A complete list of the Blitzball weapons available in Final Fantasy X. The abilities that come attached to each armor that drops are somewhat randomized but the common abilities are listed below.

Check out the Abilities for more information on abilities that you can find on weapons and armor.

Blitzball	Abilities
Ace Striker	Attack +X% Attack +X% Attack +X% Attack +X%
Ace Wizard	Magic Attack +X% Magic Attack +X% Magic Attack +X% Magic Attack +X%
All-Rounder	[Empty Slot] [Empty Slot] [Empty Slot] [Empty Slot]
Blackout	Darkstrike
Blind Pass	Darktouch
Blowout	Triple AP Overdrive → AP Triple Overdrive
Breakaway	First Strike
Buzzerbeater	SOS Overdrive
Catcher	Capture
Center Forward	Piercing
Comeback	Alchemy
Delay of Game	Slowtouch
Double Header	Any two: Firestrike Thunderstrike Waterstrike Icestrike
Double Penalty	Any two: Darktouch Silencetouch Sleeptouch Poisontouch Stonetouch Deathtouch Zombietouch Slowtouch
Double Score	Double AP
Dream Team	Sleeptouch
Fire Ball	Firestrike
First Goal	Initiative
Four-on-One	Firestrike Thunderstrike Waterstrike Icestrike
Free Agent	Gillionaire
Grand Slam	Break Damage Limit
Halftime	Half MP Cost
Hyper Ball	Strength +5%
Ice Ball	Icestrike
Magic Ball	Magic +3%
Mirage Ball	Magic Booster
Muffler	Silencestrike
Noisebreaker	Silencetouch
Official Ball	[Starting Weapon - No Abilities]
Ovation	Attack +X% Magic Attack +X%
Over the Top	Magic Booster Magic Attack +X% Magic Attack +X% Magic Attack +X%
Overtime	One MP Cost
Penalty Master	Any four: Darkstrike Silencestrike Sleepstrike Poisonstrike Stonestrike Deathstrike Slowstrike Zombiestrike
Power Ball	Strength +3%
Power Play	Attack +X% Attack +X% Attack +X%
Prism Ball	Magic Counter
Rematch	Counterattack Evade & Counter
Rookie Star	Overdrive → AP
Rough Play	Deathtouch
Rout	Overdrive → AP Triple Overdrive
Rulebreaker	Poisontouch
Rune Ball	Magic +5%
Scoring Spree	Double Overdrive
Scout	Sensor
Sleeper	Sleepstrike
Stone Cold	Stonestrike
Striker	Strength +10% - or - Strength +20%
Sudden Death	Deathstrike
Switch Hitter	[Empty Slot] [Empty Slot] [Empty Slot] - or - [Empty Slot] [Empty Slot]
T.K.O.	Stonetouch
Thunder Ball	Thunderstrike
Tie Breaker	Double AP Double Overdrive
Timeout	Slowstrike
Trickster	Magic +10% - or - Magic +20%
Tricolor	Any three: Firestrike Thunderstrike Waterstrike Icestrike
Triple Penalty	Any three: Darkstrike Silencestrike Zombiestrike Sleepstrike Poisonstrike Stonestrike Deathstrike Slowstrike
Triple Score	Triple AP
Turnover	Magic Counter Counterattack - or - Evade & Counter
Violation	Poisonstrike
Virtuoso	Magic Attack +X% Magic Attack +X% Magic Attack +X%
Water Ball	Waterstrike
Winning Streak	Triple Overdrive
World Champion (Celestial Weapon)	Break Damage Limit Triple Overdrive Double AP Evade & Counter