So I have (had AI generate) a new better model, in which the sweet/spicy/bulk dimensions have continuous values, each independently having a piecewise linear effect on feast quality. In one version, the piecewise linear functions have a flat middle, with drop offs at higher and lower values. This results in a range in which all feasts are equivalent. In another version, there’s a peak at low spiciness and we try to pick near that spiciness peak. A combined hedge version has us pick as low a spiciness value as possible within the flat range. The resulting feast pick is:
I’m still not that satisfied with it: it’s pretty ad hoc, with non-integer values, and I haven’t properly understood the error sources (there’s some theory that there might be a base error distribution with possibly stochastic penalties for going too high in each dimension and possibly deterministic penalties for going too low). Anyway, full model specification of these questionable models in a reply post again for ease of separately hiding it.
edit: changed my mind. I’m not going to hedge towards the alternate model with the peak, I’ll instead hedge toward the center of the (claimed in the simpler model) flat zone, which seems safer. It also seems dumb because probably I don’t need to go all the way to the center to be reasonably safe, so probably I could hedge to lower spiciness without penalty. Still, I’m at this point considering myself “done” (in the sense of not feeling it worth it to keep going, not in the sense that I couldn’t keep going or am satisfied). I will see what I failed to account for soon enough! The centered feast, which is now my pick, is:
# Feast Quality Model: Full Parameter Specification (simon note: AI generated)
## Executive Summary
This document presents two piecewise linear models for predicting feast quality based on the balance of spicy, sweet, and bulk characteristics. Both models use learned per-dish weights for each dimension, with penalties applied when totals fall outside optimal zones.
**Key Finding:** The “spicy peak” model shows marginal RMSE improvement and is **marginally significant** (p=0.034) by F-test, but **BIC favors the simpler flat model**. Given the mixed evidence, we recommend targeting the **center of the flat model’s optimal zones** for maximum robustness.
---
## Model Comparison
| Metric | All-Flat Model | Spicy Peak Model |
|--------|----------------|------------------|
| RMSE | 1.9635 | 1.9583 |
| Parameters | 64 | 67 |
| AIC | 2440.9 | 2437.9 |
| BIC | 2789.5 | 2802.8 |
**Statistical Test (F-test):**
- F-statistic: 2.892
- Degrees of freedom: (3, 1647)
- **p-value: 0.034**
**Interpretation:** The peak model’s improvement is marginally significant (p=0.034), but BIC favors the simpler flat model (delta = −13.3). This mixed evidence suggests caution in adopting the more complex model.
---
## Model 1: All-Flat (3-Piece Piecewise Linear)
### Structure
For each dimension (spicy, sweet, bulk):
- **Below optimal zone:** Linear penalty with slope
- **In optimal zone:** No penalty (flat)
- **Above optimal zone:** Linear penalty with slope
1. **Peak model has mixed evidence:** The F-test p-value of 0.034 is below 0.05, but BIC favors the flat model. The evidence is not conclusive.
2. **High degeneracy:** 119 different feasts fall within all optimal zones of the flat model. The center-targeting approach provides a principled way to select among them.
3. **Weights are continuous:** The per-dish weights are fitted continuous values. Integer or simple-fraction approximations may exist but are not explored here.
4. **Variance heterogeneity:** Residual variance increases when above optimal thresholds (especially for bulk). This is not captured in the point predictions above.
5. **Model uncertainty:** All predictions have associated uncertainty (~2.0 quality points RMSE). The differences between top feasts are often smaller than this uncertainty.
---
## Summary
**Use the center-targeted recommendation** for maximum robustness:
further followup:
So I have (had AI generate) a new better model, in which the sweet/spicy/bulk dimensions have continuous values, each independently having a piecewise linear effect on feast quality. In one version, the piecewise linear functions have a flat middle, with drop offs at higher and lower values. This results in a range in which all feasts are equivalent. In another version, there’s a peak at low spiciness and we try to pick near that spiciness peak. A combined hedge version has us pick as low a spiciness value as possible within the flat range. The resulting feast pick is:
**[‘Geometric Gelatinous Gateau’, ‘Pegasus Pinion Pudding’, ‘Roc Roasted Rare’, ‘Troll Tenderloin Tartare’, ‘Vicious Vampire Vindaloo’]**Which I guess is now my pick.I’m still not that satisfied with it: it’s pretty ad hoc, with non-integer values, and I haven’t properly understood the error sources (there’s some theory that there might be a base error distribution with possibly stochastic penalties for going too high in each dimension and possibly deterministic penalties for going too low). Anyway, full model specification of these questionable models in a reply post again for ease of separately hiding it.
