Chakra Standard Deviation, Total Chakra Volume

Hiroki was jogging!

Hiroki did not stop. He walked back and forth across the stream as if he were on flat ground, even trying to crouch down and touch the cold stream water with his fingers. The entire process was effortless and natural, as if he were simply breathing.

Another success on the first try!

No, it was more thorough than just a success—he was as proficient as if he had practiced it countless times.

Nawaki's mouth hung open as he watched Hiroki, the expression on his face shifting from the brimming confidence of the morning to blank bewilderment. Hiroki was two years younger than him!

Kushina also stared blankly at the back of the figure walking on the water, unable to say a word.

"How—how did you do that?" Finally, Nawaki couldn't help but ask, his voice tinged with obvious frustration. Hiroki walked back from the water and stood before them, his expression remaining calm.

The answer was that he only needed to rely on his cheat code to succeed.

But this answer was clearly not suitable for teaching children, so Hiroki thought about it seriously and gave a very positive, inspiring answer: "Effort, reflection, and study."

"Just now, Orochimaru-sensei said that tree-climbing requires one-third of the chakra used for the Transformation Technique, and water-walking requires two-thirds." Hiroki extended his right hand and opened his palm. "But that description is still too vague. Relying solely on feeling to imitate makes it easy to make mistakes. We need a visible standard."

He slowly condensed chakra into his palm.

A pale blue, almost transparent energy mass slowly emerged, steadily maintaining a point of light about the size of a thumbnail, floating quietly without the slightest tremor.

"If we calculate the total chakra consumed by one basic Transformation Technique as 100 units, I call it 100 'Kaka'." Hiroki explained, "Then what is in my hand right now is exactly 1 'Kaka'. You can treat it as a ruler, a basic unit of measurement—just like 1 centimeter or 1 gram."

Of course, for Hiroki to maintain this standard unit of output, he only needed to write the corresponding code in his programming.

If he wrote an output of 1 Kaka per second, then it was 1 Kaka per second.

Never more, never less; this was the systematic utility of his cheat.

Hiroki retracted his chakra and looked at the two of them: "Now, you try it too. You don't need much, just try to output an amount of 1 'Kaka'."

Kushina and Nawaki looked at each other, both seeing a competitive spirit in the other's eyes.

Kushina took a deep breath and, following Hiroki's example, gathered chakra into her palm.

A ball of blue chakra suddenly burst out like an uncontrollable flame, instantly expanding to the size of a fist before rapidly shrinking, flickering and jumping incessantly above her palm.

The instability was visible to the naked eye.

Nawaki gritted his teeth and began to try as well. The chakra light ball in his palm was slightly better controlled in size, but it suffered from the same problem of violent flickering, like a loose lightbulb.

Fine beads of sweat seeped from both of their foreheads.

This seemingly simple "1 Kaka" was actually harder than climbing a tree!

"Interesting."

Orochimaru's voice suddenly sounded, carrying a hint of coldness.

His golden slit pupils were fixed on Hiroki, his tone strange: "Hiroki-kun, do you know what you just did?"

Without waiting for Hiroki to answer, Orochimaru continued himself:

"You have established an unprecedented quantitative system for chakra control."

"In the decades since the founding of Konoha, countless genius ninja have studied how to better control chakra. But all teaching methods have remained stuck in vague descriptions like 'practice more' or 'feel it with your heart.' Even the First Hokage could not translate this feeling into a teachable standard."

"Only you, Hiroki!"

"And you, with a simple 'Kaka' as a unit, have solved this problem. This is not just a simple unit of measurement—it means that from today on, chakra control training can be precisely evaluated, recorded, and improved!"

But is this really Hiroki's own idea?

Orochimaru stared into Hiroki's eyes. He would rather believe it was the masterpiece of the Second Hokage; after all, the Second Hokage had developed countless ninjutsu and was the founder of the Konoha Ninja Academy. It would be most appropriate for this quantitative indicator to have been designated by him!

However—in the nearly thirty years since the Second Hokage founded Konoha, he had never thought of this. Would he have hidden this before his death, telling a test subject instead of his own disciples?

