A long time ago, the company I worked for sold a computer to those who developed the Standard & Poors stock Index.

At that time, it was my understanding that the average was calculated by multiplying the price of each stock by the number of shares outstanding, adding up all the products, and dividing the grand total by the total number of shares.

If a stock split two for one, there was no special adjustment. The new price per share (now about half the old price) was multiplied by the double number of shares outstanding. If a stock was added or taken out of the average, there was no special adjustment: The calculations was the same as before with a different mix of stocks.

Due to the large number of stocks and the method of computing the average, stock splits and the addition or removal of a stock from the the set used did not have a large imediate effect on the value of the average. This was unlike the Dow/Jones average which added up the value of thirty or so stocks and divided by some number (originally the number of stocks in the average). The Dow method of computing the average had to be finagled to adjust for splits and/or a change in the stocks in the average.

How is the Standard & Poors average computed now? I get the impression that is is different from the original method.

...I get the impression that is is different from the original method.Why?

BTW, I do not know the answer to your question, but can guess. (See end section this post.) I assume you know that the product of the share price and the number of shares is usually called the "market capitalization." - I only mention this convenience in remainder of post and for others, less well informed than you.

You are correct that stock splits should have no effect on the market capitalization but often, and certainly on average they tend to increase it as the lower price after the spilt makes it possible for more people to buy a "round lot" (100 sh multiples) and this increases the “buy-side” demand.

However if the total, essentially unchanged, market capitalization is divided by the after split larger number of shares the average price of the "typical share" must go down, and you error* to state otherwise.

Perhaps they have changed (as the Dow Jones index does) the divisor so that the lowering effect of stock splits is removed. I.e. divide by some number slightly smaller than the number of shares.
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* after re-read of your post I noticed your qualifier "large" so not an "error", you just miss-lead me in a quick read.

The SPX is a base-weighted calculation, this article explains it better:

http://www.cftech.com/BrainBank/FINANCE/SandPIndexCalc.html