They're offered based on your clout level, published article count and the diversity of your published content. You first have to show AC that your article topics are well rounded. If they know that you write well on a number of subjects then you have a better chance of getting them offered. Secondly, it's based on clout. I start getting them offered at between a clout level 5-7 on my accounts. Lastly, they factor in your total page views vs. the number of articles you have published.
For instance, if you have 100 articles published but only have 5,000 total views on those articles, you're less likely to get them offered to you. Not just with partner calls but basically every pay system with AC, including upfront offers. All of the earning potential is based on article views vs. total articles published.
Also, here lately the partner calls haven't been staying up very long in the assignment desk. Within 20 minutes or so of being posted they're usually all claimed.