> But so far as shorting stocks (betting that they'll fall) and buying stocks (betting that they'll rise), there isn't much real math, is there?
A lot of the math is automated these days. PE ratios, SMA (simple moving average), etc. etc.
The basis of most stock analysis is price per earnings, or also known as "How much does $1 of profits cost?". Ex: PE of 20 means that it costs $20 to buy $1/year of profits. PE of 100 means it costs $100 to buy $1/year of profits.
Using this as a baseline, you can estimate the future performance of many stocks. You then correct for public sentiment, bailouts, supply changes (are chips getting rarer and/or more expensive?), and try to predict _future_ profits, not just historical profits.
The company with the most profits, at the lowest price, wins in the long run. Buying $100/year worth of profits for just $1000 investment is better than buying $100/year worth of profits for $50,000.
But the "math" is easy. You just take the profits from last year, then divide it by the #shares * $value of the shares. You can also try to be "forward-PE" by predicting next year's profits and dividing it with today's #shares * $value of shares.
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The #shares changes over time. Companies can make new shares or "buyback" shares at any time. That is why when you hear about company "share buybacks", the stock goes up (fewer shares means lower PE, meaning the people who are buying the remaining shares get more $profits per $investment).
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EDIT: Note that under this theory, it doesn't "matter" what the company does with its profits. Profits can go back to the investors through dividends. Or, profits can be spent back on the same company through Capital-Expenditures (ie: building bigger factories or larger systems). "Growth" companies issue no dividends, because they "recycle" all profits into growing. Or the company can buy another company with the profits. Etc. etc.
While "Value" companies tend to return the money as dividends to the share holders.
Shareholders don't really care. If the profits are given to the shareholders, then shareholders can buy up more of the stock (growing their %ownership, and they themselves get more % of the profits next cycle).
If the profits are invested into itself, then shareholder value goes up as appropriate (instead of $1-million worth of factories, next year the company is doing everything with $1.1-million worth of factories and gets 10% higher profits all around).
If another company was bought, same thing, except the factories are separated by different names / locations.
Of course, the "details matter". Some industries are better suited for growth than others. But the fundamental assumption is "control more profits for fewer dollars".
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EDIT2: Anyway, what ends up happening is that the math-part is easy. Its the prediction part that's hard.