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Is the Reworked Gold Assist formula broken? #8671

Open jsindos opened 1 year ago

jsindos commented 1 year ago

Description

Let me know if this has been posted elsewhere, but it seems like the new gold assist formula operates differently to the 7.33 patch notes.

The Reworked Gold Assist in 7.33 was posted as:

Old Formula: (30 + (VictimNetworth * 0.038) ) / NumHeroes

New Formula: 10 + ((50 + (VictimNetworth * 0.037) / NumHeroes)

It seemed like in the early game I should expect to receive an extra ~20 assist gold for a kill with me and my lane partner, compared to 7.32 (10 + the additional 20 divided by 2, victim net worth is negligible).

However, it felt like I was getting too much extra gold from early kills, so I went into a replay.

MATH PART

Even though it's not mentioned, I assume the Net Worth difference factor still adjusts the assist gold in the same way.

Looking at an example of a kill in my replay:

1186 NW of victim as he dies.

NW of victim team = 7040

NW of killing team = 6850

k (Net Worth difference factor) = 1 + (190 / 7040) = 1.027

2 killers

Expected assist gold: 10 + ((50 + (1186 0.037)) 1.027 / 2) = 58 gold

Actual assist gold:

Kill is marked as 222 + 81 to 1 hero (so the assist gold per hero is 81 gold).

However, we can get approximately 81 if we take the 50 out of the parantheses:

60 + ((1186 0.037) 1.027 / 2)) = 83 gold

Another example from the same game:

2274 NW of victim as he dies.

NW of victim team = 9030

NW of killing team = 8280

k (Net Worth difference factor) = 1 + (750 / 9030) = 1.083

2 killers

Expected assist gold: 10 + ((50 + (2274 0.037)) 1.083 / 2) = 83 gold

Actual assist gold:

Kill is marked as 264 + 107 to 1 hero (so the assist gold per hero is 107 gold).

Take 50 out of the parantheses:

60 + ((2274 0.037) 1.083 / 2)) = 106 gold

Late game example:

16384 NW of victim as he dies.

NW of victim team = 104530

NW of killing team = 85230

k (Net Worth difference factor) = 1 + (19300 / 104530) = 1.185

4 killers

Expected assist gold: 10 + ((50 + (16384 0.037)) 1.185 / 4) = 204 gold

Actual assist gold:

Kill is marked as 636 + 753 to 3 heroes (so the assist gold per hero is 251 gold).

Take 50 out of the parantheses:

60 + ((16384 0.037) 1.185 / 4)) = 240 gold

(this one is a bit off, I think the Net Worth difference factor might actually multiply the whole amount rather than the inner amount).

In any case, in all of the examples, absorbing the inner 50 gold into the outer amount is closer than using the expected formula.

Assuming this is true, it means a kill with one assister is worth ~50 gold more in the early game, and scales up by ~50 gold for every additional assister on the kill, i.e. a 5 man kill in the early game is worth ~200 more gold than the expected assist gold.

Example Match ID (and possibly Timestamp)

No response

Screenshots

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dampf1 commented 1 year ago

New Formula: 10 + ((50 + (VictimNetworth * 0.037) / NumHeroes) This is what they posted in the patch. It has one more open bracket than closing.

If we just take this part (50 + (VictimNetworth * 0.037) / NumHeroes) it is clear that giving more extra bonus gold for every additional hero is intended.

From what I found by testing is that true formula being used is something close to (60+(VictimNetworth 0.037) / NumHeroes)) NetworthEnemyTeam / NetworthOwnTeam

The networth difference factor was changed without notes. It being NetworthEnemyTeam / NetworthOwnTeam means it is still the same for the leading team as before but losing team gets a bigger boost.

IngEyn commented 1 year ago

I believe I have found another example for this issue even though it would not work with the thesis described above.

In match 7275104004 at minute 32:15, Nature's Prophet is killed by Skywrath Mage for 999 gold, which is supposed to include the hero kill bounty and the assist bounty. However, while I could confirm that the hero kill bounty has been calculated correctly, I was unable to get to the same result as the game for the assist bounty using the old, the new or the false formula discussed above.

The precise values can be observed in the replay when the kill is happening. The values presented were +738 and +261 gold.

For calculating the correct values, I have referred to the Dota 2 Wiki^1 and the patch notes for patch 7.31^2 as well as 7.33^3.

The hero kill bounty calculation can be done with this formula, which is the same throughout all sources:

This leaves us with the correct value of 125 + 17 * 8 + 0 + 0 = 261 even though streak and first blood bonuses aren't mentioned in the official patch notes.

The assist bounty calculations can be done with these formulae, depending on the source:

This formula has been edited by me as it appears to not have been updated on the Wiki despite it being mentioned in the changelogs. The NetWorthDifferenceFactor is based on if the killer's team is either losing or leading in net worth and can be calculated like this:

As the killer in this case has been part of the losing team, the calculated value based on the Wiki is 10 + ((50 + (15262 * 0.037)) * (1 + (11233 / 76646)) / 1) = 648, which would be 90 gold below what the killer actually achieved.

In this case, the calculated value based on the patch notes would have been 10 + ((50 + (15262 * 0.037)) / 1) = 625, which would be even lower.

The assumption, that the 50 could have been added to the 10 instead by mistake, as discussed above, would lead to the value looking like this: 60 + ((15262 * 0.037) * (1 + (11233 / 76646)) / 1) = 707, which would be about 30 off.

Ultimately I do not know how the system got to the value 738 and I'd like there to be a single reliable source where players could find all of the important formulae they could ever need. I was surprized that the glossary did not include or mention any formula for calculating those bounties. I hope this find can help solving this issue as I believe it is a pretty important one that should be addressed.