Document // Engine lab

How accurate is the adaptive estimate?

calibration.json · schema v2 · seed 20261103

The Track tab's adaptive engine turns daily weigh-ins and logged calories into an estimate of expenditure as logged: the calories per day that make what you log match your weight trend. It was tested on 5,000 synthetic people from a simulator that is deliberately messier than the model: their expenditure adapts as they diet, their water weight swings for days at a time, and they under-log, skip days and mistype weigh-ins. None of it follows the filter's assumptions. By day 56 its median error is 68 kcal/day against the formula's 189, and its 80% band holds the true value for 81% of people.

Median error, day 56, kcal: 68; formula 189 · 64% less
Inside the 80% band, day 56: 81%; 50/80/95: 52/81/94
Posterior SD, day 56, kcal: 105; 286 at day 7
Within 150 kcal by day 56: 85%; median from day 35

Accuracy over time

Median absolute error by day across the realistic cohort. The engine starts from its prior, the formula lowered 10% for typical under-logging, and learns from there. It pulls below the prior for good from day 20. By day 28 its error is 109 kcal against the prior's 121 and the formula's 185; by day 56, 68 against 113 and 189.

Median absolute error, kcal per day. Solid: the engine. Dashed: the raw formula. Dotted: the prior, the engine's starting point. Neither baseline is ever updated. Dots mark the checkpoint days in the table.

Median absolute error at the checkpoint days, kcal per day
Day	Engine	Formula	Prior
7	125	185	131
14	132	184	127
28	109	185	121
56	68	189	113

Every day (57 rows)

Median absolute error on every day, kcal per day
Day	Engine	Formula	Prior
0	141	185	141
1	138	185	140
2	132	184	139
3	128	184	137
4	127	184	136
5	125	185	134
6	124	185	133
7	125	185	131
8	128	185	131
9	129	184	130
10	130	184	129
11	130	184	128
12	131	184	128
13	132	184	128
14	132	184	127
15	131	184	127
16	130	184	126
17	129	184	125
18	128	183	125
19	126	184	124
20	123	184	124
21	122	184	124
22	120	184	124
23	117	184	123
24	114	185	123
25	114	185	122
26	112	184	122
27	112	185	122
28	109	185	121
29	107	185	120
30	105	184	121
31	102	185	120
32	100	185	120
33	99	185	120
34	97	185	119
35	97	186	119
36	92	186	119
37	90	187	119
38	88	187	119
39	87	187	119
40	87	186	118
41	85	187	118
42	84	186	118
43	82	187	117
44	80	187	117
45	80	187	116
46	78	187	116
47	76	187	115
48	75	187	115
49	74	187	115
50	72	188	115
51	72	187	115
52	73	188	114
53	71	189	114
54	70	189	113
55	69	189	113
56	68	189	113

Calibration

A band is honest when it holds the true value as often as it claims. By day 56 the 50/80/95% bands hold 52/81/94%. Early on they hold more, because they are still mostly the prior's: at day 7 the prior alone would hold 69/94/100%. For people who log accurately the bands are on target once data arrive: 51/81/96% at day 28 and 49/82/95% at day 56.

Dashed line: the share a band claims to hold. Dot: the share of people whose true value was inside it. A dot above its line means the band was wider than it needed to be; below, narrower than it claimed.

Observed coverage at each checkpoint day, percent, with points from nominal
Day	50% band	80% band	95% band
7	69 +19	94 +14	99 +4
14	60 +10	89 +9	97 +2
28	53 +3	82 +2	95 0
56	52 +2	81 +1	94 −1

Robustness to under-logging

The prior assumes people under-log by 10% on average. To see what happens when they log better or worse, the sweep reruns 2,000 realistic people at each mean logging bias. Across every level and day the bands are at most 2.6 points narrower than they claim (50% band, 20% bias, day 7), and at most 17.5 points wider (50% band, 10% bias, day 7). Each cohort's measured logging gap was within 0.5 points of its level.