edit: changed my mind. I’m not going to hedge towards the alternate model with the peak, I’ll instead hedge toward the center of the (claimed in the simpler model) flat zone, which seems safer. It also seems dumb because probably I don’t need to go all the way to the center to be reasonably safe, so probably I could hedge to lower spiciness without penalty. Still, I’m at this point considering myself “done” (in the sense of not feeling it worth it to keep going, not in the sense that I couldn’t keep going or am satisfied). I will see what I failed to account for soon enough! The centered feast, which is now my pick, is:
**BBQ Basilisk Brisket, Displacer Dumplings, Geometric Gelatinous Gateau, Killer Kraken Kebabs, Opulent Owlbear Omelette, Pegasus Pinion Pudding, Troll Tenderloin Tartare**
The reply post will contain the full description of the models discussed here.
# Feast Quality Model: Full Parameter Specification (simon note: AI generated)
## Executive Summary
This document presents two piecewise linear models for predicting feast quality based on the balance of spicy, sweet, and bulk characteristics. Both models use learned per-dish weights for each dimension, with penalties applied when totals fall outside optimal zones.
**Key Finding:** The “spicy peak” model shows marginal RMSE improvement and is **marginally significant** (p=0.034) by F-test, but **BIC favors the simpler flat model**. Given the mixed evidence, we recommend targeting the **center of the flat model’s optimal zones** for maximum robustness.
---
## Model Comparison
| Metric | All-Flat Model | Spicy Peak Model |
|--------|----------------|------------------|
| RMSE | 1.9635 | 1.9583 |
| Parameters | 64 | 67 |
| AIC | 2440.9 | 2437.9 |
| BIC | 2789.5 | 2802.8 |
**Statistical Test (F-test):**
- F-statistic: 2.892
- Degrees of freedom: (3, 1647)
- **p-value: 0.034**
**Interpretation:** The peak model’s improvement is marginally significant (p=0.034), but BIC favors the simpler flat model (delta = −13.3). This mixed evidence suggests caution in adopting the more complex model.
---
## Model 1: All-Flat (3-Piece Piecewise Linear)
### Structure
For each dimension (spicy, sweet, bulk):
- **Below optimal zone:** Linear penalty with slope
- **In optimal zone:** No penalty (flat)
- **Above optimal zone:** Linear penalty with slope
```
Quality = Intercept + SpicyEffect + SweetEffect + BulkEffect
SpicyEffect = -slope_low * max(0, t1 - total_spicy) - slope_high * max(0, total_spicy—t2)
SweetEffect = -slope_low * max(0, t1 - total_sweet) - slope_high * max(0, total_sweet—t2)
BulkEffect = -slope_low * max(0, t1 - total_bulk) - slope_high * max(0, total_bulk—t2)
```
### Optimal Zones and Penalties
| Dimension | Lower Threshold (t1) | Upper Threshold (t2) | Slope Below | Slope Above |
|-----------|---------------------|---------------------|-------------|-------------|
| Spicy | 3.213 | 3.558 | 1.573 | 0.899 |
| Sweet | 3.068 | 4.461 | 1.593 | 1.273 |
| Bulk | 7.136 | 8.677 | 0.877 | 1.028 |
**Intercept:** 16.742
### Per-Dish Weights
| Dish | Spicy Weight | Sweet Weight | Bulk Weight |
|------|-------------|--------------|-------------|
| Ambrosial Applesauce | 0.000 | 1.456 | 0.000 |
| BBQ Basilisk Brisket | 0.821 | 0.831 | 1.404 |
| Chili Con Chimera | 1.304 | 0.078 | 1.502 |
| Displacer Dumplings | 0.052 | 0.075 | 0.086 |
| Ettin Eye Eclairs | 0.124 | 2.815 | 0.371 |
