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@mvnla2 I believe the start of the Arena week in California is 12 pm on Sunday. At this time, you (mvnla2) get 3 new objectives. At 12 am, you get a new set of objectives. And you get another set of objectives at 12 am on each of the following days. On the Sunday morning you can continue to try to finish your last set of objectives before the new week starts at 12 pm.
Someone in London gets their first objectives for the arena week at 8 pm on Sunday night, and they get their next set of objectives at 12 am. So they have a 4 h period to finish their first objectives. And if they continue to play after midnight they could complete 2 sets of objectives within 5 h of starting the new Arena week. But on the following Sunday they have until 8 pm to finish their final objective. So generally you get the same number of new objectives over the week where ever you are, you just get more or less time to complete objectives at the start and end of the week.
The rewards from the objectives totals 5,500. The max reward from battles is 75 points. So you need a lot of battles to make up for a missed objective.
I think in your case you have been put into a leaderboard where someone (23k) has completed 3 objectives and completed a lot of extra battles. Somewhere between 17.5 and 18.5k looks like a typical score after 3 sets of objectives and doing a small number of additional battles.