How to Calculate Expected Value (EV) on In-Game Hextech Loot Boxes

By LOLValue Team · October 18, 2026

Opening a Hextech Chest in League of Legends can be exciting, but excitement does not always equal value. If you want to decide whether a chest is worth your time, keys, or Riot Points, expected value (EV) offers a practical way to estimate the average reward from repeated openings.

EV does not predict what will appear in your next chest. Instead, it combines each possible outcome with its probability to estimate the long-term average value of the loot system.

What Is Expected Value?

Expected value is a probability-weighted average. The standard formula is:

• EV=(P1×V1)+(P2×V2)+⋯+(Pn×Vn)

Here:

• P is the probability of receiving a particular reward.
• V is the value you assign to that reward.
• Each probability must be written as a decimal rather than a percentage.

For example, a 50% chance becomes 0.50, while a 10% chance becomes 0.10.

The difficult part is not the formula. It is deciding what each reward is worth to you. A skin shard may have high value if it matches a champion you play, but little value if you already own the skin or do not want to spend Orange Essence crafting it.

Current Hextech Chest Odds

Before calculating expected value, confirm the latest reward probabilities. Riot Games publishes the official Hextech Chest odds in its Hextech Crafting FAQ, including the chances of receiving skin shards, champion shards, permanent emotes, Orange Essence, Mythic Essence, and bonus Chests and Keys.

The published Hextech Chest probabilities used in this example are:

| Reward | Chance |

|--------------------------------------------------|--------|

| Skin shard | 50% |

| Champion shard | 25% |

| Permanent emote | 10% |

| Ward skin shard plus 150 Orange Essence | 11.5% |

| Summoner icon permanent plus 150 Orange Essence | 3.5% |

Some rewards are additional bonus drops rather than replacements for the main chest content:

| Bonus reward | Chance |

|-----------------------|--------|

| 10 Mythic Essence | 3.6% |

| Bonus Chest and Key | 10% |

Riot’s official information also lists bonus rewards, including a 3.6% chance of receiving 10 Mythic Essence and a 10% chance of receiving a bonus Chest and Key. Because these rewards can appear in addition to the main chest content, they should be calculated separately. A bonus Chest and Key may also lead to further openings, which can affect the long-term EV.

Step-by-Step EV Calculation

1. List the possible rewards

Start by creating a complete reward table. Avoid combining rewards too early because different players may value them differently.

For example, you could separate:

• A skin shard.
• A champion shard.
• A permanent emote.
• A ward skin shard.
• The 150 Orange Essence attached to some outcomes.
• A summoner icon.
• Mythic Essence.
• A bonus Chest and Key.

2. Assign a value to each reward

There is no universal cash value for cosmetic loot. A better approach is to use a personal utility value or an estimated crafting value.

For instance, imagine that you assign the following values:

| Reward | Example personal value |

|-------------------------------------|------------------------|

| Skin shard | 80 units |

| Champion shard | 25 units |

| Permanent emote | 15 units |

| Ward skin shard plus Orange Essence | 20 units |

| Summoner icon plus Orange Essence | 10 units |

| 10 Mythic Essence | 30 units |

| Bonus Chest and Key | 80 units |

These numbers are only an example. You can replace them with values based on your own collection, crafting plans, or the amount you would realistically pay for similar content.

3. Multiply probability by value

Now calculate the main reward EV:

• Skin shard: 0.50×80=40
• Champion shard: 0.25×25=6.25
• Permanent emote: 0.10×15=1.5
• Ward shard and Orange Essence: 0.115×20=2.3
• Summoner icon and Orange Essence: 0.035×10=0.35

The main-reward EV is therefore:

• 40+6.25+1.5+2.3+0.35=50.4

Next, calculate the expected value of bonus rewards:

• Mythic Essence: 0.036×30=1.08
• Bonus Chest and Key: 0.10×80=8

The combined EV is:

• 50.4+1.08+8=59.48

Under these assumptions, one Hextech Chest has an estimated EV of 59.48 personal-value units.

This simplified EV calculation treats the Bonus Chest and Key as one additional reward. It does not include the value of any further bonus chests that the initial bonus chest may generate.

