If they are under the cap in Year 1, the Yankees pay no luxury tax, so they save 50% in Yr 1, then in YR 2 save the difference between 50% and 17%, which is 33% savings, then in year 3 save the difference between 50% and 30% which is 20% savings, then in year 4, the difference between 50% and 40%, which is a 10% savings. So over a 4 year period 50% +33% +20% +10% = 113% over 4 years Then they can reset back to zero again and start those same savings all over again. Of course, they could reset in the middle of the time frame. Also, in addition to the salary cap penalties, I believe that there might also be non-financial penalties for being over 50% 2 or more years in a row. one good point is that the salary cap will also climb each year from the $189 K.
Ok, first, your math is highly against acceptable principles. You cannot add percentages together to get a total. Percentages are multipliers, and to get a total you need to have the other variables in place. Like, 50% of what? Since we are not there yet, we cannot answer.
Now, just looking at 2012 in context, the Yanks spent like 206 mil, with the threshold around 178. That is ~28 million over the threshold. At the 17% rate, the yanks would pay and extra 28*$170,000=4.7 million... now those same numbers using 50% would be 14 million... almost a $10 million difference... to put that in perspective... that is the money to pay a player in the range of hiroki kuroda range, just thrown away with nothing to show for it.
I am sure management has tossed a few numbers around and realized that getting under for 2014, resets as well all know, but before the next 5 year window is up, a few of the bigger contracts will also fall off the table (ARod, CC, Tex...etc) making it even easier to get below the threshold again.