i counted 3400 footballs from (20 days * 35 = 700 + the sum of the quests on wiki) - and it seems a little less than 'certain' that you can get a fully upgraded pillar even if that's your focus without diamonds. I'll agree it's likely though.
I just finished my personal analysis of the chests and i will say it's one of the more interesting events. I'm going to start with an overview of my thoughts on the 10 coolers that can show up so i don't have to cover that repeatedly (from most expensive to least):
1) Special Building Cooler ; 210 balls for 8-9 yards. 15% Chance of Special (plus 10% of 3 of the special buildings from the event)
Good For : If you like a couple of the event buildings it has a relatively high chance to produce something nice.
Bad For : Yards, if the specials you're focused on aren't one of the ones already in this chest
2) Item Cooler ; 150 balls for 8-9 yards. 7% Chance of Special.
Good For : Best yards per ball. If you need 1-up kits.
Bad For : Everything else.
3) Building Cooler ; 135 balls for 6-7 yards. 20% Chance of Special.
Good For : Balance of yards and cost to draw specials
Bad For : Chest contents other than specials.
4) Blueprint Cooler ; 120 balls for 6-7 yards. 10% Chance of Special.
Good For : Yards. If you need Ibservatory prints.
Bad For : Special efficiency, chest contents if you don't need Observatory prints.
5) Boost Cooler ; 100 balls for 4-5 yards. 10% Chance of Special.
Good For : A mediocre fallback chest that isn't the worst in yardage or special chance (but not particularly good either)
Bad For : Terrible nonspecial contents.
6) Orange FP Cooler ; 90 balls for 4.5 yards. 7% Chance of Special.
Good For : Above average yardage per ball. Decent amounts of FP.
Bad For : Special efficiency.
7) Special Unit Cooler ; 85 balls for 4-5 yards. 10% Chance of Special.
Good For : Excellent yardage per ball. Average Special efficiency.
Bad For : Other contents unexciting. Not top pick in any category, but about middle of the pack.
8) Blue FP Cooler ; 80 balls for 2-3 yards. 15% Chance of Special
Good For : Best Special efficiency.
Bad For : Poor yardage per ball. Unimpressive amounts of FP.
9) Medal Cooler ; 65 balls for 2-3 yards. 10% Chance of Special
Good For : Special efficiency. If you need medals.
Bad For : Below average yardage per ball. Who needs medals for very long?
10) Unit Cooler ; 60 balls for 1 yard. 10% Chance of Special
Good For : Excellent Special efficiency.
Bad For : Worst yardage per ball. Unexciting other prizes.
Given that there's 3 chests presented to you at a time at what's seemed to be relatively even likelihood you can choose 2 of the 10 chests to never ever pick, and prioritise the other 8 from favorite to least favorite. You will then wind up picking:
First Choice : 30% of the time
Second Choice : 23.3% of the time
Third Choice : 17.5% of the time
Fourth Choice : 12.5% of the time
Fifth Choice : 8.3% of the time
Sixth Choice : 5% of the time
Seventh Choice : 2.5% of the time
Eighth Choice : 0.8% of the time
83.3% of the time it will be one of your top 4 choices
Some of the strategies to consider using just 3400 free footballs
1) Pure yardage efficiency
Pick Priority : Item, Blueprint, Special Unit, Orange FP, Building, Boost, Special Building, Medal
Never Picking : Unit, Blue FP
Expected yards : 180 (3 TDs)
Expected daily specials : 2.7
While this is likely to complete a Pillar if you wait til day(s) when pillar upgrade is the daily special to spend your footballs, there's a very significant chance of not getting the 2 upgrade specials you need.
Edit : ~23% Chance to Fail to complete Pillar for free
Edit2 : ~2200 diamonds of balls to extend this an additional 70 yards and take 5 touchdowns thus requiring only 1 pillar upgrade. This would reduce chance of failure to ~1%.
2) Pure special efficiency
Pick Priority : Blue FP, Unit, Medal, Building, Special Unit, Boost, Blueprint, Orange FP
Never Picking : Item, Special Building
Expected yards : 125 (2 TDs)
Expected daily specials : 5.3
This is very likely to complete a pillar and have time to chase other specials besides. Someone with exceptionally bad luck however may walk out with almost nothing - especially considering the top 4 chests have really poor contents other than the special. This being a ways short of the 3rd touchdown would need ~1100 diamonds worth of footballs extra if you wanted to extend it that far.
Edit : ~9% Chance to Fail to complete Pillar for free
Edit2 : ~1% Chance to Fail including the diamonds to get 3rd TD
3) Hybrid - Seeing as the first strategy didn't make 4 TDs anyways this considers 50 yards and a special as equal goals.
Pick Priority : Blue FP, Building, Medal, Special Unit, Unit, Blueprint, Boost, Orange FP
Never Picking : Item, Special Building
Expected yards : 142 (2 TDs)
Expected daily specials : 5.1
Closer to the 3 touchdowns but still not quite there (~400 diamonds to complete). Not much difference in the daily special count. I did look at a modified version of this biased further towards the specials side (2 TD = one special) for the perspective of if one was using diamonds to go for multiple pillars. It just swaps the order of special unit and unit ; and blueprint and boost. It's a very minor difference not worth another entry considering it's a small change in ordering of 4th priority or lower picks. It loses about 6 yards for 0.1 more specials from the free footballs.
Edit : ~10% Chance to Fail to complete Pillar for free
Edit2 : ~2% Chance to Fail inlcuding the diamonds to get 3rd TD
4) Touchdown-biased Hybrid - In an attempt to make it to 3 touchdowns to more reliably complete pillar without spending diamonds treating 50 yards as 2 specials in consideration.
Pick Priority : Building, Special Unit, Blue FP, Medal, Blueprint, Boost, Orange FP, Item
Never Picking : Unit, Special Building
Expected Yards : 158 (3 TDs)
Expected Daily specials : 4.6
You would need to be exceptionally unlucky not to manage to complete a fully upgraded pillar if you wait til a daily special = pillar upgrade day with this strategy.
Edit : ~4% Chance to Fail to complete Pillar for free
5) "Good Stuff" - Having now examined an assortment of strategies revolving around merely completing a pillar a final thought went to biasing towards touchdowns and chests that have contents that are actually desirable on their own right (of which specials are certainly 'good stuff' but I also included the event buildings in the special building chest, 10+ FP, and 1 up kits as 'good stuff' worth biasing towards).
Pick Priority : Orange FP, Special Building, Building, Item, Special Unit, Blue FP, Medal, Blueprint
Never Picking : Boost, Unit
Expected Yards : 158 (3 TDs)
Expected Daily specials : 3.1
This goes back to only slightly better chance than the first TD-only strategy in terms of likelihood to complete a pillar. But you are likely to if you wind up screwed at least walk out with having made a bunch of FP and maybe a few event buildings where the TD-only strat was likely to walk out with not much of anything.
Edit : ~17% Chance to Fail to complete Pillar for free
It is of course possible based on early results to switch strategies in midevent. I.e. you might start out with strategy 4 and once you have your 2 pillar upgrades switch to strategy 5 since you only need to maintain yardage at that point.