| Fiery Formian Fritters | 1.337 | 0.000 | 0.918 |
| Geometric Gelatinous Gateau | 0.176 | 2.078 | 0.583 |
| Honeyed Hydra Hearts | 0.000 | 1.537 | 0.851 |
| Killer Kraken Kebabs | 2.146 | 0.054 | 2.434 |
| Mighty Minotaur Meatballs | 0.069 | 0.181 | 2.233 |
| Opulent Owlbear Omelette | 0.008 | 0.016 | 1.788 |
| Pegasus Pinion Pudding | 0.124 | 0.621 | 0.786 |
| Roc Roasted Rare | 0.004 | 0.290 | 3.493 |
| Scorching Salamander Stew | 2.138 | 0.035 | 1.520 |
| Troll Tenderloin Tartare | 0.062 | 0.000 | 0.960 |
| Vicious Vampire Vindaloo | 3.015 | 0.148 | 1.570 |
| Wyvern Wing Wraps | 0.657 | 0.181 | 0.749 |
---
## Model 2: Spicy Peak (4-Piece for Spicy, 3-Piece for Sweet/Bulk)
### Structure
For spicy: 4-piece continuous function with potential peak
- Piece 1: spicy < t1 → slope s1
- Piece 2: t1 ⇐ spicy < t2 → slope s2 (if positive, quality increases)
- Piece 3: t2 ⇐ spicy < t3 → slope s3 (if negative, quality decreases = peak at t2)
- Piece 4: spicy >= t3 → slope s4
For sweet/bulk: Same 3-piece flat structure as Model 1.
### Spicy Parameters (4-Piece)
| Parameter | Value | Interpretation |
|-----------|-------|----------------|
| t1 (breakpoint 1) | 1.016 | Below this: slope s1 |
| t2 (breakpoint 2) | 2.697 | **Peak location** (if s2>0, s3<0) |
| t3 (breakpoint 3) | 5.872 | Above this: slope s4 |
| s1 (slope 1) | 2.043 | Slope for spicy < t1 |
| s2 (slope 2) | 1.856 | Slope for t1 ⇐ spicy < t2 |
| s3 (slope 3) | −1.253 | Slope for t2 ⇐ spicy < t3 |
| s4 (slope 4) | −0.268 | Slope for spicy >= t3 |
**Peak Location:** ~2.70 (where slope changes from positive to negative)
### Sweet/Bulk Parameters (3-Piece)
| Dimension | Lower Threshold | Upper Threshold | Slope Below | Slope Above |
|-----------|-----------------|-----------------|-------------|-------------|
| Sweet | 3.028 | 4.591 | 1.600 | 1.299 |
| Bulk | 6.692 | 8.486 | 0.980 | 1.126 |
**Intercept:** 13.752
### Per-Dish Weights (Peak Model)
| Dish | Spicy Weight | Sweet Weight | Bulk Weight |
|------|-------------|--------------|-------------|
| Ambrosial Applesauce | 0.000 | 1.452 | 0.000 |
| BBQ Basilisk Brisket | 0.642 | 0.871 | 1.395 |
| Chili Con Chimera | 1.020 | 0.071 | 1.427 |
| Displacer Dumplings | 0.036 | 0.062 | 0.089 |
| Ettin Eye Eclairs | 0.070 | 2.904 | 0.410 |
| Fiery Formian Fritters | 1.079 | 0.000 | 0.973 |
| Geometric Gelatinous Gateau | 0.139 | 2.104 | 0.522 |
| Honeyed Hydra Hearts | 0.000 | 1.515 | 0.745 |
| Killer Kraken Kebabs | 1.693 | 0.042 | 2.322 |
| Mighty Minotaur Meatballs | 0.000 | 0.182 | 2.228 |
| Opulent Owlbear Omelette | 0.052 | 0.010 | 1.673 |
| Pegasus Pinion Pudding | 0.125 | 0.592 | 0.653 |
| Roc Roasted Rare | 0.000 | 0.279 | 3.229 |
| Scorching Salamander Stew | 1.691 | 0.041 | 1.614 |
| Troll Tenderloin Tartare | 0.071 | 0.000 | 0.914 |
| Vicious Vampire Vindaloo | 2.361 | 0.163 | 1.545 |
| Wyvern Wing Wraps | 0.518 | 0.157 | 0.711 |
---
## Optimal Feast Recommendations
### Degeneracy Analysis
Both models have **degenerate optimal solutions** - multiple feasts achieve the same (or nearly the same) predicted quality:
| Model | Best Score | # Degenerate Solutions |
|-------|------------|------------------------|
| Flat Model | 16.74 | 135 |
| Peak Model | 16.87 | 6 |
| In All Flat Zones | 16.74 | 119 |
To break this degeneracy, we select the feast **closest to the center** of each optimal zone, providing maximum robustness against model uncertainty.
