Experience

In order to level a character up it is necessary to get more experience. Currently there is only one source for experience in this game, which is killing monsters. Every monster gives experience depending on the type of the monster, its rarity, the area level and certain stats affecting the monster or the area it is in. The amount for the next level increases very fast.

Experience table
The amount is the same for every character in every league. The number shows how much total experience is necessary to reach the level.

Death
In default leagues, loss of experience is incurred upon death. The penalty is a percentage of the total required for the next level and is applied as follows: Losing experience in this way will not cause you to lose a level.
 * 0% loss in Act 1 to Act 5 and normal Labyrinth
 * 5% loss in Act 6 to Act 10 and cruel/merciless Labyrinth
 * 10% loss in any area reached from the map device and the Eternal Labyrinth

In player-versus-player battles, the experience penalty does not apply. Likewise, a hardcore character that dies in PvP will not be lost.

Experience penalties


The player suffers a penalty to experience gained if the player is too far above or below the monster's level. There is a safe level range where no penalty is applied, which is equal to three plus one for every sixteen complete player levels:

$\text{SafeZone} = \left \lfloor 3 + \frac{\text{PlayerLevel} }{16} \right \rfloor$

For example, a level 24 character has a safe zone of 4 levels. Any additional level difference in excess of this safe range is the effective level difference. So from monster level 20 to 28, there is an effective difference of 0; at monster levels 19 and 29, the effective difference is 1.

$\text{EffectiveDifference} = \max\left( | \text{PlayerLevel} - \text{MonsterLevel} | - \text{SafeZone}, 0 \right)$

A monster at a certain level will give a certain amount of experience. If the player is outside the safe zone the following multiplier will be applied to the raw experience earned from the monster, with a minimum of 1% of the raw experience:

For player levels below 95: $\text{XPMultiplier} = \max\left( \left({\text{PlayerLevel} + 5 \over \text{PlayerLevel} + 5 + \text{EffectiveDifference}^{2.5} }\right)^{1.5}, 0.01 \right)$

For player levels equal to or higher than 95: $\text{XPMultiplier} = \max \left( \left(\frac{\text{PlayerLevel} + 5 }{\text{PlayerLevel} + 5 + \text{EffectiveDifference}^{2.5} }\right)^{1.5} * \frac{1}{1 + 0.1 * (\text{PlayerLevel} - 94)} * \frac{1}{ \text{3.1 XP Penalty} }, 0.01 \right)$

3.1 XP Penalty is a new penalty for level 95 and above listed in the following table: Continuing our example, a level 24 character receives 95% experience for level 19 monsters, 52.5% experience for level 17 monsters, and 20% experience for level 15 monsters.

The plot below displays how the experience penalty varies with different zone and player levels. Notice that the safe zone with no experience penalty gets larger with higher player levels and that near max level it is impossible to play with no experience penalty.

By following the safe zone recommendations for each player level a high experience gained per map ratio is guaranteed. However that does not necessarily mean it is the most efficient use of a players time. For example the difficulty in the safe zone might be too high leading to the map being cleared slowly and a low experience gained per hour even if the experience gained per map is high. Therefore to level efficiently a high experience gained per hour is necessary, not staying inside the safe zone of the experience penalty.

Areas with monster level above 70 are considered to have a lower monster level for the purpose of experience penalty calculations. This has no effect on the stats of the monsters in the area or the loot that those monsters drop.

An analytically deduced formula for the preceding table is: $\text{EffectiveMonsterLevel} = -0.03 * \text{MonsterLevel}^{2} + 5.17 * \text{MonsterLevel} - 144.9$

Combining together the experience penalty for high level characters and the adjustment of monster level, here are some example sets of experience penalties, one for tier 8 (Effective monster level 74.10), one for tier 10 (Effective monster level 75.32), and one for tier 15 (Effective monster level 77.32).

So a level 99 player will be earning 1.9% experience for clearing tier 8 content, 2.5% experience for clearing tier 10, and 4% experience for clearing tier 15. In practical terms, this means that if the player can clear a tier 8 more than twice as fast as a tier 15, they will be much better off clearing tier 8 content when looking at experience efficiency per hour (because 4.0 is a bit more than two times 1.9). And if they can clear tier 10 content at most 31.5% slower than tier 8 content, then they are better off clearing tier 10 content (because 2.5% is 31.5% more than 1.9%). Bear in mind that this changes with player level and with the density of monsters in a map as well.

