D&D 4E Heavy Concrete Data on 4e's Skill Challenge System (long, lots of tables)

[Stalker0]

EDIT: I have added TABLE 4, now showing the effects of aid another with differing numbers of people.

I started a bit of a firestorm in my other thread when I showed math that indicated 4e's skill challenge system did not work. I realize now that I should have provided you all a great deal more data when challenging such a core mechanic. I am prepared to do that now.

I will write a description of each table beneath that table, detailing the facts I am showing. Then I will draw up some conclusions at the bottom. This post will be long.

Assumption: Party of 5 people, each has a medium skill aptitude (see below). Using medium DC at each level, COMPLEXITY: 5 challenge.

Table 1. Skill Modifiers for Various Skill Aptitudes

[b]Level	bad	med	good	stat	item[/b]
1	2	9	15	0	0
[b]2	3	10	16	0	0[/b]
3	3	10	17	0	1
[b]4	4	11	18	0	1[/b]
5	4	11	18	0	1
[b]6	5	12	19	0	1[/b]
7	5	12	19	0	1
[b]8	6	14	22	1	2[/b]
9	6	14	22	1	2
[b]10	7	15	23	1	2[/b]
11	7	15	23	1	2
[b]12	8	16	24	1	2[/b]
13	8	16	25	1	3
[b]14	9	18	27	2	3[/b]
15	9	18	27	2	3
[b]16	10	19	28	2	3[/b]
17	10	19	28	2	3
[b]18	11	20	30	2	4[/b]
19	11	20	30	2	4
[b]20	12	21	31	2	4[/b]
21	13	22	32	3	4
[b]22	14	23	33	3	4[/b]
23	14	23	33	3	4
[b]24	15	24	34	3	4[/b]
25	15	24	35	3	5
[b]26	16	25	36	3	5[/b]
27	16	25	36	3	5
[b]28	17	27	39	4	6[/b]
29	17	27	39	4	6
[b]30	18	28	40	4	6[/b]

These are the skill modifiers I used as the assumption for my work. The bad collumn is a character that invests very poorly in a skill. I assumed a 14 in the stat, no skill training, and the only times he puts ability points in that skill are at 11th and 21st level.

The medium column is your standard character. I assumed a 18 stat base, +5 for skill training. The character always puts 1 of his ability bumps into that stat. The stat column shows you when he gets a bump to skill as a result of that ability bump. Other than that, there's no skill focus or items that bump his skills.

In the good column I would like to introduce Skilly McAwesome, our resident skill god. Skilly has +5 in his stat to start, +5 for training, +3 skill focus, and +2 racial. He puts points in that stat whenever he can, and he gets items to boost his skills to the maximum. I used sylvan armor from the PHB as a basis for the item column, which shows the item bonus Skilly is receiving.