There was no such logic. Even if he emotionally wanted to believe it was the Second Hokage's masterpiece, Orochimaru still had to admit that Hiroki, as the legacy of the Second Hokage, was a genius in his own right!

Subsequently, Orochimaru turned to Kushina and Nawaki:

"Uzumaki Kushina, calculating by Hiroki's standard, the chakra you output per second just now reached about 6 Kaka at its highest, and even less than 0.1 Kaka at its lowest."

Kushina's face flushed red instantly.

"Nawaki, your average output was around 2.5 Kaka, with a fluctuation range between 0.8 and 4.2 Kaka." Orochimaru narrowed his eyes. "Better controlled than Kushina, but still far from stable enough."

Hearing the series of precise numbers reported by Orochimaru, both of them were stunned.

Chakra output—could it actually be calculated like this?

And Hiroki was also stunned.

How did Orochimaru perceive the amount of chakra they were outputting? And how did he estimate it so precisely and with such certainty!?

In his WiFi, the name Orochimaru hadn't flashed for even a second!

Could it be that Orochimaru was just spouting nonsense?

Or was it possible that Orochimaru had a way to perceive things while bypassing his WiFi interface?

While Hiroki was still thinking, Orochimaru continued to explain to the two children.

"Your problem isn't a lack of output, but rather poor control. Your chakra output is constantly fluctuating, like a faucet turning on and off, so naturally, you can't form a stable support point on the wall or the water surface."

Orochimaru watched their thoughtful expressions and decided to make the concept more concrete.

"We can represent this degree of instability with a numerical value." He looked at Hiroki. "Hiroki-kun, if it were you, how would you define this metric?"

Hiroki's train of thought was interrupted, but faced with the question, he pondered for a moment and replied: "You could call it 'fluctuation value' or 'standard deviation.' It represents the average magnitude by which the chakra output deviates from the target value. The smaller this number, the better the control."

"Brilliant." Orochimaru nodded in approval. "Then, following this definition—"

He extended his hand, and a pale blue light point appeared in his palm, stable to the point of near-stillness:

"My standard deviation is approximately ±0.02 Kaka, which is already negligible. And you, Hiroki-kun—"

Orochimaru's voice paused, a flicker of strange emotion crossing his eyes:

"In my perception, your output has absolutely no fluctuation. The standard deviation is close to zero."

01

Is this a level of control a human can achieve?

How is that possible!

Yet, in Orochimaru's perception, Hiroki's reaction was so precise that it made one suspect he was an artificial construct.

After all, even Orochimaru himself could not achieve such precise control!

Regarding control, Orochimaru felt that the only people in the village who could surpass him were Tsunade-hime and his own teacher, the Third Hokage, Sarutobi Hiruzen.

—Could it be said that he is worthy of being chosen by the Second Hokage?

Orochimaru could only speculate, temporarily setting aside his thoughts on Hiroki.

"Nawaki, according to the definition we just described, your standard deviation is ±1.7 Kaka." Orochimaru continued, "Kushina, yours is ±2.9 Kaka."

"To complete the tree-climbing training, you need to control your standard deviation within ±0.5 Kaka. To complete the water-walking training, you need to reach within ±0.2 Kaka."

Standard deviation—±2.9 Kaka—

These unfamiliar terms and precise numbers were like a key, instantly opening a new door in the minds of Kushina and Nawaki.

It was the first time they felt that having to attend classes even after graduating from the Ninja Academy was so annoying—why did ninjas, who spent their days fighting and killing, have to calculate numbers?

But it was also the first time they had such an intuitive and clear realization of the gap between themselves and Hiroki—it was no longer a vague sense of "he's amazing" or "I can't do it," but a performance they couldn't hope to catch up to.

Chakra control with absolutely no fluctuation!

How did he do it!?

"But—"

Nawaki suddenly pouted and asked unconvinced: "If we only look at control, wouldn't those with a larger total amount of chakra be at a disadvantage? A ninja's strength certainly doesn't rely solely on chakra control."

"Good question."

Orochimaru rarely showed an expression of gratification and relief:

"This is the most exquisite part of Hiroki-kun's theory—it not only quantifies control but also opens a door for us, allowing us to systematically evaluate a ninja's strength."