Coverage of the 50, 80 and 95% bands by mean logging bias and day, percent. Bias levels from 0 to 15% are in the gated range.
Bias	Band	Day 7	Day 14	Day 28	Day 56
0%gatedmeasured gap 0.5%	50%	57	54	52	53
	80%	88	85	81	82
	95%	98	96	95	95
5%gatedmeasured gap 5.0%	50%	66	61	52	53
	80%	93	88	83	82
	95%	99	97	95	95
10%gatedmeasured gap 10.1%	50%	68	60	52	52
	80%	94	89	83	80
	95%	99	97	95	94
15%gatedmeasured gap 14.8%	50%	62	61	56	53
	80%	91	88	83	81
	95%	99	97	95	94
20%not gatedmeasured gap 20.1%	50%	47	51	52	49
	80%	80	81	82	79
	95%	96	96	95	93

more than 6 points too narrow (past the gate's floor)
3–6 points too narrow
within 3 points of nominal
3–12 points too wide
more than 12 points too wide

GatedCI asserts mean bias from 0 to 15%: at days 7 and 14 no band may fall more than 6 points under nominal. At day 56 every level, 20% included, must sit within 6 points under and 12 over. Other days are reported, not gated.

Limit20% mean under-logging is the limit. At 20% the early bands sit at the edge, 47/80/96% at day 7, and nothing asserts them. Above 20% they will be too narrow until the weigh-ins catch up.

Why this prior: the same people were also run under a prior centred on the raw formula (widen only). Its worst distance from nominal was 33.5 points, against 17.5 for the prior that ships, lowered 10% from the formula (widen and recentre).

Edge cohorts

The same engine on people the realistic cohort under-represents. Errors are median absolute errors in kcal per day; coverage is the share inside the 50/80/95% bands.

Accurate loggers

1,000 people

The realistic population, logging exactly what they eat.

Error, day 56: 72 kcalformula 113
Coverage, day 56: 49/82/95of 50/80/95%
Within 150 kcal: 86%median from day 35

The prior assumes some under-logging, so for them it starts 213 kcal low on average. The engine only beats the raw formula from day 30. By day 56 its error is 72 kcal against 113.

Missing weeks

1,000 people

As realistic, with days 14–27 missing: no weigh-ins and no calories.

Error, day 56: 70 kcalformula 182
Coverage, day 56: 56/84/96of 50/80/95%
Within 150 kcal: 84%median from day 38

With nothing to learn from, its error goes from 124 kcal on day 13 to 130 on day 27. It then falls to 70 by day 56, against 182 for the formula.

Maintainers

1,000 people

Eat at their true expenditure, so tissue weight stays flat. They still under-log.

Error, day 56: 46 kcalformula 186
Coverage, day 56: 70/93/98of 50/80/95%
Within 150 kcal: 94%median from day 29

Their expenditure does not adapt, so the drift the engine allows for dieters leaves their bands wide: 70/93/98% at day 56 against 50/80/95. The error still falls to 46 kcal, against 186 for the formula.

No logs

1,000 people

Weigh-ins only. No calories are ever logged.

Error, day 56: 119 kcalformula 190
Coverage, day 56: 78/97/100of 50/80/95%
Within 150 kcal: 60%median from day 17

Weight change alone cannot separate intake from expenditure, so the estimate stays exactly on the prior: its error matches the prior's at every checkpoint (119 kcal at day 56).

Known limits

It estimates expenditure as logged, not true TDEE. A scale and a food log cannot tell a steady under-logging habit from a lower expenditure, because the two only ever show up as their sum, so the engine never estimates the bias itself.
The prior is lowered 10% for typical under-logging, which costs people who log honestly: for them it starts about 213 kcal low, and the engine only beats the raw formula from day 30.
The gate's margins are thin. Its tightest check on this run is that the realistic cohort's 80% band at day 7 may sit at most 3 points further from nominal than the prior alone; it passes by 3.3 points. Sampling noise on a coverage share has a standard deviation of up to 0.7 points at this cohort size, and CI runs a smaller cohort on another seed, so a change that costs a few points of early coverage will fail it.
The gate covers mean under-logging of 0–15%. At 20% the early bands sit at the edge (47/80/96% at day 7), and beyond it they will be too narrow until the weigh-ins catch up.
A day without logged calories is filled in from the 14-day average of what was logged. Skipping the days you overeat hides those calories: your weight rises more than the log explains, so the estimate reads low, by about the skipped days' surplus over your usual intake, spread over every day, much as under-logging does.

