The same thing that makes any kind of theory convincing, having some sort of study, observation, or proof to ba<x>se it on.
Proofs. Evidence that shows proof that validate the theory. Science uses studies to question, test, evaluate and prove the premise ...or disprove it. Many theories are found to not have enough evidence to prove them or they turn out to have no validity at all. <br />
Many "theories" are still called theories even after there is insurmountable evidence that they are valid. Like the Theory of Gravity, the Theory of Electromagnitism, the Theory of the limits of the Speed of Light, the Theory of Evolution or the Theory of Global Climate Change.
A theory is the highest construct of human knowledge. To get to a theory science first looks at the facts and then groups these facts into laws and creates hypotheses to explain the laws. These hypotheses produce predictions and if the hypothesis is a useful tool for predicting what happens in nature and it survives criticism then it becomes a theory. So theories are convincing because the explain the natural world and so have utility. In short: they work. If they don't work then they're not accepted as science because obviously they don't model nature.
You have to have catch phrases like: by accident, unknown cause, chance over time, through happenstance, and for no reason. Then you surround those phrases with observable, testable, concrete evidence to support your theory. If anyone refutes your theory, you call them a nut-job for not accepting the obvious; then demand that they disprove any of your facts, while avoiding any discussion about those catch phrases that your facts surround.
No-one except really ignorant people who choose to be ignorant thinks that evolution happened by accident. Do the reading.
I guess you've failed to evolve a since of humor. Also, "by accident" does not apply to evolution, it applies to abiogenesis; which is trying to disprove a law: the law of biogenesis. There is nothing accidental about the Theory of Evolution.
There's nothing accidental about abiogenesis. The Law of Biogenesis was exactly that, a scientific Law which is a set of repeated observations under certain conditions. It refutes the idea that complex life can spontaniously arise but there's nothing in it that says that complex chemical reactions can't become so complex over time as to be considered life.
What? Biogenesis clearly states that life only comes from life. That is the bare essence of the law. Abiogenesis clearly states A = without, bio= life, genesis = origin; life from non-life, spontaneous or over time. Your statement "Complex reactions over time can become so complex as to be considered life," is the same thing as saying "chance over time". Saying "complex over time" just sounds more scholarly, therefore does not alienate scientific minds.
Usefulness to the possessor of the theory, in prediction, intervention, and explanation.