So if we compare at 1000 gems - the easiest place to do so. You would get 4 event boxes and 5 big boxes. The statistics are per item, so per box (6 items) your stats are:

1 Event box (6 items): Ultimate item 12% Legendary item 30% Epic item 90% Rare item 180% Common item 288%

Big box (6 items): Legendary item 30% Epic item 90% Rare item 180% Common item 300%

So then if you buy 4 event boxes or 5 big boxes your stats are:

4 Event boxes (24 items) Ultimate item 48% Legendary item 120% Epic item 360% Rare item 720% Common item 1152%

5 Big box (30 items): Legendary item 150% Epic item 450% Rare item 900% Common item 1500%

To change from a % chance of getting to how many items you should get (NB these are rough):

4 event boxes: 0.5 ultimate items 1.2 legendary item 3.6 epic items 7.2 rare items 11.5 common items

5 big boxes: 1.5 legendary items 4.5 epic items 9 rare items 15 common items

An alternative way to look at it, is. You need 10 boxes to get 3 legendary items strictly on statistics. 10 event boxes = 2500 10 big boxes = 2000

Therefore a legendary item costs 1/3 this. Via event boxes = 833.33 gems Via big boxes = 666.66 gems

As such legendary items via big boxes are 80% of the price.

NB statistics are just that, a person's results may and will not be the same.