Phantasy Star One

[OblivionKnight]

Welcome to PS1's stat topic!  A great game really does deserve something awesome...especially a redone stat topic!  Rank PS3!

This game is pretty simple on mechanics, now that I took the time to figure them out and test them.  Everything is very basic, and all evasion, accuracy (well, both are related to defense in a way, so...), and speed is randomized.  Despite what repeated playthroughs have theoretically taught me >_>

Mechanics
Battles are turn-based, with characters and enemies acting in random orders.  Stats are fairly explainable below. 

Vital Statistics and What They Mean
HP: Life force!  Losing these makes you look more like Zombie Cochran than you'd like to be
MP: Magic points!  Using these is important for casting the magicks that kills people
Attack: Physical attack power!  Smiting evil, 9-5
Defense: Reduces damage taken power or something - pure subtraction, so easy to work with.

Random note - there is a very stupid damage overflow bug that kicks in if characters have higher defense than an opponent has attack.  In these cases, the negative amount of damage a character would theoretically do is instead turned positive, and higher defense characters take more than lower defense characters.  For example, if Alis had 200 defense, and Myau had 100 attack, the damage overflow bug would cause Myau to deal 100 damage to Alis (well, before random variance - numbers like this rarely if ever actually come up in-game).  However, said character could also "miss" - in fact, missing is pretty much entirely a function of defense, so high defense is good and bad in this case: good because it gives you evasion, bad because you can actually receive more damage than you should.  This is why it seems like Noah misses with every attack - his attack power is really crappy.  I ignore this completely, though you are free to take it however you want <_<

Levels are taken at 26.  You can beat the game as low as 18, but why?  Alis technically levels slower and Noah technically levels faster (actually, the difference for Noah is fairly significant, but he joins later, so it's all fairly equal overall), but there's not a huge enough difference in the end.   All equipment is unique or storebought.  Yay, and such.  That actually concludes the introduction.  On with the show!



Alis Landale
Level 26
HP: 210
MP: 29
Attack: 52 (112)
Defense: 119 (209)

Equipment:
Laconian Sword: +60 Attack
Diamond Armour: +60 Defense
Laser Shield: +30 Defense

Attack: 22 damage

Heal (2 MP): Heals 20 HP 
Fire (4 MP): 7-11 damage per hit (9 average), hits 2 times total (14-22 total damage, 18 average), may focus on the same target
Rope (4 MP): Binds a target 100%, effectively paralyzing them; there is a 50% chance each turn that this will wear off and the target will be able to act again; however, the "un-roping" turn is forfeited



Myau
Level 26
HP: 210
MP: 51
Attack: 82 (112)
Defense: 114 (184)

Equipment:
Silver Fang: +30 Attack
Thick Fur: +30 Defense
Gloves: +40 Defense

Attack: 22 damage (63 damage with Help in effect)

Cure (6 MP): Heals 80 HP 
Help (10 MP): Adds to the recipient's Attack stat an amount equal to 50% of base Attack; this adds 41 Attack to Myau's Attack stat at this level
Wall (10 MP): Invincibility for the turn cast, MT



Odin
Level 26
HP: 188
MP: 0
Attack: 43 (123)
Defense: 70 (190)

Equipment:
Laconian Axe: +80 Attack
*Laser Gun: +50 Attack; deals 20 ITD damage, MT
Laconian Armour: +80 Defense
Mirror Shield: +40 Defense (arguably immunes Stone status based on the plot...which technically doesn't exist in-game outside of plot >_>)

Attack: 33 damage



Noah
Level 26
HP: 191
MP: 79
Attack: 71 (81)
Defense: 119 (189)

Equipment:
Wand: +10 Attack
Frade Mantle: +40 Defense
Laser Shield: +30 Defense

Attack: 0 damage (9 damage with overflow bug)

Cure (6 MP): Heals 80 HP 
Fire (4 MP): 7-11 damage per hit (9 average), hits 2 times total (14-22 total damage, 18 average), may focus on the same target
Wall (10 MP): Invincibility for the turn cast, MT
Wind (12 MP): 12-16 damage per hit (14 average), hits 3 times total (36-48 total damage, 42 average), may focus on the same target
Thunder (16 MP): 40 damage, MT


Averages

HP: 200
1) Alis - 210
2) Myau - 210
3) Noah - 191
4) Odin - 188

Defense: 193
1) Alis - 209 (8% [16] less damage taken on average from physicals)
2) Odin - 190 (2% [3] more damage taken on average from physicals)
3) Noah - 189 (3% [4] more damage taken on average from physicals)
4) Myau - 184 (5% [9] more damage taken on average from physicals)

Damage: 30
1) Noah - 42 (Wind)
2) Odin - 33 (Attack)
3) Alis - 22 (Attack)
4) Myau - 22 (Attack)

[Dhyerwolf]

1. I finished the game at L24. L30 was way off for now.
2. No one really has accuracy issues. Accuracy just makes one check a battle, so if you miss once on the first attack, so miss every time.
3. Speed is randomized in the same way.
4. Wall and Protect are both pretty bad.

