med'], [82520, 'ind'], [5448, 'med']]}, 59], ['mixed claim history 4', {'expected': 827000, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[31790, 'ind'], [13488, 'ind'], [71208, 'ind'], [13222, 'med']]}, 67], ['mixed claim history 5', {'expected': 464000, 'split': 17000, 'weight': 150, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[17834, 'ind'], [18093, 'med'], [30643, 'med'], [29993, 'med'], [55402, 'med'], [31809, 'ind'], [13749, 'med']]}, 80], ['large medical-only claim', {'expected': 469100, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[101036, 'med'], [5613, 'ind']]}, 65], ['claim free risk', {'expected': 687800, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': []}, 53], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 721000, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[15423, 'ind'], [31956, 'ind']]}, 57]], [['mixed claim history 0', {'expected': 610400, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[53344, 'ind'], [48923, 'ind'], [52350, 'ind'], [50819, 'ind'], [10135, 'ind'], [12464, 'ind'], [67060, 'ind'], [12311, 'med']]}, 77], ['mixed claim history 1', {'expected': 402300, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[17334, 'ind'], [22438, 'ind'], [22151, 'med'], [26026, 'ind'], [7894, 'med']]}, 65], ['mixed claim history 2', {'expected': 498400, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[48132, 'ind'], [8715, 'ind'], [59441, 'ind'], [20248, 'med'], [17905, 'ind'], [58937, 'med'], [80627, 'ind'], [7990, 'med']]}, 82], ['mixed claim history 3', {'expected': 464700, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[13610, 'ind'], [3088, 'ind'], [43730, 'ind'], [8434, 'med']]}, 65], ['mixed claim history 4', {'expected': 879300, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[13389, 'ind'], [32420, 'med'], [20542, 'ind'], [47517, 'ind'], [16287, 'ind'], [82017, 'ind'], [9410, 'med']]}, 67], ['mixed claim history 5', {'expected': 652900, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[22810, 'ind'], [40463, 'ind'], [74251, 'ind'], [9218, 'med']]}, 67], ['large medical-only claim', {'expected': 703800, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[84297, 'med'], [2962, 'ind']]}, 62], ['claim free risk', {'expected': 479000, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 80000, 'claims': []}, 59], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 447500, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[11462, 'ind'], [38751, 'ind']]}, 66]], [['mixed claim history 0', {'expected': 688800, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[56711, 'ind'], [12536, 'med'], [30221, 'ind'], [51849, 'ind'], [13637, 'med']]}, 62], ['mixed claim history 1', {'expected': 402400, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[14109, 'med'], [42085, 'ind'], [59677, 'ind'], [55680, 'ind'], [6934, 'med']]}, 78], ['mixed claim history 2', {'expected': 773600, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[11209, 'med'], [26799, 'ind'], [10934, 'med'], [16129, 'ind'], [11873, 'ind'], [52155, 'ind'], [10727, 'med']]}, 70], ['mixed claim history 3', {'expected': 741200, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[53124, 'ind'], [16325, 'ind'], [4833, 'ind'], [21033, 'ind'], [6837, 'ind'], [38580, 'ind'], [55554, 'ind'], [13784, 'med']]}, 71], ['mixed claim history 4', {'expected': 331500, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[10786, 'ind'], [17213, 'med'], [39824, 'med'], [24282, 'ind'], [51513, 'ind'], [63075, 'ind'], [10156, 'med']]}, 86], ['mixed claim history 5', {'expected': 409600, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[54286, 'ind'], [35703, 'ind'], [30503, 'med'], [59058, 'ind'], [56149, 'med'], [41950, 'ind'], [41088, 'ind'], [8047, 'med']]}, 92], ['large medical-only claim', {'expected': 831400, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[107249, 'med'], [3434, 'ind']]}, 54], ['claim free risk', {'expected': 597500, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 80000, 'claims': []}, 55], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 