If a player is arbitration eligible, the easiest way to find out what their asking price will be in arbitration before offering it to them is to select the player you want to offer a contract, and change the contract length to 1 year. On the right side, above the 'Salary Guide' it says "Looking for X amount/year". Divide this number by 2 and you'll have a rough estimate of what arbitration players will ask for at the hearings... something you won't know otherwise until after the hearing is already over.
I checked this numerous times with different players, and all ended up the same. For instance, if a person's contract guide says they're looking for 7 mil/arbitration year, if you half this and offer the player an arbitration amount of 3.5, you will notice your 'pending offers' amount will roughly stay the same. If you offer less than their asking price, your pending offers will lessen. Offer more than their asking price, your pending offers amount will rise. Using this strategy, and offering half of what the player's contract guide suggests, the pending offers will remain the same, telling me that the offering price from me is the same as the 'hidden' asking price from the player.
If anyone else can confirm this, it would be appreciated. I don't even know if it's been noticed before, but I just discovered it, so I'd like to hear if anyone can confirm this as well.