Table 2: Main Data on Skill Challenges

[b]LEVEL	IC	PWR	ICMA	ICBA	PWRBA	ICGS	PWRGS[/b]
1	50.0%	7.3%	90.0%	76.0%	79.5%	56.0%	16.7%
[b]2	55.0%	14.7%	95.0%	83.0%	94.5%	61.0%	29.2%[/b]
3	55.0%	14.7%	95.0%	83.0%	94.5%	62.0%	32.2%
[b]4	50.0%	7.3%	90.0%	80.0%	89.4%	57.0%	18.9%[/b]
5	50.0%	7.3%	90.0%	80.0%	89.4%	57.0%	18.9%
[b]6	55.0%	14.7%	95.0%	87.0%	98.3%	62.0%	32.2%[/b]
7	45.0%	3.0%	85.0%	77.0%	82.3%	52.0%	9.7%
[b]8	55.0%	14.7%	95.0%	89.0%	99.3%	63.0%	35.4%[/b]
9	55.0%	14.7%	95.0%	89.0%	99.3%	63.0%	35.4%
[b]10	50.0%	7.3%	90.0%	86.0%	97.3%	58.0%	21.2%[/b]
11	50.0%	7.3%	90.0%	86.0%	97.3%	58.0%	21.2%
[b]12	55.0%	14.7%	95.0%	93.0%	99.9%	63.0%	35.5%[/b]
13	50.0%	7.3%	90.0%	88.0%	98.9%	59.0%	23.7%
[b]14	60.0%	26.4%	100.0%	100.0%	100.0%	69.0%	56.1%[/b]
15	60.0%	26.4%	100.0%	100.0%	100.0%	69.0%	56.1%
[b]16	55.0%	14.7%	95.0%	95.0%	100.0%	64.0%	38.6%[/b]
17	55.0%	14.7%	95.0%	95.0%	100.0%	64.0%	38.6%
[b]18	60.0%	26.4%	100.0%	100.0%	100.0%	70.0%	59.7%[/b]
19	50.0%	7.3%	90.0%	90.0%	99.5%	60.0%	26.4%
[b]20	55.0%	14.7%	95.0%	95.0%	100.0%	65.0%	42.0%[/b]
21	60.0%	26.4%	100.0%	100.0%	100.0%	70.0%	59.7%
[b]22	60.0%	26.4%	100.0%	100.0%	100.0%	70.0%	59.7%[/b]
23	60.0%	26.4%	100.0%	100.0%	100.0%	70.0%	59.7%
[b]24	65.0%	42.0%	100.0%	100.0%	100.0%	75.0%	76.5%[/b]
25	60.0%	26.4%	100.0%	100.0%	100.0%	71.0%	63.2%
[b]26	65.0%	42.0%	100.0%	100.0%	100.0%	76.0%	79.5%[/b]
27	65.0%	42.0%	100.0%	100.0%	100.0%	76.0%	79.5%
[b]28	70.0%	59.7%	100.0%	100.0%	100.0%	82.0%	93.1%[/b]
29	70.0%	59.7%	100.0%	100.0%	100.0%	82.0%	93.1%
[b]30	75.0%	76.5%	100.0%	100.0%	100.0%	87.0%	98.3%[/b]

A lot is going on in this table. I will go through each column.
IC: Individual Check percentage. This is what percentage each character has to make the DC for that level.

PWR: Party Win Rate. How likely the party is to win the challenge at that IC.

ICMA: Individual Check Percentage with Medium Aid Another. This is the percentage if you assume that 4 people out a 5 person party are aiding that 5th person, using a skill they are medium at.

ICBA: Individual Check Percentage with Bad Aid Another. This is the same as ICMA, except in this case, each character is aiding with a skill they have a bad modifier at.

PWRBA: This is the party win rate using the ICBA. I did not do one for ICMA because the numbers would always be near 100%.

ICGS: Individual Check percentage with Good Skill. For this number, I am assuming 1 of our 5 party members is now Skilly McAwesome, and has the good skill modifier. I am then averaging the party's numbers together. IMPORTANT NOTE: Because of the averaging, the numbers I have presented will be slightly higher than actual.

PWRGS: The party win rate using the ICGS.

Table 2 CONCLUSIONS:
1) Level 7 is no man's land for doing skill challenges. The DCs and modifiers just give the party an absolute garbage chance of succeeding.
2) Without aid another, a standard party won't have better than 50% chance to make a skill challenge until high epic level.
3) With aid another using their good skills, the party's win rate flies off the chart, hitting 100% win rate extremely quickly. I didn't show the win rate for this to save space, but with the ICMA so high, its easily to see that you can't have a group aiding one person all the time, else you will autopass most skill challenges.
4) The problem continues even if you aid one person with your bad skills. These numbers quickly get to +9, and once there, you are auto succeeding on aid rolls. The numbers get magnified by this, and near 100% win rates quickly result.
Conclusion: Every person aiding 1 person in a skill challenge DOES NOT work.
5) The last two columns show our boy Skilly going to work. While he has a significant impact on his party, he does not get them to 50% PWR, in many cases not even close. However, at high levels he's working overtime, and the party has a near 100% PWR with him there.
Conclusion: The Assumption of one skill guy cannot save the system.


Table 3. -5 to our Standard DCs.
This one is for the people who are thinking about using the DC table without adding the +5 from the footnote.