An additional consequence can be seen by the difference in XP multiplier across different levels. For example, tier 10 content at level 94 gives 9.6% experience, but at level 99 only gives 2.5% experience. This means that if a level 94 and 99 were to theoretically do the same tier 10 content (separately from each other), it would take the level 99 approximately 3.84 times longer doing the same content to gain the same absolute amount of experience. In other words, if a level 94 were to gain X million experience in tier 10 maps in one hour, then it would take the level 99 about 3 hours and 50 minutes to gain that same X million experience if they were going at the same pace.

As an example using only tier 10 content as a guideline, the penalties for level 90 and above, expressed with the amount of time relative to leveling up from level 90 to 91 (using level 90->91 as a baseline), we can come up with a table showing what share of total time from level 90 to 100 a given level will take, as well as the cumulative progress towards level 100. Looking at the below chart, level 95->96 will take about 8.41% of the total time, and once you are complete with that level (in other words, base level 96), you will be 23.58% complete with progress towards level 100. Additionally, it will take about 6.576 times longer going from level 95 to 96 than it took to go from 90 to 91, as there is 1.46 times as much absolute XP to gain for that level, and the multiplier is 4.5 times lower at level 95 than at level 90, so 4.5 times less experience gained per unit time * 1.46 times as much experience to gain = 6.57 times longer to go from 95->96 than to go from 90->91.

Note that changing the tier between 4 and 15 for the above chart does not change the percentage values very much, in each case, no matter which monster level the zone is, base level 98 will still be roughly 50% of the way from 90->100, and base level 99 will still be roughly 70% of the way. It works out this way because the XP multiplier only starts to bottom out at 1% when you're level 99 and running a tier 3 (effective monster level 70) zone; in higher level zones, the XP penalty formula decreases approximately linearly, and keeps roughly the same proportion between each level. This is where the efficiency aspect comes into play again. At level 99, if you can clear a tier 10 zone at most 2.5 times as slowly as a tier 3, you're better off running a tier 10 instead of a tier 3 (multiplier for level 99, tier 3 = 0.01, multiplier for level 99, tier 10 = 0.025). Similarly with Level 90 players, but it's more dramatic, as Level 90 tier 3 multiplier = 0.064, and Level 90 tier 10 multiplier = 0.306 [4.78 times as much]. So you'd need to clear a tier 3 at least 5 times as fast as a tier 10 on a level 90 character in order to be efficient.

Comparing experience gains at high levels
We can use the efficiency calculations from above to show how much experience a player of a given level must get per unit time in order to be achieving the same experience per unit time of another player level, taking into account experience penalties. If two characters are running tier 11 content, we can compare how much one is getting versus how much the other should be getting in order to keep pace with the other.
 * For example, using the chart below: a level 91 character must get 7.00 times as much experience per unit time as a level 98 player to be keeping the same pace.
 * A level 80 character must be getting 3.79 times as much experience per unit time as a level 91 character to be keeping the same pace.

Figuring out how long it will take to get from one level to a different level
We can say that if we're going a specific speed at a given level in a given tier of content, then we can compute how fast you'll move to a different level.

For example, going 10 Million XP/hour at level 96, we can compute how fast we will get to 97, 98, 99, and 100 if we continue at the same pace which was giving 10 Million XP/hour at level 96 by adjusting for each level based on the XP multiplier for that level, and then dividing the total amount of XP required to get to the next level by the rate at which we're gaining XP. Starting at base level 96, we need 253.5 Million XP to get to level 97, and we know that if we're going 10 Million XP/hour, it will take 25.35 hours (253.5/10 = 25.35). We also know that the XP multiplier at level 96 is 1.39 times higher than at level 97, so at level 97, we'd be gaining XP at 10/1.39 = 7.19 Million XP/hour, and level 97 takes 273.3 million XP, therefore, it will take 38.01 hours to go from base 97 to base 98, then we can compute the difference between the level 96 multiplier and the level 98 multiplier (or between 98 and 97, we just need to use the correct amount of XP/hour in the formula). The whole formula would look like: 253.5/10 + 273.3/(10/1.39) + 294.6/(10/1.91) + 317.5/(10/2.56) = 200.88 hours.

This does change slightly with a change in tier.
 * For example, using tier 13 content: 253.5/10 + 273.3/(10/1.41) + 294.6/(10/1.95) + 317.5/(10/2.64) = 205.15 hours.
 * For example, using tier 8 content: 253.5/10 + 273.3/(10/1.36) + 294.6/(10/1.82) + 317.5/(10/2.40) = 192.34 hours.
 * For example, using tier 3 content: 253.5/10 + 273.3/(10/1.30) + 294.6/(10/1.67) + 317.5/(10/1.82) = 167.86 hours.

