Autumn Hairband 
Ranged Damage -90%.
When receiving damage, there is a 3% chance to increase ATK by 200 for 5 seconds.
For every 2 refinements of the hat past 6, increase rate of activation by 1%.
If refinement is +7 or higher, Increase ATK by 10 for every 20 base INT.
If refinement is +9 or higher, increase recovery rate of healing items by 100%.
When the headgear is unequipped, drain 4000 HP and 400 SP.
If the +10 "bonus" were to be like that, a 10% rate would probably be better. You don't Want to be getting hit as a ranger, even with reduction gears. Also, the effect should last for more than 5 seconds, you need time to set traps and run mobs into it (consider old school trap chaining). Anywhere between 10-20 would work good for allowing adequate time to set traps.
The +9 bonus should also have something additional. Either another damage reduction for more survivability, or a damage increase to traps. I would suggest a possibility as I suggested earlier of a def/mdef reduction to those hit by traps, though I'm not sure if this effect could be worked into a hat or if it would need to be a skill change.
If that doesn't work, someone said on the first page to double the effect of trap research. If this is possible, it would also be a good +9 bonus. If they get an effective level 10 trap research, it would add +400 to the trap damage formula (instead of 200), +10 int (instead of 5), a bit more SP, and 5 to trap setting range (instead of 3). That wouldn't really be overpowered or underpowered for a +9 bonus.