Why use marginal rather than average tax rates in incentive analysis? Why do tax analysts worry about marginal tax rates, not average effective rates, in looking for incentive effects of taxes
People make decisions based on how the decision will change things.  If I work an extra \$1000 worth of time, then I have to pay $\$1000 * \text{marginal tax rate}$ in taxes.  The average rate is irrelevant to that calculation.  It's a little more complicated than that in that the marginal tax rate may change over that \$1000.  

The only time that the average tax rate would matter would be if I were asking at the beginning of the year if it would make sense to not work at all that year.  But I can reach the same result with marginal tax analysis and not be restricted to the beginning of the year.  The marginal-based analysis already has to handle things like the marginal rate changing.  

The average tax rate provides useful information so seldom that there's no real point in using it.  

The marginal rate tells us how a change from the status quo will affect things.  If my marginal rate in the example is 25%, then I can make an extra $750 by working that extra.  Is that more or less than my value of my leisure time?  That's a real decision.