Damage/Other Tests
Alis:
Physical: 21 Damage (17 at L24)
Fire: 18 Damage
Rope: 100% Hit Rate; Lasts from 1-2 Turns; Lasting 1 turn is useless

Myau
Physical: 21 Damage (17 at L24)
Helped Physcal: 63 damage (58 at L24)
Wall: Doesn't take physicals well at all. Can take some magic attacks, but most PS 1 magic attacks are so very bad (Fear the 10 damage)

Odin
Physical: 29 Damage (25 at L24); NO ACCURACY ISSUES

Noah:
Thunder: 33 average damage
Wind: 31 average damage
Fire: 18 average damage
Prot: Much like Wall

Damage Average:
Damage Order
1. Noah- 33
2. Odin- 29 (26)
3. Alis- 21 (18)
3. Myau- 21 (17)
Average: 26 (23.25) (Kill Point: 65/58)

HP
1. Alis 218
2. Myau 214
3. Noah 195
4. Odin 192
Average: 204.75

Defense
1. Alis- 210
2. Odin- 194
3. Noah- 193
4. Myau- 188
Average: 196.25

I'll work on evade tests later. For accuracy, the three PCs who wanted their physical did not miss at all during the testing (about 20 battles).

[OblivionKnight]

No one probably cares much, but here they are!  Only major and kind of important ones.  If you really want the Gold Dragon, then I can get it pretty easily <_<



Saccubus
HP: 255
Defense: 250 (Way above average - only damageable because of the damage overflow bug, granted, not a required winnable fight; 82% [211] less damage taken from physicals on average)

Attack: 84 damage

Level 8
Average HP: 74



Dr. Mad
HP: 233
Defense: 85 (Solid; 26% [22] less damage taken from physicals on average)

Attack: 61 damage

Level 14
Average HP: 123



Master Tarzimal
HP: 125
Defense: 100 (Good; 20% [20] less damage taken from physicals on average)

Attack: 0 damage (36 damage with the overflow bug)
Fire: 7-11 damage per hit (9 average), hits 2 times total (14-22 total damage, 18 average), may focus on the same target

Level 18
Average HP: 137



King Lassic
HP: 238
Defense: 180 (Excellent; 53% [95] less damage taken from physicals on average)

Attack: 50 damage
Thunder: 40 damage, MT

Level 22
Average HP: 178



Dark Falz
HP: 510
Defense: 150 (Great; 40% [60] less damage taken from physicals on average)

Attack: 62 damage, attacks twice

Level 26
Average HP: 200
*Dark Falz is technically 2 creatures with 255 HP each fought at the same time - you can't target specific Dark Falzs individually, since damage done to groups is randomly dealt across the group - usually halfway through the battle, one of them will die, so Dark Falz will only get one attack each turn after that

[OblivionKnight]

Back to updating old topics!  I was doing well with it for a while, but got behind.  But back in action!  This one has been needing it since the RPGP.  Notes are updated, so enjoy them...if you care about the game >_>

[SnowFire]

Thread necro time!  Reiska was talking about replaying the Sega Ages version of the game (with speedup, 4x XP, reduced encounter rate, etc. options).  And, well, beats me if Google is ever highlighting this page anymore in the sea of algorithmically generated slop, but some better documentation of PHANTASY STAR 1 MECHANICS has since been done based on decompiling the SMS version.  Basically see here:

• Phantasy Star 1 Speedrunning Guide by Ziggy - Sega Ages version
  

Notable stuff:

• Basic physical damage algorithm: Damage = (ATK * [0.75..1]) - (DEF * [0.75..1])
• • If calculated damage <= 0, fallback to a defense break formula:
  • Enemy attacks: [1.. (1+(Target’s Level / 2))]
  • Player attacks: [1.. (1+Attacker's Level))]
• Dodge chance: 1 - (ATK/DEF), with a 0.5 upper bound.  (Unsure about the bug Dhyer mentioned involving later dodge checks being skipped?)

So yes, there is no "underflow bug".  It's not a bad guess for why weak earlygame monsters seemingly deal more damage as the game goes on, or why Noah's physical can deal damage at all, it's just wonky coding.  Also note that a sane algorithm would have always made the alternate min roll then taken the max of the two values, but this is PS1 so it's insane, so a roll of 200 - 199 is guaranteed 1 damage, but 200-200 triggers the defense break formula and thus potentially more damage.

Note that since there are two rolls, the result is a binomial distribution that favors the "middle" of the possible range.  However, damage variance under this system is extreme.  As an example,  an enemy 240 ATK vs. 180 DEF for the PC means that if ATK high-rolls and DEF low-rolls, that's 240 - 135 = 105 damage = you just lost half your health even at stat topic levels.  If ATK low-rolls and DEF high-rolls, that's 180 - 180 = defense break (so somewhere from 1 to ~11-14 damage with levels in the 20s).  A pitiful 40HKO or something.

Note that if you enforce this mechanic in the DL, this only really comes up against enemies with massive multihit attacks where each hit is subject to subtractive defense, like some sort of WAXF Nightstalker's Six-Shooter on crack.  If you could somehow get 40-defense subject hits in quick, then that might do something.

A few boss quirks:

• Lassic's Thunder, despite the name, is a defense-subject 230 power multitarget physical attack and not a spell.  (Orlandu's Lightning Stab says hi?)  Per above, this means that the damage variance is extreme - it might deal 1 damage, it might deal 85 damage.
• DarkFalz (Dark Force): Since damage is distributed randomly, the second attack will generally fall off much later than halfway through the battle - more like 85-95% of the way through without good targeting luck.  However, there is one quirk.  Multitarget attacks do NOT deal "double" damage by damaging both DarkFalzes in a trenchcoat...  but...  they're guaranteed to hit DarkFalz1 (if he's alive).  So if you somehow used only MT attacks (unlikely / impossible in-game), then you'd be guaranteed to knock DF down to just 1 attack halfway through the fight, since they'd always focus on the single target.  (In practice, spamming them makes it more likely that the second attack falls off, say, 70-80% of the way through the fight, which is still helpful.)