"Since we already have a standard value for chakra quantity, we can roughly establish an index for total chakra, and even more indicators regarding a ninja's strength."

He walked in front of the three and held up three fingers:

"However, today we only need to start with the indicators related to a ninja's chakra; at the very least, it should include three key metrics."

"First, total chakra." Orochimaru looked at Kushina. "The total chakra of an average Chunin should be around 6,000 to 12,000. And Uzumaki Kushina, your total chakra is around 25,000 Kaka, thanks to your Uzumaki Clan bloodline."

Kushina's eyes lit up.

"Nawaki, you are at about 18,500 Kaka, already exceeding the Chunin level."

Nawaki also chuckled, and both he and Kushina looked at Hiroki, wanting to see how much this guy had.

Orochimaru's gaze also fell on Hiroki.

Hiroki's chakra, on the contrary, was not much.

"Hiroki-kun, your total is the lowest, only about 3,200 Kaka. This determines your endurance and the number of ninjutsu you can cast. Taking Lightning Style: False Darkness as an example, releasing this jutsu requires about 3,000 Kaka of chakra."

Hiroki nodded.

This judgment was almost identical to his actual situation; if it weren't for the fact that he lacked the Lightning nature transformation, using Lightning Style: False Darkness once would have just about exhausted his own chakra.

"Second, maximum instantaneous extraction." Orochimaru's tone became more meaningful. "This determines the upper limit of the power of the ninjutsu you can cast. It's like the diameter of a water pipe, which determines how much water it can release at once."

"Even if the total amount is the same, if the extraction speed cannot keep up, you cannot cast large-scale ninjutsu."

"Third, control precision, which is the 'standard deviation' proposed by Hiroki-kun." Orochimaru concluded, "This determines your chakra utilization efficiency and whether you can perform precise operations."

He looked at the three of them, revealing that signature, inscrutable smile:

"Total amount, extraction speed, control precision—these three data points together determine a ninja's chakra application ability. From today on, your training will revolve around improving these three metrics."

"Orochimaru-sensei."

Kushina suddenly raised her hand, her eyes sparkling with excitement:

"If we follow Hiroki Theory, does that mean we can create targeted training plans?"

"Exactly." Orochimaru gave her an approving look. "For example, Kushina, you have a large total capacity but poor control, so you should focus on precision exercises. As for Hiroki, since his total capacity is lower, he needs to focus on improving his chakra extraction efficiency and increasing his maximum capacity."

"That is the significance of quantification."

Nawaki muttered to himself: "So that's how chakra control can be trained—"

He suddenly looked up, his eyes burning with fierce fighting spirit:

"Hiroki! I will definitely lower my standard deviation to be even lower than yours! I will surpass you!"

"Me too!" Kushina refused to be outdone. "Even though I'm at 2.9 Kaka right now, I'll definitely be able to train it down to below 0.1 Kaka!"

Watching their fighting spirit, Orochimaru curled the corners of his mouth imperceptibly, then gave Hiroki a deep look.

Compared to the more mature and steady Hiroki, Orochimaru still preferred cheerful and innocent children like Kushina and Nawaki.

After all—

The snake glanced at Hiroki again.

Who knew how many secrets this child was still hiding?

Thinking of this, Orochimaru suddenly spoke up:

"Hiroki, I will compile this theory of yours into a complete teaching system and report it to the Third Hokage. If it can be promoted throughout Konoha, it will be a revolutionary advancement for the strength of the entire village."

He paused and said earnestly:

"This theory should be named after you—Hiroki Theory."

Hiroki was stunned for a moment.

He had only wanted to create a corresponding program using his cheat, and the so-called standardization of chakra levels was just to make it easier for him to write code; he hadn't expected to cause such a stir.

Orochimaru's words left Hiroki unsure of how to respond.

He had no choice but to look around, then found a reason to change the subject: "Let's proceed with the mission first!"

As Hiroki said this, he quickly grabbed the cat named Tora required by the previous mission.

And just at that moment, an Anbu suddenly appeared:

"Report! Lord Orochimaru, the Third Hokage requests that you and the members of Team 7 head to the Hokage's office immediately."

Hm?

At this time?

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