[b]LEVEL	IC	PWR	ICGS	PWRGS[/b]
1	75.0%	76.5%	81.0%	91.4%
[b]2	80.0%	89.4%	86.0%	97.7%[/b]
3	80.0%	89.4%	87.0%	98.3%
[b]4	75.0%	76.5%	82.0%	93.1%[/b]
5	75.0%	76.5%	82.0%	93.1%
[b]6	80.0%	89.4%	87.0%	98.3%[/b]
7	70.0%	59.7%	77.0%	82.3%
[b]8	80.0%	89.4%	88.0%	98.9%[/b]
9	80.0%	89.4%	88.0%	98.9%
[b]10	75.0%	76.5%	83.0%	94.5%[/b]
11	75.0%	76.5%	83.0%	94.5%
[b]12	80.0%	89.4%	88.0%	98.9%[/b]
13	75.0%	76.5%	84.0%	95.8%
[b]14	85.0%	96.8%	94.0%	100.0%[/b]
15	85.0%	96.8%	94.0%	100.0%
[b]16	80.0%	89.4%	89.0%	99.3%[/b]
17	80.0%	89.4%	89.0%	99.3%
[b]18	85.0%	96.8%	95.0%	100.0%[/b]
19	75.0%	76.5%	85.0%	96.8%
[b]20	80.0%	89.4%	90.0%	99.5%[/b]
21	85.0%	96.8%	95.0%	100.0%
[b]22	85.0%	96.8%	95.0%	100.0%[/b]
23	85.0%	96.8%	95.0%	100.0%
[b]24	90.0%	99.5%	100.0%	100.0%[/b]
25	85.0%	96.8%	100.0%	100.0%
[b]26	90.0%	99.5%	100.0%	100.0%[/b]
27	90.0%	99.5%	100.0%	100.0%
[b]28	95.0%	100.0%	100.0%	100.0%[/b]
29	95.0%	100.0%	100.0%	100.0%
[b]30	100.0%	100.0%	100.0%	100.0%[/b]

Table 3 Conclusions:
1) With this system, its a ping pong match between 75% and 90% win rates until you get to higher levels in which case 100% win rate starts taking over.
2) Our boy skilly once again ramps up the rates, easily getting near 100% in very short order.

Table 4. Variations of Aid Another

[b]LEVEL	PWR(0)	PWR(1)	PWR(2)	PWR(3)[/b]
1	7.3%	10.45%	17.98%	41.97%
[b]2	14.7%	20.02%	31.19%	59.68%[/b]
3	14.7%	20.02%	31.19%	59.68%
[b]4	7.3%	10.45%	17.98%	41.97%[/b]
5	7.3%	10.45%	17.98%	41.97%
[b]6	14.7%	20.02%	31.19%	59.68%[/b]
7	3.0%	4.74%	9.30%	26.39%
[b]8	14.7%	20.02%	31.19%	59.68%[/b]
9	14.7%	20.02%	31.19%	59.68%
[b]10	7.3%	10.45%	17.98%	41.97%[/b]
11	7.3%	10.45%	17.98%	41.97%
[b]12	14.7%	20.02%	31.19%	59.68%[/b]
13	7.3%	10.45%	17.98%	41.97%
[b]14	26.4%	33.77%	47.53%	76.53%[/b]
15	26.4%	33.77%	47.53%	76.53%
[b]16	14.7%	20.02%	31.19%	59.68%[/b]
17	14.7%	20.02%	31.19%	59.68%
[b]18	26.4%	33.77%	47.53%	76.53%[/b]
19	7.3%	10.45%	17.98%	41.97%
[b]20	14.7%	20.02%	31.19%	59.68%[/b]
21	26.4%	33.77%	47.53%	76.53%
[b]22	26.4%	33.77%	47.53%	76.53%[/b]
23	26.4%	33.77%	47.53%	76.53%
[b]24	42.0%	50.73%	65.68%	89.43%[/b]
25	26.4%	33.77%	47.53%	76.53%
[b]26	42.0%	50.73%	65.68%	89.43%[/b]
27	42.0%	50.73%	65.68%	89.43%
[b]28	59.7%	68.42%	81.48%	96.81%[/b]
29	59.7%	68.42%	81.48%	96.81%
[b]30	76.5%	83.62%	92.57%	99.53%[/b]

This table shows the PWR if different numbers of people are aiding each round. The assumption is people are aiding with their medium skills. The first is no aid, the second 1 person is aiding, then 2 and then finally 3 people aiding. The effects of 4 people aiding are provided in table 2.
Table 4 Conclusions:

1) The big thing to note is where is the massive jump between 2 people and 3 people aiding.

