In Brawl, all of Lucario's aura-effect attacks are affected by the aura mechanic, which are all of his attacks except Extreme Speed, dash attack, back throw, down throw, and floor attacks. The strength formula is as follows:
where r is the percentage of the damage dealt (for example, if r is 80, the attack is at 0.8× strength) and d is Lucario's current damage.
Effectively, Lucario's attacks deal normal damage when it is at 75%, weakening to as low as 0.7× damage when it is at 20% or lower, and strengthening to as high as 1.4× damage when it is at 170% or higher.
It is known from the official Brawl website that aura is not only affected by damage percentage, but also by Lucario's placing in the match, making it stronger when it's behind (less stocks/points) and weaker when it's ahead (more stocks/points). However, these numbers are not currently compiled.
In SSB4, the effect of aura has been increased overall — the limits are more extreme, as are the multipliers at those extremes. All of Lucario's attacks are now affected, regardless of whether they have an aura effect or not.
Effectively, Lucario's attacks deal normal damage when it is at 70%, weakening to as low as 0.66× damage when it is at 0%, and strengthening to as high as 1.7× damage when it is at 190% or higher. Overall, this amounts to a buff compared to Brawl, except when Lucario is at a minuscule 8% damage or lower.
In addition to the above, the multiplier is multiplied again with a complicated factor based on Lucario's placing in the match and how many players there are (excluding CPUs). When Lucario's position changes, it takes 6.25 seconds for the new value to scale into full effect; if Lucario's position changes again during this time, the multiplier immediately skips to its new value. The mechanic is named Stock Aura by players. The extra multiplier s that Lucario receives from Stock Aura is determined by the following formula.
In this formula:
This formula has an additional wrinkle in modes other than stock. In time mode, Lucario's lead/trail is equal to 1 until the difference between it and the leader/trailer is 5, at which point the lead/trail is 2. In coin mode, the value is 0 when Lucario is even and 2 otherwise.
For practical purposes, the most common multipliers in serious play are thus:
Once all these factors are combined, the final aura multiplier cannot be lower than 0.6× or higher than 1.8×.
Mega Lucario's aura attacks always deal 1.8× damage regardless of its current damage percentage.
In Ultimate, Aura has been slightly changed from how it worked in SSB4:
The new formulae are r = 66 + (34/65)d for d ≤ 65 and r = 100 + 0.48(d - 65) for 65 ≤ d ≤ 190