What's a good [Dragons Den] pitching model?

Would-be start-up's pitching to VCs (at least, on Dragons Den) need to offer a % of their business, in exchange for an agreed amount of up-front capital & (sometimes) a bit of business guidance.

There seems to be one or more underlying models, eg, that relate the amount of capital requested, value of equity in the business (so far, if any) & the all-important % of the new business, that will be offered to attract the interest of one or more dragons.

Has anyone worked out some models (from either the televised programs or - perhaps more useful - from larger numbers of real-world deals) that might indicate how the various parameters are related?

(Perhaps an additional parameter should be added that represents the risk of failure.)

The basic rules apply: Be calm, clear, and collected. Come prepared to answer any questions you can anticipate, show your product, if you can. Have a clear plan on what you will do with the money. Have an exit strategy for them. Most of all, be realistic.

A model wouldn't work, as sometimes the Dragons invest, or not, due to something that the pitcher says, which can't be predicted. That's the point of the show really, sometimes there is an unexpected outcome.