Final Conclusions:
1) Aid another does not fix the system. In many cases, it causes an overload effect, ramping up the party to 100% win rates.
2) The system has a trouble tolerating a skill guy in the party, and can quickly get the party up to 100% win rates.
3) The system is very sensitive to variation. Even the slightest change in the parties skills can have a strong impact on the system.
4) Epic DCs are too low.
5) -5 to DCs does help, but it does not fix the problem.


I hope this data will give you a wider view of the skill challenge problem. If you believe the system is broken and would like a solution, I have already constructed a much stronger, numerically tighter system that addresses most of the big problems...and I'm currently working on making it better. You can find that here: http://www.enworld.org/showthread.php?t=229796

 

[Lhorgrim]

I appreciate the work you've done on this.

I agree that the skill challenge system has some issues that would cause problems for an inexperienced DM. I feel that more veteran DMs would "adjust on the fly" to make the system more appropriate during play.

The question I have about all of this is what happened during the playtest phase? Has there been any official statement or clarification from WotC about the skill challenge system?

I have a hard time believing that this made it through playtest unless there is something either erroneously added to, or left out of, the rules.

 

[Terramotus]

Bravo, Stalker0. Thank you for doing all of this math. My group knew the system was broken the first time we played it. I think this math makes it clear that even when steps are taken to make the system playable, such as with Aid Another or lowering the DCs by 5, it still leaves a highly flawed system that does not provide a good, easily scaled tool for the DM to challenge his party.

I still can't fathom how this made it into the final books.

I do have one question, though. Let's say that the DC table is totally wrong, shouldn't have been in the books at all, and there's a different, totally differently balanced table. I know you've lowered the variance in your version, but is there hope for the system with a better table of DCs? I'm really just thinking aloud here, wondering if that was where the mistake was made.

 

[FadedC]

I don't really have a problem with Skilly McAwesome always or almost always winning skill challenges related to his own skill. But the aid another thing is a good demonstration. Seems like if they are going to have skill checks scale with level, they need to have the aid another DC scale with level too.

 

[Morrus]

So skill challenges actually have the opposite problem to the one you initially claimed? In other words, instead of being nigh-impossible, they're near-autosuccesses now?

 

[Rystil Arden]

So skill challenges actually have the opposite problem to the one you initially claimed? In other words, instead of being nigh-impossible, they're near-autosuccesses now?

It's only broken in that direction if aid another is allowed in the challenge without limitation, which seems unlikely given that many of the sample challenges have skill uses that are similar to aid another (in that they give a +2 to someone else using one skill in the challenge) but have vastly higher DC than Aid Another does, so you would essentially be penalised for using those options instead of using Aid Another (to see some examples, check Urban Chase and Lost in the Wilderness. Both allow Perception to give a +2 for an Easy check, which is always harder than an Aid Another).

Also, I think one of his main points since the beginning was that the system was not very tolerant to minor changes in the PCs' favour and quickly goes off the charts with high success rates, which this reinforces.

 

[Stalker0]

So skill challenges actually have the opposite problem to the one you initially claimed? In other words, instead of being nigh-impossible, they're near-autosuccesses now?

As Rystil mentioned, those skyrocket win rates are the results of aid another. Without them, the party's win rate remains very low until the highest levels.

 

[Dave Turner]

Do the Table 3 conclusions assume that each PC making a skill check is "medium", as per your initial assumptions?

 

[Morrus]

It's only broken in that direction if aid another is allowed in the challenge without limitation, which seems unlikely given that many of the sample challenges have skill uses that are similar to aid another (in that they give a +2 to someone else using one skill in the challenge) but have vastly higher DC than Aid Another does, so you would essentially be penalised for using those options instead of using Aid Another.

I wonder if this is because we're comparing optimum and err... antioptimum(?)... circumstances, though? Most of the time neither case will apply; it'll be somewhere in between. And where optimum circumstances exist, I guess it should be easy.

I'm not dedicated anoutgh to analyse the tables above; however Mr. Skilly McSkill won't get to use his optimum skill on ALL five of the rolls. There's gonna be a range in there; perhaphs two people will have veery high skills they can use, another couple will have medium skills and the last with crappy skills in this particular instance (although in a different skill challenge he might rival Skilly's scores in the first challenge).

Aid Another is going to vary from 0 to 4 uses in a particular skill check by a 5-man party.

