Were the Heroic Spirits that powerful in their lives?

Question

Were the Heroic Spirits that powerful in their lives? Consider:

Some heroes had "reasonable" powers:

• Fate Zero's Caster has a spellbook that granted him massive amounts of mana.
• Fate Zero's Lancer had two magical lances.
• Stay Night's Caster has a contract-breaking dagger.
• Fate Zero's Assassin could split into several shadows (I think it's reasonable, as if it was just some sort of complicated spell).

But other heroes had ridiculous powers:

• King Arthur's holy sword could shoot an epic anti-fortress beam.
• UBW's Lancer's Gae Bolg did an anti-army explosion.
• Gilgamesh's Ea was an anti-world weapon (whatever that means, but it destroyed Rider's reality marble).
• Heracles could regenerate from death several times.

Was King Arthur's Excalibur really capable of such beam? Was Lancer's Gae Bolg really that destructive? Or were such attributes given when they were summoned by the Grail, based on their legends?

And also, there is the physical strength factor. Most heroes make holes in the walls and ground while fighting, and can jump great heights (in UBW, episode 1, I remember Saber jumped to the roof of Shirou's house, looking for nearby enemies).

Answer 1

When a Hero dies and ascends to the Throne of Heroes to become a Heroic Spirit they will gain strength based off the worship of their legend as such the more fame and renown one gets the stronger they become. when they are summoned, there are factors which determine how much strength they have in relation to what they have from the Throne of Heroes

• Cultural Sphere in which the Servant is summoned and the Recognition they receive there are two factors that play a role in their strength. The closer the are to the stage of their legend, a geographical boost, and the more that they are known makes them "stronger", bringing them closer to the strength they had in their legend and providing them with more of their equipment displayed in their legend.

• Magic energy of the Master - The more powerful the magical energy of the Master, the greater the Servant will be able to reach the strength they displayed in their legend.

• Container Parameters: Unmodified by the strengths and weaknesses of specific Heroic Spirits, the containers of the seven standard Servant classes of the Fuyuki Grail War possess known base parameters.

Source: - Servant - Strength - Factors

For instance with those, Cú Chulainn, Heracles and Arturia would be stronger in Europe. Arturia's Strength fluctuates from her different Masters with Rin being the strongest because of Rin being an excelent Magus in comparison to Shirou or Kiritsugu.

Cú Chulainn, being an excellent fighter, would be lesser so when Summoned as a Caster which as seen in Fate/Grand Order when he is summoned as a Lancer and a Caster by The Protagonist

             Lancer | Caster
Strength:       B   |   E   
Mana:           C   |   B
Endurance:      C   |   D
Luck:           E   |   D
Agility:        A   |   C
N. Phantasm:    B   |   B

Sources: Servant Stats for Protagonist Lancer (Fate/stay Night) | Caster (Fate/Grand Order - Cú Chulainn)

As you can see when Summoned as a Caster Cú Chulainn looses Strength, Endurance and Agility but gains Mana and Luck which then makes him much like most Casters and not suited for a head on battle

As the above Quote uses the word "Legend" which is

a traditional story sometimes popularly regarded as historical but not authenticated.

I would assume that after ascension they gain ever greater strength so while a Heroic Spirit may not have been insanely strong in real life their legends argument their strength further

Another instance of a Servant being stronger that they actually were in real life because of their "legend" is with Angra Mainyu who was an ordinary villager and was randomly chosen as the "source of all evil in the world" by his village and was tortured and sacrificed in the following rituals, so while his legends states that he is the evil god of Zoroastrianism he actually isn't

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The things you have identified are all Noble Phantasms

• Gilles de Rais's Anti-Army Prelati's Spellbook
• Diarmuid Ua Duibhne's twin Anti-Unit Lances Gae Buidhe and Gae Dearg
• Medea's Anti-Thaumaturgy Rule Breaker
• The Hundred-Faced Hassan Self Targeted Anti-Unit Zabaniya： Delusional Illusion
• Arturia's Anti-Fortress/Anti-Unit¹ Excalibar
• Cú Chulainn's Gae Bolg
• Gilgamesh's Anti-World Ea
• Heracles's Anti-Unit God Hand

These are

"crystallized mysteries", powerful armaments made using the imagination of humans as their core, and weapons or abilities owned by Heroic Spirits.

Source - Noble Phantasm

so these would be under the most influence from one's legends with their original weapon being the basis and arguments/altered by their legends, for instance with Ea it's actual strength is around the level of Excalibur, its effect is unquestionably that of the legend of "ripping the world"

with Cú Chulainn's Gae Bolg it is in fact 2 Noble Phantasm, the first (Barbed Spear that Pierces with Death) being a single Anti-Unit of the legend of a cursed spear but the second (Soaring Spear that Strikes with Death) is Anti-Army without it's curse to reverse cause and effect which in his Legend

It distorts space to create a "tapestry of action" that splits into numerous spearheads that pour down over the enemy. It is said that it split into thirty in his legend, but it seems that the number has increased after Cú Chulainn became a Heroic Spirit.

so Soaring Spear that Strikes with Death is in fact more powerful than the original legend, possibly because of his legend being embellished over the years

Was King Arthur's Excalibur really capable of such beam?

it actually isn't a beam, on the Wikia Page it says

While the result is what looks like a large beam of light, only the tip of the attack, which is a wave of light that can mow through the surface of the Earth, is capable of doing damage, as the beam is the result of the "dislocation" of everything the attack destroys in its path. Even if it is dodged, those in close proximity can still be temporarily distracted by its intensity.

also when we see Arturia use it we see her swing her sword rather than point it

but as already mentioned since a Nobel Phantasm is influenced by the imagination of humans more than likely it is King Arthur's Legend of being a king who was the only one to wield a sword forged by gods and when people think of weapons forged by gods they think very, very destructive (ie Thor's Hammer, Odin's Spear)

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^{1: In the Fate/Zero material - Servant Status: Saber, p.012-013 (Citation) states that Excalibur: Sword of Promised Victory is Anti-Unit while all other places state it is Anti-Fortress, am unsure if this is a translation error or not}

Answer 2

Actually it's depends on the individual. As Garden of Avalon, supplementary materials reveal that Excalibur DID had the power to generate a Sword Beam. I guess it depends on whether they come from a mythical or historical background. Those such as Heracles who had the power to lift the sky and according to some myths create the Strait of Gibraltar which separates Spain and Africa is obviously weaker as Servant. While heroes closer to the modern era are explicitly stronger as Servants than real life. Shakespeare would be a good example, as he had zero magical ability in real life and relies on his noble phantasm.