Conquistador, Not a bad question. I am a 25 year veteran and can advise that the Illinois resident firearm lottery stats are a complete mystery. They have never published anything. I can only tell you of my observations. I always apply for a high demand property buck tag and select 2nd season only as well. Then for my second choice a little known property I know well. I draw my first choice about 25% of the years. I draw the 2nd choice about 50% of the years. No tag 25% of the years. These same patterns apply for my friends. I don't know about any antlerless only sites, but if you applied for one I'm sure you would draw. I suggest only doing that for your 2nd choice. You have a good chance at getting a buck tag for your first choice. That is IF you pick a property at least 2 hour drive from Chicago and 1 hour from St. Louis. In those areas I have NEVER drawn a gun permit so I quit trying.
Sorry we don't publish stats that's because our state employees are too busy counting the days and minutes until their outrageous unsustainable state employee pensions kick in while we pay our $15,000/year property tax bills for 3BR/2BA dumps. We need Scott Walker to overthrow Mike Madigan.