770300, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[13951, 'ind'], [35547, 'ind']]}, 55]], [['mixed claim history 0', {'expected': 303600, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[20599, 'ind'], [56506, 'ind'], [28670, 'ind'], [70657, 'ind'], [13633, 'med']]}, 88], ['mixed claim history 1', {'expected': 729600, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[14990, 'med'], [18865, 'ind'], [35152, 'ind'], [37220, 'med'], [45354, 'ind'], [6673, 'med']]}, 59], ['mixed claim history 2', {'expected': 697600, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[36216, 'ind'], [18993, 'ind'], [14909, 'ind'], [50234, 'med'], [88465, 'ind'], [7853, 'med']]}, 70], ['mixed claim history 3', {'expected': 334500, 'split': 17000, 'weight': 150, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[8211, 'ind'], [19267, 'med'], [4256, 'med'], [47071, 'ind'], [74176, 'ind'], [8958, 'med']]}, 83], ['mixed claim history 4', {'expected': 758400, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[24450, 'med'], [45271, 'ind'], [32248, 'med'], [53086, 'ind'], [11516, 'med']]}, 67], ['mixed claim history 5', {'expected': 883600, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[42495, 'ind'], [9679, 'ind'], [36464, 'ind'], [26823, 'ind'], [63484, 'ind'], [12267, 'med']]}, 63], ['large medical-only claim', {'expected': 318100, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[102133, 'med'], [5058, 'ind']]}, 68], ['claim free risk', {'expected': 634700, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': []}, 60], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 457400, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[12750, 'ind'], [32633, 'ind']]}, 65]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
mixed claim history 0	`81`	`78`	Failed
mixed claim history 1	`80`	`75`	Failed
mixed claim history 2	`65`	`62`	Failed
mixed claim history 3	`68`	`64`	Failed
mixed claim history 4	`65`	`63`	Failed
mixed claim history 5	`78`	`75`	Failed
large medical-only claim	`65`	`62`	Failed
claim free risk	`48`	`48`	Passed
invalid expected losses	`invalid expected`	`invalid expected`	Passed
mod rounding near half point	`63`	`63`	Passed

SHA-256 / 4be358126498e3fc0cf6db00e5da7bcfbe25687660bf6cd908eea9073b7571df

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    E=x['expected']
    if E<=0: return 'invalid expected'
    S=x['split']; W=Fraction(x['weight'],1000)
    vals=[Fraction(amt)*Fraction(30,100) if kind=='med' else Fraction(amt) for amt,kind in x['claims']]
    ap=sum(min(v,S) for v in vals)
    ae=sum(vals)-ap
    ep=Fraction(E*x['primary_ratio'],1000); ee=E-ep
    B=x['ballast']
    mod=(ap+W*ae+(1-W)*ee+B)/(E+B)
    return int(mod*100+Fraction(1,2))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mixed claim history 0', {'expected': 311400, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[33740, 'ind'], [37448, 'ind'], [55230, 'ind'], [10817, 'med']]}, 78], ['mixed claim history 1', {'expected': 767200, 'split': 17000, 'weight': 150, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[42590, 'med'], [38435, 'med'], [27276, 'ind'], [26563, 'med'], [15138, 'ind'], [4744, 'ind'], [87257, 'ind'], [10244, 'med']]}, 75], ['mixed claim history 2', {'expected': 858400, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[54743, 'med'], [57687, 'ind'], [5771, 'med'], [32069, 'ind'], [9463, 'med']]}, 62], ['mixed claim history 3', {'expected': 677800, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[20283, 'ind'], [10778, 'ind'], [6643, 'med'], [45395, 'med'], [59048, 'ind'], [5648, 'med']]}, 64], ['mixed claim history 4', {'expected': 650900, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[37467, 'ind'], [13425, 'med'], [17798, 'ind'], [25433, 'ind'], [13608, 'med']]}, 63], ['mixed claim history 5', {'expected': 447400, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[41535, 'ind'], [48038, 'ind'], [32890, 'ind'], [5200, 'med']]}, 75], ['large medical-only claim', {'expected': 323600, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[101990, 'med'], [5314, 'ind']]}, 62], ['claim free risk', {'expected': 