Now, you might look at that and wonder why higher tier content means that you're going slower. The reason is that we're calculating independent of how much XP each individual Map would give, we're only concerned with the tier, and we're telling it that we're getting a given amount of XP at level 96 in that tier. The XP Multiplier drops off slightly differently between different tiers, and bottoms out much more quickly at lower tiers. This is where changes in map type for efficiency come into play. If you can actually meet a given XP rate in a given tier of map, there is going to be a sweet spot in terms of which tier of maps you would actually want to run. In practical terms, people run maps for a given layout and density.

A hyperbolic example to explain why it's "faster" at lower tiers:
 * Getting 200 M XP/hour at level 96 in tier 11: 253.5/200 + 273.3/(200/1.39) + 294.6/(200/1.91) + 317.5/(200/2.56) = 10.04 hours.
 * Getting 200 M XP/hour at level 96 in tier 3: 253.5/200 + 273.3/(200/1.30) + 294.6/(200/1.67) + 317.5/(200/1.82) = 8.39 hours.
 * Getting 200 M XP/hour at level 96 in a level 67 zone: 253.5/200 + 273.3/(200/1.03) + 294.6/(200/1.03) + 317.5/(200/1.03) = 5.82 hours.

You will note that it simply would not be possible to run enough Level 67 zones in an hour to get 200 M XP/hour at level 96. It is, however, possible [though practically out of reach for all but the most insane of players] to run enough tier 11 maps to get 200 M XP/hour at level 96 (translates to 78.13 M/hour at 99). Note that at level 99 the tier 11 content that was giving a pace of 200 M/hour at 96 is now giving a pace of 78.13 M/hour; and the Level 67 content that was giving a pace of 200 M/hour at 96 is now giving a pace of 194 M/hour at level 99 because the XP multiplier is just 1% for level 97+ players running Level 67 content.

Another way to think of this discrepancy is due to XP efficiency between the different tiers. The XP multiplier at level 96 for Level 67 content is 1.03%, and for tier 11 content is 7.19%. This means you will generally be gaining 6.98 times as much XP doing tier 11 content as you will be gaining in Level 67 content. It is a bit difficult to actually state how much someone would be gaining, simply because you cannot do a direct comparison between the two. They are different monster levels and give different raw experience, but in general, it should be a good measuring-stick to tell that you would need to run about 7 times as many Level 67 zones as tier 11 maps in the same amount of time to get the same amount of experience. It doesn't quite work like that, but it should be close.

This also shows that the difference in XP multiplier governs how much you'll be gaining at a given level within a given tier of content. So notice that the level 67 zones bottom out at 1% XP Multiplier at level 97, 98, and 99. This means that if you are able to gain a given amount of XP at level 97, you will gain the same amount of XP at level 98 and 99. The XP Multiplier drops down to the minimums much more quickly (or degrades more slowly) for lower level content due to the way the XP Multiplier formula works. So this means that you are not slowing down as much in terms of XP gains when you increase in level. This also means that we should be able to find a theoretical sweet spot for Map tier versus XP gained through empirical tests. Because it is clear that it takes much longer to get to level 100 while running level 67 content than it does while running tier 11 content.

Great! Now maybe we know that we just want to run tier 11 content from 80 to 100. How long will it take? We can re-arrange the formula from calculating the 96->100 values to insert an X for the amount we gain per hour: That means we take the sum of our XP amounts per level multiplied by the ratio of XP multipliers between the levels being compared:
 * 253.5/X + 273.3/(X/1.39) + 294.6/(X/1.91) + 317.5/(X/2.56)
 * This can be expressed as: 1/x*(253.5 + 273.3*1.39 + 294.6*1.91 + 317.5*2.56)
 * 80-100: 1/x*(74.1 + 80.18*1.00 + 86.72*1.00 + 93.75*1.00 + 101.35*1.00 + 109.52*1.02 + 118.34*1.12 + 127.81*1.3 + 138.03*1.62 + 149.03*2.11 + 160.89*2.81 + 173.65*3.79 + 187.37*5.09 + 202.15*6.81 + 218.04*8.99 + 235.16*12.9 + 253.54*13.9 + 273.36*19.37 + 294.63*26.48 + 317.52*35.58) = 1/x * 37737.2521
 * So at 400 Million XP/hour at level 80, you'd expect it to take 94.34 hours to hit level 100.
 * And at 100 Million XP/hour at level 80, you'd expect it to take four times as long, so 377.37 hours to hit level 100.

We can see that this is actually a very simple formula when we pre-compute most of it, and we'll end up with just a single division operation. We can therefore generate a table for tier 11 content, showing the Numerator of the division operation (expressed in Millions of XP), so that we can quickly compute how long it will take to go from one level to a different level. It is also important to note, that for most tiers, these values will not change much, and particularly for tiers near to 11 (such as tiers 8-13), this table should be close enough to get a very accurate estimate of the time it will take. Note the numerator for 80->100 in the table is slightly different from the value calculated above, because above just rounded the XP from one level to the next, and the table uses the exact values.

