Some counter math with multiple scenarios, since this is all hypothetical (estimating daily ranking over a month out, estimating drops of a material that's supposed to be rare but has potentially shown up 75% of the time, etc.)
It should take you 49 days as top 100 to collect all the blueprints you need to access the zeta challenge starting fresh from the tutorial as F2P (so, pretend this is last Tuesday, 9 days ago). This number was calculated using the Ship Acquisition Tool (which automates all that for me).
If you started at top 100, and steadily drop (since you won't be getting half the blueprints/shards that someone staying in top 100 could get), I could see you getting the following payouts:
- 7 days 51-100 = 7 * 1250 = 8750
- 14 days 101-200 = 14 * 1200 = 16800
- 21 days 201-500 = 21 * 1000 = 21000
- 7 days 501+ = 7 * 800 = 5600
- 49 days daily activity = 49 * 100(I think this is what it is...it's close to this, anyway) = 4900
- Total: 57,050 / 2000 = 28.5 zetas
So now we have to calculate the break-even point from here. Which will be 28.5 + (900/2000)*X = 0 + (1350/2000)*X + (Y/7)*X, where X = number of days to break even and Y = number of zeta mats from challenge you get in a week. No-ships-rush side gets only 800 tokens a day because their fleet is weak and will never be as strong until it hits 6-7* after the others have hit 6-7* long before.
6 total attempts, chance of 0-2 per attempt = 0-12 total zetas possible
50% * 12 = 6
25% * 12 = 3
16.67% * 12 = 2
50%:
- 28.5 + 0.45X = 0.675X + 6/7X
- 28.5 = 1.082X
- X = 26 days
25%:
- 28.5 + 0.45X = 0.675X + 3/7X
- 28.5 = 0.654X
- X = 44 days
16.67%:
- 28.5 + 0.45X = 0.675X + 2/7X
- 28.5 = 0.511X
- X = 56 days
I vote we go for 25% because I think it's a decent compromise (though who knows what zeta drop rate really is). In that case, 44 days after the initial 49 days, both sides will have 46 zetas (just plugged 44 into the break-even equation). So, at 93 days after the launch of ships, both sides will have 2 zeta abilities unlocked (closer to like 85ish days, which we can use so long as it's recognized that a one week lead of 2 to 1 zeta abilities will not be significant). However, after 93 days after launch, the player who pushed zetas from shipments will fall way behind. Another 3 months out from then (since this game is all about the long-game), going out another 87 days:
46 + 0.45(87) = 85 zetas 6 months after release of ships
46 + 0.675(87) + (3/7)(87) = 142 zetas 6 months after release of ships
Yes, if the player who only buys zeta mats can somehow get a competitive edge back and earn higher rewards, then sure, they would speed up a little. But 7 zeta abilities versus 4 is quite the difference, especially considering in 6 months they're likely to release more zeta abilities that we want to get.
*Edit* The zeta shipment player will reach the zeta challenge in basically double the time (cause roughly half the gain, and this even gives the player a free Sun Fac). 49 * 2 = 98 days. So the zeta shipment player, who yes, can get to the zeta challenge strictly from GW, will be 5 days behind the zeta challenge player. Since they are both operating at the same challenge drop rates, but the zeta challenge player gets more fleet tokens, the zeta shipment player will always be behind unless they can make some miraculous recoveries in fleet arena while simultaneously the zeta challenge player falls from grace and face plants on the bottom of fleet arena..