I comes across to me as a lot of sliding variables which are all being set at 0 together, or all being set at 10 together; this probably isn't a situation that's likely to occur.

 

[Eldorian]

So skill challenges actually have the opposite problem to the one you initially claimed? In other words, instead of being nigh-impossible, they're near-autosuccesses now?

Reread table 2. Pay particular attention to the columns PWR, PWRBA, and PWRGS.

PWR is what he originally worked with. As you can see, you don't win until late epic with anything approaching regularity.

PWRBA is what happens if you let aid anothers be used. You usually win, latter on you always win.

PWEGS is what happens if you don't aid another, but you have someone in the party who is amazingly good at the skill in question. Numbers are ALL over the place, another thing mentioned in the earlier analysis.

The next table is what happens if you lower all DCs by 5. Crazyness happens.

All this data shows that the skill challenge system, as currently written, is crap. It's a sad day. Hopefully WotC throws Stalker0 on the payroll, as he seems willing to work on fixing it =P

 

[Mezzer]

@ the OP: The skill challenge system also leaves a lot of room to the DM for tweaking, in various ways, so that the challenge is more appropriate for this game. Once the DM gets the hang of them, he should be able to tailor them to his group and adjust them, so that the PCs have a better chance of succeeding using skills which make sense for the challenge, and a smaller chance with other skills, and so on. He can apply conditional bonuses, he can adjust things on the fly, he can reward creative thinking and he can deny really silly ideas.

The problem with the math, in this case, is twofold; the model can't possibly encompass the wide variety of options inherent in the system, and the event sample is just too small for the math to be relevant.

If you feel more comfortable creating your own system, then by all means go for it, but you should make it more clear (since you've already gone to all the trouble of presenting all of that in such a manner) that all that math is there solely for supporting your opinion that the system is flawed, nothing more.

 

[Morrus]

As Rystil mentioned, those skyrocket win rates are the results of aid another. Without them, the party's win rate remains very low until the highest levels.

But what if, say, 2 characters are aiding one, another one is making his won check on his own, and the last two are working together?

And the many combinations of this posssible... multiplied by the different combinations of skill ranks owned by each character. It seems to me that there are dozens of possible columns on that table, not just the three or so given.

I may be not understanding the tables well - it is late, and I'm not inclined to analyse them, so if I've completely misunderstood then feel free to just say so.

 

[Lurker37]

Dare I even mention the possibility of a character with a trained skill linked to a stat which does not increase?

E.G. Religion for a paladin with only 13 int. No points in Int except at 11 and 21. I can see this happening if they wanted to qualify for a multiclass or other feat.

I know you've put a lot of work into these, but I'm hoping they still exist in spreadsheet form so you add another column and see what effect this has. This would be a step between bad and medium, so I expect you'd assume no items or skill focus.

 

[Stalker0]

But what if, say, 2 characters are aiding one, another one is making his won check on his own, and the last two are working together?

And the many combinations of this posssible... multiplied by the different combinations of skill ranks owned by each character. It seems to me that there are dozens of possible columns on that table, not just the three or so given.

I may be not understanding the tables well - it is late, and I'm not inclined to analyse them, so if I've completely misunderstood then feel free to just say so.

The table only shows the effects of 4 people attempting to aid the first person, so your not wrong. As to your question, the system mentions in aid another a +8 is the limit, so there's no reason the scenario I mentioned can't happen. Further, by mid heroic tier, party members start autopassing aid another rolls, so if they are willing to aid, why wouldn't they all try to aid 1 person?

Aid Another is one of the first rules I fixed in my new system, to prevent this kind of abuse.

 

[Eldorian]

II'm not dedicated enough to analyze the tables above;

Then you honestly have nothing to say. Not trying to be rude here, but if you don't understand what he's saying, then you can't make any conclusions about what he's saying. In fact, stating that you didn't read and comprehend his work and then judging it is kinda rude.

@ the OP: The skill challenge system also leaves a lot of room to the DM for tweaking, in various ways, so that the challenge is more appropriate for this game. Once the DM gets the hang of them, he should be able to tailor them to his group and adjust them, so that the PCs have a better chance of succeeding using skills which make sense for the challenge, and a smaller chance with other skills, and so on. He can apply conditional bonuses, he can adjust things on the fly, he can reward creative thinking and he can deny really silly ideas.