Reproduce it

Every number on this page is read at build time from calibration.json, which one command regenerates byte for byte.

npm ci
npm run calibrate
npm test

Seed: 20261103
Cohorts: realistic 5,000; accurate loggers 1,000; missing weeks 1,000; maintainers 1,000; no logs 1,000
Bias sweep: 2,000 people at each of 0%, 5%, 10%, 15% and 20% mean bias, the same people under each of the 2 priors
Horizon: 56 days, checkpoints at days 7, 14, 28 and 56
Prior: mean formula × 0.90, SD 14.1% of the formula
Schema: version 2

Engine parameters

Engine parameters used for every cohort
Parameter	Value
kcalPerKg	7700
trendSdKg	0.02
expenditureDriftKcal	12
waterPersistence	0.85
waterSdKg	0.45
scaleSdKg	0.35
missingIntakeSdKcal	800
intakeMemoryDays	14
outlierGateSd	3
initialWeightSdKg	10
plausibleWeightKg	25–350
plausibleIntakeKcal	0–12000

CI runs npm test on every push and pull request. The gate in calibration.test.ts reruns a smaller seeded cohort and fails the build if coverage or error regresses past its tolerances, and a second check fails if this file no longer matches the engine's parameters or schema.

← Back to Calculator

Day	Engine	Formula	Prior
0	141	185	141
1	138	185	140
2	132	184	139
3	128	184	137
4	127	184	136
5	125	185	134
6	124	185	133
7	125	185	131
8	128	185	131
9	129	184	130
10	130	184	129
11	130	184	128
12	131	184	128
13	132	184	128
14	132	184	127
15	131	184	127
16	130	184	126
17	129	184	125
18	128	183	125
19	126	184	124
20	123	184	124
21	122	184	124
22	120	184	124
23	117	184	123
24	114	185	123
25	114	185	122
26	112	184	122
27	112	185	122
28	109	185	121
29	107	185	120
30	105	184	121
31	102	185	120
32	100	185	120
33	99	185	120
34	97	185	119
35	97	186	119
36	92	186	119
37	90	187	119
38	88	187	119
39	87	187	119
40	87	186	118
41	85	187	118
42	84	186	118
43	82	187	117
44	80	187	117
45	80	187	116
46	78	187	116
47	76	187	115
48	75	187	115
49	74	187	115
50	72	188	115
51	72	187	115
52	73	188	114
53	71	189	114
54	70	189	113
55	69	189	113
56	68	189	113

Day	Engine	Formula	Prior
0	141	185	141
1	138	185	140
2	132	184	139
3	128	184	137
4	127	184	136
5	125	185	134
6	124	185	133
7	125	185	131
8	128	185	131
9	129	184	130
10	130	184	129
11	130	184	128
12	131	184	128
13	132	184	128
14	132	184	127
15	131	184	127
16	130	184	126
17	129	184	125
18	128	183	125
19	126	184	124
20	123	184	124
21	122	184	124
22	120	184	124
23	117	184	123
24	114	185	123
25	114	185	122
26	112	184	122
27	112	185	122
28	109	185	121
29	107	185	120
30	105	184	121
31	102	185	120
32	100	185	120
33	99	185	120
34	97	185	119
35	97	186	119
36	92	186	119
37	90	187	119
38	88	187	119
39	87	187	119
40	87	186	118
41	85	187	118
42	84	186	118
43	82	187	117
44	80	187	117
45	80	187	116
46	78	187	116
47	76	187	115
48	75	187	115
49	74	187	115
50	72	188	115
51	72	187	115
52	73	188	114
53	71	189	114
54	70	189	113
55	69	189	113
56	68	189	113

Day	Engine	Formula	Prior
0	141	185	141
1	138	185	140
2	132	184	139
3	128	184	137
4	127	184	136
5	125	185	134
6	124	185	133
7	125	185	131
8	128	185	131
9	129	184	130
10	130	184	129
11	130	184	128
12	131	184	128
13	132	184	128
14	132	184	127
15	131	184	127
16	130	184	126
17	129	184	125
18	128	183	125
19	126	184	124
20	123	184	124
21	122	184	124
22	120	184	124
23	117	184	123
24	114	185	123
25	114	185	122
26	112	184	122
27	112	185	122
28	109	185	121
29	107	185	120
30	105	184	121
31	102	185	120
32	100	185	120
33	99	185	120
34	97	185	119
35	97	186	119
36	92	186	119
37	90	187	119
38	88	187	119
39	87	187	119
40	87	186	118
41	85	187	118
42	84	186	118
43	82	187	117
44	80	187	117
45	80	187	116
46	78	187	116
47	76	187	115
48	75	187	115
49	74	187	115
50	72	188	115
51	72	187	115
52	73	188	114
53	71	189	114
54	70	189	113
55	69	189	113
56	68	189	113