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because i use a Sweepa with stacked attack stats / super condensed swee's in my crew and its attack stat is way higher than anything else i've seen so far. everything falls before the might of the moustache.
Alpha pals are bigger and come with more HP and may have rarer traits than their normal counterparts.
Lucky and Alpha pals are both needed for breeding to get the best trait builds.
I will say, after spending literally half the day checking IVs because I learned that's a thing and there is calculator for it, while the base stats might be the same, Alphas on average seem to have higher IVs (which makes sense). I checked well over 90 pals today (I seriously stopped keeping track after 80~, but kept checking more), and normal ones had IVs that were generally early teens/very rarely mid-twenty+ stat (just a singular one) meanwhile, almost every Alpha had ~mid twenty range. The lowest stat on an alpha I saw was 18, while a few had the full 30%.
So I know my sample size is pretty small overall, I can say that I noticed a trend of Alphas having better IVs. As for Lucky, I only had like 4 to look at, and 3 of them were cats and 1 a chickpi. Their IVs did seem a little higher, but its hard to tell because too small of a comparison.
Lucky Pals always come with the Lucky passive skill. This is ONLY available on Lucky Pals, and this is what makes them lucky. This passive is a flat +15% Work Speed, +15% Attack, and is great for your Base Pals. It is also a good passive for your Team Pals before you get hold of the Legend passive. The objective here then is to breed your captive Lucky Pal with other Pals that both provide decent passives you want the resulting child to have.
Breeding is a complicated, and extensive process but the gist of it is this:
A wild Pal will have at most 2 decent passives, sometimes 3 but the likelyhood is they do not mesh well for what task you want the Pal to perform. There are 6 main tasks you can have your Pal's perform, and you will want to breed into those Pals passives that provide the most benefit for the purpose.
For example, say a Wild Pal is captured with Artisan, Stronghold Strategist, and Ferocious. These are all top tier passives, but do not work together. Artisan provides +50% Work Speed, which is good for Farmer Pal, Stronghold Strategist provides the player +10% Defence good for a Support Pal, while Ferocious provides +20% Attack for the Pal, only useful for a Combat Pal.
Through breeding however, we can obtain a Pal that is the epitome of the task you want it to perform.
Below are examples of the best "all-rounder" for each Creed. You could opt to omit a buff in favour of a complimentary buff for enhanced performance in that particular aspect of the task sacrificing another aspect in the process, such as swapping out movement speed for additional work speed on a farmer, or the Lucky passive for example.
Pal Creeds
Combat Pal: Ferocious +20 Attack, Burly Body +20% Defence, Diet Lover -15% Hunger Loss, and Swift +30% Movement.
Support Pal: Stronghold Strategist +10% Defence, Vanguard +10% Attack, and say Mining, and Logging Foreman passives for +25% to those tasks.
Certain Pals offer additional support based on their type. For example, the early game Catvia (and some others) provide a carry weight bonus of +50. This stacks, so 4 Catvia would offer +200 carry weight. Those same 4 Catvia tweaked with Support Pal creed would also offer +40% Attack and Defence and +100% Mining and Logging proficiency.
Alternatively, some Pals provide elemental support. For example, Kelpsie increases the attack power of water pals, so a water Combat Pal will get a boost per. And some provide specific bonuses in tandem to specific Pals (see Elizabee and Beeguards)
Crafter Pal: Artisan +50% Work Speed, Workaholic -15% Sanity Loss, Diet Lover -15% Hunger Loss, and Swift +30% Movement
Farmer Pal* (Crops): Artisan +50% Work Speed, Workaholic -15% Sanity Loss, Diet Lover -15% Hunger Loss, and Swift +30% Movement
Farmer Pal (Ranch): Workaholic -15% Sanity Loss, Diet Lover -15% Hunger Loss, and Swift +30% Movement
Work Speed is irrelevant in the ranch, pal drops have a set timer that can only be increased by upgrading their star level (a whole 'nother ballgame lol) so you could double up on speed with Runner +20% in this case, without any actual sacrifice involved.
*Same as Crafter, but given that a lot of people assume "farmer" means "pals that work on the ranch" I felt the need to make the distintion.
at low levels the difference is negligible with the alpha having 100 - 200 more hp and around the same in attack stats, etc.
after levelling the alpha and lucky up to level 33 the lucky appears to have better stats including the following.
+100 extra hp
+39 base attack stat
+32 defence
+10 work speed
the Lucky also has 1 extra move from Dark Type (dark laser) which is came with for a total of 6 moves whereas the alpha only has 5
overall lucky appear to be better as far as the ALPHA/LUCKY comparison without factoring breeding. this makes sense because as OP mentioned they are harder to come by.