How can Technical Analysis work on Indices

Hi, I have a really interesting question but I can’t seem to find the answer, I wonder if you can help me with this.
Forgive me if I am wrong, but many many traders look at the same charts and see Support and Resistance levels, trend lines waiting to be broken, double tops, double bottoms, Fibonacci levels, special cycles, patterns, moving averages, divergences etc. and they all use those same levels to decide their entry and exit points.
So therefore price will bounce off a trend line or fibo level, broken support will become resistance etc. simply because there are so many traders looking for those levels, they make it happen. I can’t think of a better explanation for why Technical analysis works on Forex, shares etc.
If the above is a true explanation for why TA works then what has me puzzled is why it works on indices
Now let’s look at the FTSE100 which is a representation of those top 100 companies in UK. My question is, an index that has 100 companies plotting their move all the time, surely the charts would be completely random. wouldn’t the value of the index itself be chaotic - as it is made up of the TA applied to so many different shares, all of which behave in different ways at any given moment?
How can it be possible for technical analysis to work and the patterns so predictable when ideally the charts should be completely randomly moving. When I apply trend line, support and resistance, it touches accurately and turns or breakthrough these levels. How is this possible on indices which is made up of so many companies. I would have thought the charts for FTSE and all other indices would be completely random but they are so predictable when you apply technical analysis

Index TA completely follows the principles of all other price TA. Which means quite well but not perfectly. Prices change due to supply and demand. The stock index is driven up by demand for the member stocks, and down by a demand to put money into other assets (including cash). Actually, the stocks in the FTSE100 or any other stock index are not all moving randomly - when the index is up, you will usually find that 80% of the members are up also (except if you’re just looking at very short time-frames.

In some ways its easier to rely on index TA than individual stocks. As a parallel, you might have noticed how much easier it is to predict the behaviour of a crowd of people who want to get through a busy airport than any individual traveller.

PS. The FTSE is one tricky index as it has two characters each day - before New York opens and after New York opens. Sometimes the City players set off buying in the London morning session, and end up selling when Wall Street takes a more bearish view.

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That does not really answer my question. Let me repost,
If the DAX is a index of 30 companies and the DAX chart plots the prices for these 30 companies then why do we get interesting patterns on the DAX like double bottoms, double tops, trendline breakouts etc. I would have thought the DAX charts would not respect technical analysis as prices would just make swings and not respect technical setups. Many times I have seen price bounce off 00 levels. Does people trade the DAX which then affects the stock price or do people trade stocks which then moves the index??

The answer is Yes to both. Both are happening. This is because it is humans who are making the buying and selling decisions and they will take account of information that helps in this process, such as the DAX value and its TA. The big banks can of course influence the DAX a .little and this can help them in certain circumstances when they wish to buy or sell part of some position. Of course, the TA of the DAX is not just of interest to players with DAX member shares, there are more German stocks which are not in the DAX than are in the DAX, but all players take account of its TA.