### Target Centers (Flat Model)
| Dimension | Optimal Zone | Center | Width |
|-----------|--------------|--------|-------|
| Spicy | [3.21, 3.56] | 3.386 | 0.344 |
| Sweet | [3.07, 4.46] | 3.764 | 1.393 |
| Bulk | [7.14, 8.68] | 7.907 | 1.540 |
---
## RECOMMENDED FEAST (Center-Targeted)
This feast is in all optimal zones AND closest to the center of each zone.
| Dimension | Value | Target Center | Deviation |
|-----------|-------|---------------|-----------|
| Spicy | 3.388 | 3.386 | 0.003 |
| Sweet | 3.675 | 3.764 | 0.089 |
| Bulk | 8.041 | 7.907 | 0.135 |
**Predicted Quality:** 16.74 (flat model), 16.80 (peak model)
**Normalized Distance from Center:** 0.160
**Dishes (7):**
- BBQ Basilisk Brisket
- Displacer Dumplings
- Geometric Gelatinous Gateau
- Killer Kraken Kebabs
- Opulent Owlbear Omelette
- Pegasus Pinion Pudding
- Troll Tenderloin Tartare
---
## Alternative Recommendations
### Best by Flat Model
*(135 feasts tied at this score)*
**Example:** Predicted Quality: 16.74
- Spicy: 3.388, Sweet: 3.675, Bulk: 8.041
- Dishes (7): BBQ Basilisk Brisket, Displacer Dumplings, Geometric Gelatinous Gateau, Killer Kraken Kebabs, Opulent Owlbear Omelette, Pegasus Pinion Pudding, Troll Tenderloin Tartare
### Best by Peak Model
*(6 feasts tied at this score)*
**Example:** Predicted Quality: 16.87
- Spicy: 2.695, Sweet: 3.138, Bulk: 6.864
- Dishes (5): Geometric Gelatinous Gateau, Pegasus Pinion Pudding, Roc Roasted Rare, Troll Tenderloin Tartare, Vicious Vampire Vindaloo
---
## Caveats and Limitations
1. **Peak model has mixed evidence:** The F-test p-value of 0.034 is below 0.05, but BIC favors the flat model. The evidence is not conclusive.
2. **High degeneracy:** 119 different feasts fall within all optimal zones of the flat model. The center-targeting approach provides a principled way to select among them.
3. **Weights are continuous:** The per-dish weights are fitted continuous values. Integer or simple-fraction approximations may exist but are not explored here.
4. **Variance heterogeneity:** Residual variance increases when above optimal thresholds (especially for bulk). This is not captured in the point predictions above.
5. **Model uncertainty:** All predictions have associated uncertainty (~2.0 quality points RMSE). The differences between top feasts are often smaller than this uncertainty.
---
## Summary
**Use the center-targeted recommendation** for maximum robustness:
**BBQ Basilisk Brisket, Displacer Dumplings, Geometric Gelatinous Gateau, Killer Kraken Kebabs, Opulent Owlbear Omelette, Pegasus Pinion Pudding, Troll Tenderloin Tartare**
This feast:
- Falls within all optimal zones of the flat model
- Is closest to the center of each zone (normalized distance: 0.160)
- Scores well on both flat (16.74) and peak (16.80) models