Calibration as position sizing: one over-confident asset, six under-confident, no single fix

Linearity is the whole mechanism, and it leaves no slack. Each term in the score is a probability multiplied by a fixed payoff ^[2], so a probability that is wrong by a factor enters the score wrong by the same factor ^[3]. Nothing downstream absorbs it, because the number that decides whether to fire is the number that decides how large.

Run the two failure modes through that arithmetic. ETH's top bin states 93.8% and delivers 45.5% ^[9], a ratio of about 2.06 ^[1], so a score built from that bin is close to double what the observed hit rate supports. XRP's [0.60, 0.70] bin runs the other way, 93.1% delivered against 64.9% stated ^[10], a factor of about 1.44 ^[2], which discards roughly 30% of the score before the gate evaluates it ^[3]. LTC sits at 1.40 in the same bin ^[11][7].

The counts decide which of those is the larger bill. ETH's bad bin holds eleven samples ^[9], 2.2% of the 500-row evaluation set ^[4]. The two understated bins hold 116 and 115 ^[10][11], 231 together ^[5], about twenty-one times as many observations ^[6]. Over-confidence mis-sizes a thin tail. Under-confidence declines a fat middle of trades that were good ^[22], and it leaves no losing fill behind to investigate.

Having both directions inside one universe is what rules out the cheap fix. Platt and temperature scaling apply a single monotone correction, so they cannot pull ETH's tail down and lift XRP's middle at the same time, and fitted globally they land on the average of two opposed errors ^[13]. The per-asset Venn-Abers wrapper works here because it takes each asset's own reliability curve without assuming a shape ^[14].

The provenance of the under-confidence is the part worth sitting with. min_data_in_leaf=400, num_leaves=8 and max_depth=3 were introduced specifically to stop terminal leaves reaching 1.0 and claiming certainty the model had not earned ^[15]. They did that, and they also produced a structural under-confidence pattern across the other six assets ^[16], while ETH still saturates in the rare cases where it is genuinely certain ^[17]. The leaf constraints did not remove a calibration problem. They swapped a loud one in one asset for a quiet one in six, and an aggregate accuracy figure would have reported a modest improvement and shown nothing else, since averaging is the operation that hides a bin ^[18].

LINK-USD is the loose end. It misses the acceptance gate on both axes, -41.5% on ECE and -1.2% on log-loss, against thresholds of 50% and 5% ^[19][20], and it is not short of data: 8,736 training rows, the same as every other asset ^[21], which puts 6,988 rows under the wrapper fit, the same 80% share the others got ^[6][8]. The author reads this as the LightGBM already being better calibrated for LINK, leaving less for the wrapper to take ^[23]. That is plausible and this test does not establish it. A wrapper that fails to improve a model has told you only that the wrapper did not help; distinguishing an already-flat reliability curve from a wrapper fitting noise takes LINK's own diagram.