An index level is not a sum of prices — it is a ratio. The general formula is Index = (Sum of adjusted member values) / Divisor. The divisor is a scaling constant that keeps the index continuous when composition changes, shares split, or members are swapped. Without divisor adjustments, a 4-for-1 split at a large weight would mechanically crash the index overnight.

Two famous divisor stories:

Dow (DJIA): price-weighted, divisor shrinks over time. It began at 11.11 in 1896 (12 stocks, sum/12). Today it sits near 0.15, which is why a $1 move in a Dow stock moves the index roughly 6.7 points.
S&P 500: float-adjusted market-cap weighted, divisor set so 1941–43 = 10. Divisor changes are published daily by S&P DJI.

Event	Effect on Divisor	Effect on Index Level
Stock split (Dow)	Decreases	None (neutral)
Constituent swap	Adjusted to preserve continuity	None at rebalance moment
Share count change (S&P)	Adjusted	None from the change itself