Chosen tzaddikim carry the nation's power

בפסוק ורדפו מכם חמשה מאה ומאה כו' רבבה.

On the pasuk: "And five of you shall pursue a hundred, and a hundred of you shall pursue ten thousand" (Vayikra 26:8).

The Sefas Emes opens with the Torah's promise that, when Bnei Yisrael are deserving, a small number will rout vastly larger enemy forces.

וקשה וכי כך החשבון.

And it is difficult: is this how the arithmetic works out?

The numbers are not proportional — five chasing a hundred is one-to-twenty, but a hundred chasing ten thousand is one-to-a-hundred — so the ratio breaks down, and the Sefas Emes asks why.

וי"ל כי הרמז ורדפו מכם חמשה הוא הנבחרים מכללות ישראל שהם עומדים להלחם מלחמות ה'.

And one may say that the hint of "five of you shall pursue" refers to the chosen ones out of the totality of Yisrael, who stand ready to fight the wars of Hashem.

The "five" are not ordinary soldiers but the select few — the spiritual elite drawn from the whole nation — who go out to wage milchamos Hashem.

כענין אלף נכנסים למקרא יוצאין מאה למשנה וא' לתלמוד.

Like the matter of: "A thousand enter to study Mikra (Scripture), a hundred emerge to Mishnah, and one to Talmud" (cf. Vayikra Rabbah 2:1).

Just as only a small remnant of those who begin learning reach the highest level, so too the choicest few rise out of the larger body of the nation.

כן הנבחרים מתוך כללות ישראל והמה באים בכח הכלל.

So too the chosen ones from within the totality of Yisrael — and they come with the power of the collective.

These select individuals do not stand alone; they carry within them the combined strength of the entire klal (community) from which they were drawn.

ולכן יתכן שאם זוכין בנ"י להעמיד מאה אנשים כאלה בוודאי רבבה ירדופו.

Therefore it makes sense that if Bnei Yisrael merit to produce a hundred men like these, certainly they will pursue ten thousand.

This resolves the arithmetic: a larger group of such elite men carries proportionally far more of the nation's collective power, so a hundred of them can rout ten thousand even though five could only rout a hundred.

ומצינו בגדולי ישראל שאמרו אין בנו כח לרדוף כו' הרי כי הרודפים הם כדוד וכדומה דכ' בי' ארדוף אויבי ואשיגם:

And we find regarding the great ones of Yisrael that they said, "We do not have the strength to pursue," etc. — this shows that the pursuers are like David and the like, of whom it is written: "I pursued my enemies and overtook them" (Tehillim 18:38).

The pursuing described in the pasuk demands an exalted madreigah such as David HaMelech's, for even great men sometimes lacked the strength to "pursue" — proving that this victory belongs specifically to the select tzaddikim who carry the power of the whole nation.

Summary: The non-proportional numbers in the pasuk hint that the "pursuers" are the chosen elite of Bnei Yisrael, who fight Hashem's wars carrying the collective power of the entire nation. The more such select tzaddikim the nation produces, the greater the strength each one wields — explaining how a hundred can overcome ten thousand.