Hovering Sombrero

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Familiar number: 18
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Hovering Sombrero
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

	Ultimate Cage Match	Scavenger Hunt	Obstacle Course	Hide and Seek

Mumming Trunk Abilities:

*Hover for details

Cannot breathe underwater

Combat Messages

• Regular message:

<name> bends its brim into an approximation of a smile.

• With lucky Tam O'Shanter equipped:

<name> hovers even more vigorously than usual, and some extra Meat materializes.

• With miniature gravy-covered maypole equipped:

<name> baila una baila tradicional de su gente. (Translation: It dances a traditional dance of its people.)

• With wax lips equipped:
  

<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

• 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 gives a bonus of approximately sqrt(monster level * sombrero weight) / 10.
• Currently, the point where a Hovering Sombrero breaks even with a Volleyball of equal weight is thought to be monster level 100.
• 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 s and m:
  • W(s, m) = (sm)^1/2/10 + 3 for the wax lips
  • P(s, m) = (s(m + 5))^1/2/10 + 1.25 for the pitchfork
  • F(s, m) = ((s + 5)m)^1/2/10 for the familiar equipment
  • L(s, m) = ((s + 3)m)^1/2/10 for the lead necklace
• If s is held fixed while m is varied, the partial derivatives 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:
  • F_m(s, m) = (s + 5)^1/2/(20m^1/2)
  • L_m(s, m) = (s + 3)^1/2/(20m^1/2)
  • W_m(s, m) = s^1/2/(20m^1/2)
  • P_m(s, m) = s^1/2/(20(m + 5)^1/2)
• In practice, the break-even monster level for comparing the equipment can be calculated as a multiple of s, say m^* = cs. Some rudimentary algebra coupled with judicious applications of the quadratic formula show that:

• 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.
• 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.

s	1	5	10	15	20	40	60	80	100
c	77.73	38.79	33.11	31.13	30.11	28.56	28.03	27.77	27.61
m*	78	194	332	467	603	1143	1683	2222	2761

• 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.

s	1	5	10	15	20	40	60	80	100
c	428.36	209.82	178.18	167.14	161.5	152.87	149.94	148.47	147.58
m*	429	1050	1782	2508	3230	6115	8997	11878	14758

• Thus, for almost all situations (except for highly scalable monsters), the wax lips are best, followed by the pitchfork, the maracas, and the lead necklace.

History

• Before NS13, the best approximation for sombrero stat gain was: (sqrt(monster level) * weight * 3) / 100
• 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 Levels 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.
• Before South of The Border was implemented, the Hovering Sombrero was Jick's seldom-seen personal familiar.

References

• A direct reference to the They Might Be Giants song "Hovering Sombrero."

See Also

• Stat Gains from Fights