Include the Cost of Opening

A reward is not automatically good value simply because it has positive EV. You must compare the EV with the cost of obtaining and opening the chest.

Use this formula:

• Net EV=Reward EV−Chest Cost−Key Cost

Suppose a player values a Chest and its Key at a combined cost of 250 Riot Points. That amount can be compared with the estimated reward value after both figures have been converted into the same unit.

If 100 personal-value units equal 250 Riot Points in your model:

• Reward EV: 59.48 units.
• Equivalent cost: 100 units.
• Net EV: −40.52 units.

This would indicate a negative average return. However, the result depends entirely on how you value cosmetic content. A player collecting every skin may assign a much higher value to skin shards than a player who mainly cares about ranked performance.

Optional: Modeling Bonus Chest Chains

The calculation above values only the first Bonus Chest and Key. The 10% bonus Chest and Key chance can also be modeled as a potential chain of additional openings. If each subsequent chest has the same 10% chance to generate another bonus Chest and Key, the expected number of total chests can be represented as:

• 1 + 0.10 + 0.10^(2) + 0.10^(3) + ...

This is a geometric series:

• 1 ÷ (1 − 0.10) = 1.111

In other words, one initial chest produces an average of approximately 1.111 total chests when the bonus chain is considered over a large number of openings. This does not mean that every individual opening will produce a bonus chest.

This chain model is an optional extension rather than an adjustment to the 59.48-unit example above. You can either use the standalone-value method to calculate a simple EV of 59.48 units or apply the 1.111 chain factor to model repeated bonus openings. Do not combine both methods, as that would count the same bonus openings twice.

Account Value and Duplicate Rewards

Hextech rewards can also affect the perceived value of a League account. Skins, champions, wards, icons, Blue Essence, and Riot Points may all influence how players perceive a League account. As a result, the same cosmetic reward may have different utility depending on a player’s collection. You can review how these categories influence an account appraisal with the LOLValue account valuation calculator.

Still, account value is not the same as EV. A skin might increase the appeal of an account while providing little immediate utility to the current owner. Similarly, a champion shard can be useful for a new player but nearly worthless to someone who already owns the full champion roster.

To make your calculation more accurate, divide rewards into three categories:

• Useful rewards: Content you actively want or will craft.
• Convertible rewards: Content that can be disenchanted or converted into another resource.
• Low-value rewards: Duplicates, unwanted cosmetics, or items you are unlikely to use.

This produces a personal EV rather than a theoretical marketplace value.

EV Is Not a Guarantee

Expected value works best over a large number of openings. It cannot predict whether your next chest will contain a valuable skin shard, a champion shard, or an item you do not need.

It is also important to distinguish EV from probability. A 50% skin-shard chance does not mean that every pair of openings will contain exactly one skin shard. Random results can vary significantly over short sessions.

Use EV to answer questions such as:

• Is buying keys consistent with my budget?
• Do I value the likely rewards enough to justify opening the chest?
• Would direct purchases or event rewards suit my goals better?
• How does a Hextech Chest compare with other ways to obtain cosmetics?

Other social gaming choices for readers weighing different play formats include sweepstakes casino games such as slots, table games, scratch cards, and bingo. Depending on the platform, players may use Gold Coins for entertainment-focused play or Sweeps Coins for a chance to redeem prizes, subject to the site’s rules and eligibility requirements. If you are considering play formats outside League of Legends, these options may be worth exploring. However, sweepstakes casino games work differently from Hextech loot boxes, so compare their currencies, terms, and risks separately.

Final Calculation Checklist

Before opening Hextech Chests, follow this process:

1. Confirm the current official drop rates.
2. List every main and bonus reward.
3. Assign each item a realistic personal value.
4. Multiply every value by its probability.
5. Add the main-reward and bonus-reward EVs.
6. Include the cost of the chest and key.
7. Adjust for duplicates, crafting materials, and your collection.
8. Treat the result as a long-term estimate, not a prediction.

The best EV model is the one that reflects your actual goals. If you want particular skins, direct purchases may be more efficient. If you enjoy random cosmetic rewards and already have free chests or keys, the opportunity cost may be lower. Either way, calculating EV turns a vague feeling of “good luck” or “bad luck” into a clearer, more informed decision.

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