Is there any way to accurately increase CR based on an excess of party wealth?

Question

If playing milestone leveling a ramping of treasure can occur in which the party gains gold and magical items far beyond what their normal wealth would be at a level.

And yes this issue can be avoided if you carefully amend treasure to lower values over time to even things out. But in my particular case I did not do a good job of this and thus have players who have a great deal more gold than would be normal at their level but would be normal for the amount of creatures they have defeated.

But the question here is, if the party does have more wealth than is normal for their level, say they have the wealth of a 9th level character at 6th or 7th level. Is there any accurate way to determine how much higher CR's of encounters should be in order to present appropriate Very easy, Easy, Challenging, and Very difficult encounters?

Answer 1

No, there isn't a table that exactly identifies CR increase based on party wealth.

The DMG explicitly calls this the DM's job in the game (DMG, p54):

Your job is to compare the wealth gained from the encounters in your adventure with the expected wealth gain shown on the table above. If your adventure has more treasure, reduce it.

and (p212)

Including magic items as part of a treasure is a vital task of the DM. ...A single overpowering item can ruin a whole campaign.

However, both the DMG and the DMG II have a number of resources for modifying encounter difficulty to suit players who are struggling or overpowering equal-EL encounters. On page 49 of the DMG, the section "Single Monster Encounters" provides some tips to heighten difficulty, such as "Prepare tactics in advance" or "Split up the party." On page 50, there's another section explicitly titled "Modifying Difficulty," discussing further tactics to increase the effective challenge of lower-CR enemies. The DMG II also contains a wealth of resources for 'spicing up' encounters by means such as making them in exotic environments (eg, aerial or underwater combats), which may force the players to acquire and use consumables they wouldn't have otherwise needed.

Overall, the advice seems to be:

1. Don't worry too much about adjusting short-term XP gain. If you gently reduce treasure, the players will 'catch up' to their gear.
2. Increase the difficulty for well-equipped characters by making their enemies well-prepared as well.
3. Create novel encounters which encourage the players to consume more resources.

And from my own experience, one possibility is to allow the players to expend or trade in some of that wealth for some in-game reason. For good parties, this might be a heroic act (rebuilding a destroyed town) or noble purpose (expanding a Good religious organization). For neutral or evil parties, it might be some investment that will pay off later (magical research that will yield new items or spells -- when it's level-appropriate) or personal status (titles of nobility, complete with lands and serfs).

Answer 2

First of all, you are misusing a few common terms, so let me clarify them.

Challenge Rating

Each monster in that book has a Challenge Rating (CR) that, when compared to party level, translates directly into an XP award. A Challenge Rating is a measure of how easy or difficult a monster or trap is to overcome. (Dungeon Master's Guide, page 36)

The Party Level is the average level of all characters in the party, including player characters and npcs.

ECL The effective character level (ECL) of a creature determines how powerful it is as a character or a cohort. The Monster Manual contains statistics and other details on potential cohorts. Take the level adjustment plus the Hit Dice (including class hit dice) to generate ECL.

A little more about adventurers and economy

Remember that unless something is a trade good, like gems, pieces of art, magic items it is sold by half of it's market price. Keep in mind, that player character are adventurers. They need to purchase and sustain some sort of transport. They must eat, drink and have a place to sleep. The spellcasters may need to purchase expensive material components, like the diamond used in resurrection spell, that must cost at least 10 000 gp. There are other factors as well, like hiring npcs, paying a spellcaster to cast a spell on them and purchasing one-time use goods like potions, scrolls. Whenever I play as either Game Master or a Player, the wealth is quite fastly used is some way.

The question itself

The wealth should never be used when determining the character or party level, however it could affect the gained rewards, if you find that encounters were considerably easier because of the wealth.

Modifying XP Awards and Encounter Levels

Sometimes, the circumstances give the characters’ opponents a distinct advantage. Other times, the PCs have an advantage. Adjust the XP award and the EL depending on how greatly circumstances change the encounter’s difficulty. (Dungeon Master's Guide, page 39)

There is also a small table, that suggests how you should modify Encounter Level and the awarded XP.

|       Circumstance         | XP Award Adjustment |EL Adjustment |
|   Half as difficult        |       XP × 1/2      |    EL –2     |
|Significantly less difficult|       XP x 2/3      |    EL –1     |
|Significantly more difficult|       XP × 1-1/2    |    EL +1     |
|Significantly more difficult|       XP × 2        |    EL+2      |

It is suggested to keep the further points in mind while modifying XP reward and ELs.

• Experience points drive the game. Don’t be too stingy or too generous.
• Most encounters do not need modifying. Don’t waste a lot of time worrying about the minutiae. Don’t worry about modifying encounters until after you have played the game a while.
• Bad rolls or poor choices on the PCs’ part should not modify ELs or XP awards. If the encounter is difficult because the players were unlucky or careless, they don’t get more experience.
• Just because the PCs are worn down from prior encounters does not mean that later (more difficult) encounters should gain higher awards. Judge the difficulty of an encounter on its own merits.