To use this table, find your level in the left-hand column, and then the level you would like to reach on the top row. Where they intersect gives you a "Raw XP" value (in Millions), which you can divide by your XP/hour, to see how long it'll take to get from one level to the next. You can also subtract out the XP you've gained in your current level (in Millions) from the value, and divide, in order to get a better estimate.

A few quick examples:
 * Level 86 to 93, when we are going 45 million XP/hour at 86 takes 2600.81/45 = 57.80 hours.
 * Level 90 to 100, when we are going 100 million XP/hour at 90 takes 12935.73/100 = 129.36 hours.
 * Level 92 to 95, when we are going 30 million XP/hour at 92 takes 842.14/30 = 28.07 hours.
 * If you're 83 Million XP into Level 97 and want to go to level 100, and you are gaining 25 Million XP/hour at level 97: (1259.35 - 83)/25 = 47.05 hours.

Party play
Party play experience has witnessed a revision since its first incarnation in the game. In the original system, a monster with a solo experience of 1000 would instead have PartySize * 1000 experience, which would then get split among the party members proportional to (PlayerLevel+10)^2.71. However, this system promoted lower level players boosting higher level players. To remedy this, in Patch 0.9.13e they instead took these experience values that players would get and capped them at the solo experience of the monster. This means characters can get penalized for being lower level relative to the party, but not rewarded for being higher level (both compared to solo play).

All other experience penalties and multipliers apply in addition to this party penalty.

The following formula captures the revised system, which caps out the multiplier at 1, while keeping the same effect for players who would be penalized. $\text{PartyPenalty}_x = \min\{1, \text{PartySize}*\frac{(\text{PlayerLevel}_x + 10)^{2.71} }{\sum\limits_{i=1}^n{((\text{PlayerLevel}_i + 10)^{2.71} })}\}$

In the following example a party containing a level 10 and 30 player kill a monster which gives 1000 solo experience: Percentual Old Share of experience: Revised Capped System:
 * Level 10 player would receive: (10+10)^2.71 / ((10+10)^2.71 + (30+10)^2.71) = 3355/25313 = 0.132 = 13.2% of the 2*1000 XP = 264 XP
 * Level 30 player would receive: (30+10)^2.71 / ((10+10)^2.71 + (30+10)^2.71) = 21957/25313 = 0.867 = 86.7% of the 2*1000XP = 1734 XP
 * Level 10 player: 264 exp
 * Level 30 player: 1000 exp

The table below shows the players "share" from level 1 to 100.

Miscellaneous
Killing monsters that were raised from the dead by any means (revived by Necromancers, Soul Conduit Nemesis Mod, the reviving Strongbox affix) gives no additional experience. Player-summoned minions and monsters spawned by other monsters (ex:sirens) also award no experience. Beyond demons, and monsters from Strongboxes do give experience, however.

Version history

 * 95 to 96: 6.5% more experience needed
 * 96 to 97: 11.5% more experience needed
 * 97 to 98: 18.7% more experience needed
 * 98 to 99: 28.25% more experience needed
 * 99 to 100: 40% more experience needed


 * There is a 5% experience penalty for deaths in Acts 6 through 10, level 5 and 6 Forsaken Master mission areas, and the Cruel and Merciless Labyrinths. There is a 10% experience penalty for deaths in areas reached through the Map device, level 7 and 8 Forsaken Master mission areas, and the Endgame Labyrinth. These replace the old Cruel and Merciless experience penalties, and are only active in those specific areas. Dying in any Act 5 area (or lower) after completion of Act 5 (or higher) will not incur an experience penalty.


 * Players at very high levels (95 and higher) now incur an additional experience penalty equal to 1 - ( 1 / ( 1 + 0.1 * ( level - 94 ) ) ). For example, a level 96 player receives 16.67% less experience than before.


 * The experience penalty for higher levels is now slightly higher. The penalty starts taking effect a few levels earlier than it previously did.


 * Previously, the most that experience could be penalised to was 2% of the monster's normal experience. This value has been reduced to 1%. This is to encourage players to run content appropriate for their high level.


 * Added death penalties of 5% and 10% of current level's experience on Cruel and Ruthless difficulties respectively


 * Implemented experience scaling when fighting substantially higher or lower level monsters
 * Modified experience gain to require 30% more kills per level


 * Level/experience properly displayed on character screen


 * Changed layout of experience values on the character screen to be clearer


 * Added more information to the experience bar display


 * Fixed experience popup hover
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