867900, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 50000, 'claims': []}, 48], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 797000, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[11195, 'ind'], [36197, 'ind']]}, 63]], [['mixed claim history 0', {'expected': 316700, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[10286, 'med'], [40310, 'med'], [26393, 'ind'], [5424, 'med']]}, 65], ['mixed claim history 1', {'expected': 859500, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[23316, 'med'], [15025, 'ind'], [57735, 'ind'], [16008, 'ind'], [45146, 'ind'], [11487, 'med'], [60418, 'ind'], [6233, 'med']]}, 72], ['mixed claim history 2', {'expected': 896000, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[21038, 'ind'], [5062, 'ind'], [14527, 'med'], [1264, 'med'], [4935, 'med'], [56017, 'ind'], [59572, 'ind'], [6562, 'med']]}, 67], ['mixed claim history 3', {'expected': 779700, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[57322, 'ind'], [16107, 'med'], [20840, 'med'], [82520, 'ind'], [5448, 'med']]}, 59], ['mixed claim history 4', {'expected': 827000, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[31790, 'ind'], [13488, 'ind'], [71208, 'ind'], [13222, 'med']]}, 67], ['mixed claim history 5', {'expected': 464000, 'split': 17000, 'weight': 150, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[17834, 'ind'], [18093, 'med'], [30643, 'med'], [29993, 'med'], [55402, 'med'], [31809, 'ind'], [13749, 'med']]}, 80], ['large medical-only claim', {'expected': 469100, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[101036, 'med'], [5613, 'ind']]}, 65], ['claim free risk', {'expected': 687800, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': []}, 53], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 721000, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[15423, 'ind'], [31956, 'ind']]}, 57]], [['mixed claim history 0', {'expected': 610400, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[53344, 'ind'], [48923, 'ind'], [52350, 'ind'], [50819, 'ind'], [10135, 'ind'], [12464, 'ind'], [67060, 'ind'], [12311, 'med']]}, 77], ['mixed claim history 1', {'expected': 402300, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[17334, 'ind'], [22438, 'ind'], [22151, 'med'], [26026, 'ind'], [7894, 'med']]}, 65], ['mixed claim history 2', {'expected': 498400, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[48132, 'ind'], [8715, 'ind'], [59441, 'ind'], [20248, 'med'], [17905, 'ind'], [58937, 'med'], [80627, 'ind'], [7990, 'med']]}, 82], ['mixed claim history 3', {'expected': 464700, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[13610, 'ind'], [3088, 'ind'], [43730, 'ind'], [8434, 'med']]}, 65], ['mixed claim history 4', {'expected': 879300, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[13389, 'ind'], [32420, 'med'], [20542, 'ind'], [47517, 'ind'], [16287, 'ind'], [82017, 'ind'], [9410, 'med']]}, 67], ['mixed claim history 5', {'expected': 652900, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[22810, 'ind'], [40463, 'ind'], [74251, 'ind'], [9218, 'med']]}, 67], ['large medical-only claim', {'expected': 703800, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[84297, 'med'], [2962, 'ind']]}, 62], ['claim free risk', {'expected': 479000, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 80000, 'claims': []}, 59], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 150, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 447500, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[11462, 'ind'], [38751, 'ind']]}, 66]], [['mixed claim history 0', {'expected': 688800, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[56711, 'ind'], [12536, 'med'], [30221, 'ind'], [51849, 'ind'], [13637, 'med']]}, 62], ['mixed claim history 1', {'expected': 402400, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[14109, 'med'], [42085, 'ind'], [59677, 'ind'], [55680, 'ind'], [6934, 'med']]}, 78], ['mixed claim history 2', {'expected': 773600, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[11209, 'med'], [26799, 'ind'], [10934, 'med'], [16129, 'ind'], [11873, 'ind'], [52155, 