How many battle tokens does it take to max out the msr?

According to u/338-Laplace-Dave on Reddit, it costs 8,500,872 battle token to fully maximize the MSR, and will take 140 days, 3 hours, 36 minutes and 8 seconds waiting for all the upgrades for a non-premium member.

I don't know if anyone has ever calculated that. It would be scary. Level 29 upgrade for just ONE component of your MSR is 49, 084 battlecoins. My MSR is at 7045 damage rating with no damage patch at 163% upgraded. With 85% damage patch it is over 13,033 with a headshot. Max damage for the MSR is 9857

Also, bit of advice. To afford the updates at that level, playing the Arena challenge is key. Finishing in the top two of each round is even better. You get more battle coin at that level and if you make round 50, the top 6 win the jackpot in that round. That will pay for quite a few upgrades