- For the summoner spell, see
Mark.
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Snowballs are situations that gain momentum over the course of time, analogously derived from a snowball rolling down a hill, picking up more snow and momentum as it rolls. "Snowballing" generally describes the act of using so called 'Snowball items'. A more contemporary use of the word is an individual or team that has taken advantage of a certain factor (such as the global gold from slaying the 
Dragon, or a kill to establish dominance in lane) to widen the gap between them and their opponents.
Snowball items
Snowball items are items that make a champion stronger over the course of time, unless that champion is killed on a regular basis. While granting only low stats by themselves, the items allow the champion to gain stacks of a certain effect which further increase stats (e.g. bonus ability power or attack damage). Each kill grants 4 of these stacks, while an assist grants 2 stacks. They do not retroactively grant stacks, i.e. kills and assists gained before the item was bought will not grant any stacks. The stack cap for the current set of items is 25 stacks. Upon reaching 15 stacks, an additional bonus is unlocked for as long as no stacks are lost. When the champion dies, they lose 10 of their stacks. The stacks are bound to the item, meaning that if you sell the item, the stacks will be lost. Buying the item again will not replenish the stacks.
The snowball items give a buff upon receiving one stack. When you die, you lose this buff.
The snowball items and their buffs are:
Leviathan - Leviathan Armor (item was removed)- Mejai's Soulstealer - Soul Engorgement
- Sword of the Occult - Blood Tribute (item was removed)
Exceptional Snowball Items
With patch V1.0.0.145, the snowball item 
Bonetooth Necklace has been added, which is available exclusively to the champion 
Rengar, the Pridestalker who has been added in the same patch. The item differs from the above-mentioned snowball items in the following manners:
- Upon obtaining charges, the icon of the item changes.
- Instead of giving one bonus that increases or decreases with stacks, the item grants several different bonuses depending on the number of stacks Rengar has.
- As of patch 4.5, Rengar now does not lose stacks of his Bonetooth Necklace upon death and is now a trinket item. Therefore, this may not be a snowball item anymore.
- He does not get a bonus for every stack but for every threshold of stacks he achieves. The thresholds are 3, 6, 12 and 20 stacks.
- At 3 stacks, Rengar gains bonus movement speed when in brush or out of combat.
- At 6 stacks, Rengar gains bonus leap range and the tier two trinket active.
- At 12 stacks, Thrill of the Hunt lasts for 5 more seconds.
- At 20 stacks, Thrill of the Hunt's movement speed bonus is doubled to 30% and Rengar gets the tier three trinket active.
- At 3 stacks,
Misc. Snowball-like Abilities
Cho'Gath, the Terror of the Void's R (Feast) is an ability with somewhat Snowball-like effects.
- If Feast kills the target, Cho'Gath grows larger and gains extra health and basic attack range, stacking up to six times on minions and non-epic monsters, although it stacks infinitely on champions and epic monsters, the size stacking at 10 stacks.
Cost efficiency
While snowball items grant comparably low base stats (especially compared to their gold prices), a fully stacked snowball item grants stats that exceed most other items in the game, let alone within their gold price range. 
Mejai's Soulstealer, for example, grants only 60 ability power at the cost of 1400 gold if the champion has not collected any stacks yet. At 20 stacks, however, it grants a total of 180 ability power as well as 15% cooldown reduction, surpassing 
Rabadon's Deathcap which costs 3300 gold, with any amount of stacks higher than 17.
From a cost efficiency perspective, Mejai's Soulstealer breaks even at 6 stacks (18.16 gold per point of AP) and 
Sword of the Occult breaks even at 5 stacks (34.28 gold per point of AD).
Countering
As soon as you realize that an enemy champion is getting a snowball item, it is essential to keep them from gaining stacks and kill them as quickly and as often as possible; they should be your highest priority in fights. Keep in mind that each assist grants one stack as well, making team fights very attractive for snowballing champions. Also keep in mind that, after a snowballing champion is killed, assists will still grant them stacks even after death. This makes it considerable to sometimes kill them last in order to drain the most stacks from them.