You're not getting the point of his work. The point is, a DM mediocre at judging probability would be capable of trusting the math in the book for running combat (this has been shown by the massive amount of playing that's been done for combat already). The skill challenge system would fail him utterly. Completely and utterly. He'd read the section in the book, try to run it, and it'd never perform up to expectations. Just look at the skill challenge added via web enhancement for Keep on the Shadowfell. It's nearly impossible to win with the playtest characters.

Spoiler:

Spoiler

In fact, they're far more likely to lose the final fight if they even ATTEMPT to do it, because of the attacks they get for failing their individual attempts.

 

[Rystil Arden]

The table only shows the effects of 4 people attempting to aid the first person, so your not wrong. As to your question, the system mentions in aid another a +8 is the limit, so there's no reason the scenario I mentioned can't happen. Further, by mid heroic tier, party members start autopassing aid another rolls, so if they are willing to aid, why wouldn't they all try to aid 1 person?

Aid Another is one of the first rules I fixed in my new system, to prevent this kind of abuse.

It's still not clear to me that Aid Another is supposed to be usable in a Skill Challenge. At least, if it is allowable, then they've put in some redundantly pointless options, since as you said, Aid Another is quickly an auto-success (and the options they include for + or - 2 are Easy Checks, which can usually still fail at least some of the time).

 

[Stalker0]

If you feel more comfortable creating your own system, then by all means go for it, but you should make it more clear (since you've already gone to all the trouble of presenting all of that in such a manner) that all that math is there solely for supporting your opinion that the system is flawed, nothing more.

I have worked with numbers, equations, and game mechanics for a long time...and I will say that if my more detailed analysis of the system had shown that my initial conclusions were wrong, I would say so...in a public thread where I would recant my findings and apologize for wasting people's time.

Yes, I have taken a painstaking amount of time crafting a new system, and I am very proud of it. I have also taken a painstaking amount of time detailing the evidence I have discovered about the current system, in a way that is organized and to the point. My conclusions are that the system is flawed, and I believe my numbers back that assertion up. I have even included aid another information, because the community requested it.

So you will pardon me if I sound a bit angered at your tone of post, but I am not just doing this to shout doom and gloom at WOTC or 4e. My conclusions have hard, factual evidence, and I will continue to work with the community on seeing the truth behind the current system and to continue to work on a better one...whatever truth that may lead to.

 

[Mezzer]

You're not getting the point of his work. The point is, a DM mediocre at judging probability would be capable of trusting the math in the book for running combat (this has been shown by the massive amount of playing that's been done for combat already). The skill challenge system would fail him utterly. Completely and utterly. He'd read the section in the book, try to run it, and it'd never perform up to expectations. Just look at the skill challenge added via web enhancement for Keep on the Shadowfell. It's nearly impossible to win with the playtest characters.

Spoiler:

Spoiler

In fact, they're far more likely to lose the final fight if they even ATTEMPT to do it, because of the attacks they get for failing their individual attempts.

If you trust the numbers, that is indeed what they indicate. But there is one very good reason why the numbers aren't relevant; the glaringly low event sample which the numbers address.

In my opinion, an individual DM can do much more good than any amount of number crunching in this regard, and while the idea of helping out new DMs with an easier system may have its merits, said DM will never learn how to adjust the system to his needs if he simply uses the proposed substitute. And yes, he will have to get a grasp of it, like any other system.

@Stalker0: I'm not trying to diminish your efforts in any way, I'm just saying that the data you posted is, in my opinion, a fair deal less relevant than you made it seem.

 

[Stalker0]

Do the Table 3 conclusions assume that each PC making a skill check is "medium", as per your initial assumptions?

They do. Basically in this case the players are using the actual DC written in the table, instead of the "real" DCs.

 

[Morrus]

Then you honestly have nothing to say. Not trying to be rude here, but if you don't understand what he's saying, then you can't make any conclusions about what he's saying. In fact, stating that you didn't read and comprehend his work and then judging it is kinda rude.

I've judged nothing; I've asked several questions.

Eldorian, you may be under the impression that just because I own the place I'm not entitled to benefit from the civility rules here; you are incorrect in that assumption. You do not get to say "Then you honestly have nothing to say" to anyone on this board; that includes me. Please keep the civility guidelines in mind when posting on EN World. If you have a query about these rules, you may email me for clarification.