'ind'], [10727, 'med']]}, 70], ['mixed claim history 3', {'expected': 741200, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[53124, 'ind'], [16325, 'ind'], [4833, 'ind'], [21033, 'ind'], [6837, 'ind'], [38580, 'ind'], [55554, 'ind'], [13784, 'med']]}, 71], ['mixed claim history 4', {'expected': 331500, 'split': 17000, 'weight': 250, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[10786, 'ind'], [17213, 'med'], [39824, 'med'], [24282, 'ind'], [51513, 'ind'], [63075, 'ind'], [10156, 'med']]}, 86], ['mixed claim history 5', {'expected': 409600, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[54286, 'ind'], [35703, 'ind'], [30503, 'med'], [59058, 'ind'], [56149, 'med'], [41950, 'ind'], [41088, 'ind'], [8047, 'med']]}, 92], ['large medical-only claim', {'expected': 831400, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[107249, 'med'], [3434, 'ind']]}, 54], ['claim free risk', {'expected': 597500, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 80000, 'claims': []}, 55], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 200, 'primary_ratio': 300, 'ballast': 50000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 770300, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[13951, 'ind'], [35547, 'ind']]}, 55]], [['mixed claim history 0', {'expected': 303600, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[20599, 'ind'], [56506, 'ind'], [28670, 'ind'], [70657, 'ind'], [13633, 'med']]}, 88], ['mixed claim history 1', {'expected': 729600, 'split': 17000, 'weight': 250, 'primary_ratio': 400, 'ballast': 50000, 'claims': [[14990, 'med'], [18865, 'ind'], [35152, 'ind'], [37220, 'med'], [45354, 'ind'], [6673, 'med']]}, 59], ['mixed claim history 2', {'expected': 697600, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[36216, 'ind'], [18993, 'ind'], [14909, 'ind'], [50234, 'med'], [88465, 'ind'], [7853, 'med']]}, 70], ['mixed claim history 3', {'expected': 334500, 'split': 17000, 'weight': 150, 'primary_ratio': 300, 'ballast': 80000, 'claims': [[8211, 'ind'], [19267, 'med'], [4256, 'med'], [47071, 'ind'], [74176, 'ind'], [8958, 'med']]}, 83], ['mixed claim history 4', {'expected': 758400, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[24450, 'med'], [45271, 'ind'], [32248, 'med'], [53086, 'ind'], [11516, 'med']]}, 67], ['mixed claim history 5', {'expected': 883600, 'split': 17000, 'weight': 200, 'primary_ratio': 400, 'ballast': 80000, 'claims': [[42495, 'ind'], [9679, 'ind'], [36464, 'ind'], [26823, 'ind'], [63484, 'ind'], [12267, 'med']]}, 63], ['large medical-only claim', {'expected': 318100, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 50000, 'claims': [[102133, 'med'], [5058, 'ind']]}, 68], ['claim free risk', {'expected': 634700, 'split': 17000, 'weight': 150, 'primary_ratio': 350, 'ballast': 80000, 'claims': []}, 60], ['invalid expected losses', {'expected': 0, 'split': 17000, 'weight': 250, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[1000, 'ind']]}, 'invalid expected'], ['mod rounding near half point', {'expected': 457400, 'split': 17000, 'weight': 200, 'primary_ratio': 350, 'ballast': 80000, 'claims': [[12750, 'ind'], [32633, 'ind']]}, 65]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
mixed claim history 0	`78`	`78`	Passed
mixed claim history 1	`75`	`75`	Passed
mixed claim history 2	`62`	`62`	Passed
mixed claim history 3	`64`	`64`	Passed
mixed claim history 4	`63`	`63`	Passed
mixed claim history 5	`75`	`75`	Passed
large medical-only claim	`62`	`62`	Passed
claim free risk	`48`	`48`	Passed
invalid expected losses	`invalid expected`	`invalid expected`	Passed
mod rounding near half point	`63`	`63`	Passed

SHA-256 / 1cfbef2e2cbf37158f0eda0836fcac0551b9ba9cd55c9cf8a95469548fa5871f

Verification & scope

A deterministic bounded teaching model of a stipulated toy rating contract. Amounts are integer cents and factors exact rationals; it makes no claim of conformance with any filed rating plan, bureau manual or jurisdiction. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:47:08.760176+00:00.

Case digest / 6b9c0808abe6ec221bc1a42745cf63ad8e3018b645468c0e096525ce647fe303