Armory bonus didn't seem to hae such influence until the last PvP tournament. Now it seems like it's 50% of every fight you have, and we are often paired with players whose armory bonuses are way higher than ours. Though it may seem like armory bonus sometimes decides the fights you have, it's often combination of luck and strategy. Armory bonus is only there to help you with what you've got.
So, I have few tips on how to raise your armory bonus, even if you're not buying gold in M:AA.
1. Make sure you have unlocked and researched all armory pages you can. The first page is the one you get when you start playing. 2nd page is unlocked on lvl 25, 3rd on lvl 60, 4th on 100, and the last page on lvl 150. When you approach these levels, make sure that you have enough silver for each research. They usually take more than one day to research, so make sure you hit that 'Research' button as soon as you hit that level.
Alternative: buy each armory page for 20 gold.
2. Browse through your armory pages. Are there any empty slots? Any low-bonus items that could be replaced? Any weapons whose PvP bonus was recently nerfed? Then, go to your inventory. Is there any weapon you outleveled that has high PvP bonus (and you're not using it anymore or have no intention of reforging)? I stocked my Army of One because I outleveled it by 50 levels since I got it. Do not stock Golden Weapons. I mean, sure you can, but those weapons you can't get back or win back. So it's not worth it. Any items from previous Spec Ops? I.e. I replaced all my Infernal Fangs (577/577) with Pyramidions (637/637). It seems like it's not much, but it's still better.
Alternative 1: Find weapons whose PvP bonus wasn't nerfed and farm more of those.
Alternative 2: Buy LE items and weapons and stock them. If you're wealthy enough.
3. Win your 5 daily battles in PvP. Starting from last PvP tournament, you can win various things from PvP daily spin, among them, LE items with high PvP bonus. So what could you get last season? HYDRA badge (1245/747), Heart Shaped Herb (747/1245), Dust Of Death (996/996). I got 7 of those and improved my armory a bit. This season, you can get these - Ruby Quartz Fragment (1470/732), Doombot Processor (732/1470) and Terrigen Crystals (1101/1101). Currently, I got 3 LE items from this season's PvP daily bonus.
Alternative: Buy LE items and weapons and stock them. If you're wealthy enough.
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Conclusion: This won't boost you armory enough to match those of gold spenders, but it will make you at least a bit more competitive in PvP. My armory is currently at 35k/37k, with the last armory page researching, since I hit lvl 150 few days ago (didn't have 390k silver at that moment, so it took me two days before I started it). It will be done tomorrow morning and I'll fill it with pyramidions, adding 7k to each offense and deffense. Armory bonus isn't as important as your team, agent setup and luck in pairing. But it does give a nice boost to your stats, so don't discard it too soon. I don't pay gold in this game, and I'm still sitting in top 5% with minimal effort. I'm not saying you will too, but it will help you to get whatever your goal is this season.
I went through all my deffensive fights today, opened each opponent's armory page and found the some of them are full of outdated items with low bonuses. Make yourself more competitive. It's not that hard, and it will help to lower the gap between you and wallet warriors. And everything counts there.