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| ==Notes== | | ==Notes== |
| *[[Sombrero vs Volleyball]] contains information about when sombrero- and volleyball-type familiars are best for stat gains based on familiar weights and monster level. | | *The sombrero increases stats after combat by floor(sqrt(sombrero weight) * (1 + sqrt(monster level - 4)) / 10. |
| *The sombrero gives a bonus of approximately sqrt(monster level * sombrero weight) / 10. | | *The point where a Hovering Sombrero breaks even with a Volleyball of equal weight is monster level 85. However, the sombrero stat formula is currently still floored, while the volleyball has been fixed to randomly round non-integer stat gains. |
| * Currently, the point where a Hovering Sombrero breaks even with a Volleyball of equal weight is thought to be monster level 100. | | *[[Sombrero vs Volleyball]] contains further information about when sombrero- and volleyball-type familiars are best for stat gains based on familiar weights and monster level. |
| *In terms of boosting stat gains via familiar equipment, the sombrero can be outfitted with [[wax lips]] (+3 XP), a [[lead necklace]] (+3 lbs), [[tiny maracas]] (+5 lbs), or an [[annoying pitchfork]] (+5 ML; +1.25 XP). Given an outfit configuration that lacks familiar equipment, and letting the effective weight of the sombrero be ''s'' and the effective monster level be ''m'' for that configuration, the stat gains from a fight ''with'' equipment are functions of <span title="S&M... huh huh">''s'' and ''m''</span>:
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| **''W''(''s'', ''m'') = (''sm'')<sup>1/2</sup>/10 + 3 for the wax lips | |
| **''P''(''s'', ''m'') = (''s''(''m'' + ''5''))<sup>1/2</sup>/10 + 1.25 for the pitchfork
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| **''F''(''s'', ''m'') = ((''s'' + 5)''m'')<sup>1/2</sup>/10 for the familiar equipment
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| **''L''(''s'', ''m'') = ((''s'' + 3)''m'')<sup>1/2</sup>/10 for the lead necklace
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| *If ''s'' is held fixed while ''m'' is varied, the [[Wikipedia:partial derivative|partial derivative]]s of the functions above show that as monster level gets big enough, the best equipment will be the maracas, followed by the lead necklace, the wax lips, and the pitchfork:
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| **''F<sub>m</sub>''(''s'', ''m'') = (''s'' + 5)<sup>1/2</sup>/(20''m''<sup>1/2</sup>)
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| **''L<sub>m</sub>''(''s'', ''m'') = (''s'' + 3)<sup>1/2</sup>/(20''m''<sup>1/2</sup>)
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| **''W<sub>m</sub>''(''s'', ''m'') = ''s''<sup>1/2</sup>/(20''m''<sup>1/2</sup>)
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| **''P<sub>m</sub>''(''s'', ''m'') = ''s''<sup>1/2</sup>/(20(''m'' + 5)<sup>1/2</sup>)
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| *In practice, the break-even monster level for comparing the equipment can be calculated as a multiple of ''s'', say ''m''<sup>*</sup> = ''cs''. Some rudimentary algebra coupled with judicious applications of the quadratic formula show that:
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| :*The pitchfork is better than the wax lips only when ''s'' > 62.5 and ''c'' < 1/49; essentially not in any situation where one would be grinding stats.
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| :*For the maracas to break even with the pitchfork, ''m'' must be approximately 78 times (1 lb) to 28 times (60 lb) as much as ''s'', with larger ''m'' reinforcing the maracas' advantage.
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| {| align="center" border="1px" cellspacing="0" cellpadding="3" style="text-align:right"
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| |-
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| !''s''
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| |1
| |
| |5
| |
| |10
| |
| |15
| |
| |20
| |
| |40
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| |60
| |
| |80
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| |100
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| |-
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| !''c''
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| |77.73
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| |38.79
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| |33.11
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| |31.13
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| |30.11
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| |28.56
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| |28.03
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| |27.77
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| |27.61
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| |-
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| !''m''<sup>*</sup>
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| |78
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| |194
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| |332
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| |467
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| |603
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| |1143
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| |1683
| |
| |2222
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| |2761
| |
| |-
| |
| |}
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| :*For the maracas to break even with the lips, the monster level must be at least 147 times the sombrero's weight, with larger ''m'' reinforcing the maracas' advantage.
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| {| align="center" border="1px" cellspacing="0" cellpadding="3" style="text-align:right"
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| |-
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| !''s''
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| |1
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| |5
| |
| |10
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| |15
| |
| |20
| |
| |40
| |
| |60
| |
| |80
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| |100
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| |-
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| !''c''
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| |428.36
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| |209.82
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| |178.18
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| |167.14
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| |161.5
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| |152.87
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| |149.94
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| |148.47
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| |147.58
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| |-
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| !''m''<sup>*</sup>
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| |429
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| |1050
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| |1782
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| |2508
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| |3230
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| |6115
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| |8997
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| |11878
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| |14758
| |
| |-
| |
| |}
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| :*Thus, for almost all situations (except for highly [[Special Monsters|scalable monsters]]), the wax lips are best, followed by the pitchfork, the maracas, and the lead necklace.
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| ==History== | | ==History== |
| *Before [[NS13]], the best approximation for sombrero stat gain was: (sqrt(monster level) * weight * 3) / 100
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| *Before NS13, a Hovering Sombrero would have beaten a Volleyball of the same weight at monster level 70. | | *Before NS13, a Hovering Sombrero would have beaten a Volleyball of the same weight at monster level 70. |
| *Before NS13, [[tiny maracas]] typically gave better stat gain than [[annoying pitchfork]] at [[Monster Level]]s above 50. A [[lead necklace]] was only superior to an [[annoying pitchfork]] from the [[The Castle in the Clouds in the Sky]] onwards. See [[annoying pitchfork]] for details.
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| *Before [[South of The Border]] was implemented, the Hovering Sombrero was Jick's seldom-seen personal familiar. | | *Before [[South of The Border]] was implemented, the Hovering Sombrero was Jick's seldom-seen personal familiar. |
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| Hovering Sombrero
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Airborne headgear? ¡Sí!
Almost seems to grin at you...
Qué Misterioso.
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Ability: Increases stat gains in battle, depending on enemy level
Throne/Bjorn: Unknown
Hatchling: 
hovering sombrero
Familiar-Specific Equipment: 
tiny maracas
Mumming Trunk Abilities:
Combat Messages
- <name> bends its brim into an approximation of a smile.
- <name> hovers even more vigorously than usual, and some extra Meat materializes.
- <name> baila una baila tradicional de su gente. (Translation: It dances a traditional dance of its people.)
- <name> hace una sonrisa brillante con sus labios de cera. (Translation: It makes a brilliant smile with its lips of wax.)
Arena Messages
- When entered in an Ultimate Cage Match:
- <name> cannot fight. <name> can only hover. Hover on, <name>!
Notes
- The sombrero increases stats after combat by floor(sqrt(sombrero weight) * (1 + sqrt(monster level - 4)) / 10.
- The point where a Hovering Sombrero breaks even with a Volleyball of equal weight is monster level 85. However, the sombrero stat formula is currently still floored, while the volleyball has been fixed to randomly round non-integer stat gains.
- Sombrero vs Volleyball contains further information about when sombrero- and volleyball-type familiars are best for stat gains based on familiar weights and monster level.
History
- Before NS13, a Hovering Sombrero would have beaten a Volleyball of the same weight at monster level 70.
- Before South of The Border was implemented, the Hovering Sombrero was Jick's seldom-seen personal familiar.
References
See Also
Cannot breathe underwater
