Arbitrators are like feral animals. They can smell fear. If you can't afford to lose an arb, you will lose it -- no matter how close your offer is to the demand. For that reason, I now budget to lose every arb.
On the bright side, there's always a chance you'll be able to re-sign a released player around Rule5 time for even less than you would have offered in arbitration. No guarantees, of course.