Fallout: New Vegas skills

Background
Fallout: New Vegas shares a similar skill set to its predecessor, Fallout 3, with the following important differences: Small Guns and Big Guns have been combined into the Guns skill, which now covers all conventional firearms; weapons using explosive ordnance (missiles and grenades, for example) are now covered by Explosives; new throwing weapons (such as the throwing spear) have been added, and are categorized as Melee Weapons; and the Survival skill has also been added to the roster, allowing the crafting of various items such as food, stimpaks, and poisons that augment the effectiveness of weapons.

Unlike Fallout 3, the base game will not give the player enough points to max out every skill, even taking into account every perk and skill book. It is possible to achieve a functional maximum in roughly ten skills by using skill magazines and the Comprehension perk for a temporary boost to 100 from a base level of 80. With two or more DLCs installed, 10 Intelligence, the Educated perk, and having consumed roughly 20 skill books, it is entirely possible to max out skill points by level 40.

To offset the necessity of a minimum value for a certain skill, New Vegas introduces skill magazines that provide a large but temporary boost to their associated skill (+10, or +20 with Comprehension). By using one prior to conversation, a check can be passed that might otherwise be failed. They can also be used to boost skill with weapons temporarily, or gain access to crafting recipes beyond the player's current skill.

Effect of skills
Skills can be largely thought of as either "combat" or "non-combat". "Combat skills" are skills that influence the effectiveness of weapons, such as Energy Weapons, Explosives, Guns, Melee Weapons, and Unarmed. "Non-combat skills" include Barter, Medicine, Repair, and Speech. The Good Natured trait will penalize combat skills in order to boost non-combat skills.

Combat skills
For all combat skills, having a higher score helps meet minimum weapon requirements (some weapons also have a Strength requirement). Not meeting the requirements for ranged weapons drastically penalizes your V.A.T.S accuracy and increases weapon wobble. For melee/unarmed, the penalty is a slower rate of attack.

For non-Unarmed weapons, your skill score also increases the damage done (where base damage is the damage listed on an individual weapon page):
 * $$Final\ Damage=Base\ Damage\times\Bigg(\frac{50+Skill\times0.5}{100}\Bigg)$$

In other words, at a hypothetical score of 0, a weapon will only do half the listed base damage. At 100, the weapon will do full base damage.

The Unarmed skill does not affect unarmed weapon damage, instead it adds a slight bonus damage on top of it (see the unarmed damage page for specifics). Further increases in unarmed damage are driven primarily by special unarmed attacks and special V.A.T.S moves that are unlocked at higher skill levels.

Note that the game can occasionally list incorrect damage on weapons, generally when you have a weapon selected but not equipped. This happens if you have currently equipped weapon that uses ammo type with damage multiplier. (For example, shotguns with buckshot ammo.) Unequipping current weapon, or equipping the weapon in question will fix the issue.

Non-combat skills
Non-combat skills have varying specific uses that are covered in their individual skill pages. In addition to their normal uses, many non-combat skills tend to be used as skill checks during dialogue (this being the primary purpose of Speech and a secondary purpose of Barter). Combat skills do occasionally get used in dialogue skill checks, though not nearly as frequently.

As opposed to past Fallout games, New Vegas uses a score-based skill check in place of a probability-based skill check. That is, your skills meet a minimum value, or they do not - chance plays no part. For example, in order to convince Easy Pete to provide some dynamite to protect Goodsprings during the quest Ghost Town Gunfight, the player must have a minimum Explosives skill of 25 (an example of a less-frequent combat skill check in dialogue). In the case where a player's associated skill level is too low, a dialogue option (highlighted in red) is presented that will fail the skill check, and will not grant a speech success. Unlike Fallout 3, where the same dialogue option is presented regardless of your success or failure, a check that will fail uses a humorously unconvincing response, while a passable check uses a well-thought out argument, thus reflecting the nature of the check. XP is awarded in proportion to the difficulty of the check.

Formula
The initial value of each skill is a base value of two, plus an amount depending on a character's value in the relevant attribute, plus a bonus determined by their Luck attribute, rounded up.
 * $$2 + (2 \times \mbox{Stat}) + \left\lceil\frac{\mbox{Luck}}{2}\right\rceil$$

Example: A starting Endurance of five and a starting Luck of five will give you an initial Unarmed skill of 15.
 * $$2 + (2 \times 5) + \left\lceil\frac{5}{2}\right\rceil = 15$$

Later changes to the SPECIAL stat have a similar influence on the respective skill.

During character creation, the player can "tag" three skills, which instantly increase them by 15. When leveling up, the character distributes 10 + half Intelligence skill points. (For odd intelligence scores, the "extra" skill point is given on even levels, so a character with 1 intelligence will gain 11 skill points at level 2, then 10 at level 3, etc.)

The maximum number of skill points that a character can have throughout the course of the game is partially dependent on what DLCs the player has installed, as four of them increase the level cap by 5. The level cap starts at 30 and goes up by 5 with the addition of each of Honest Hearts, Dead Money, Old World Blues, and Lonesome Road. As two quick examples, a player with 1 Intelligence and no DLCs will have only 304 skill points, whereas a player with 10 Intelligence and all DLCs will have 735.

In contrast to Fallout 3, very few perks contribute extra skill points directly, preferring instead to do this indirectly (by increasing SPECIAL stats or by increasing the yield from skill books) or not at all. The lone exception is Educated, which yields an additional 2 skill points per level (though the character has to be at least level 4 to take it).

Note that because the benefit from Educated is the number of levels the character gains after having taken it, the relative gain in skill points is based both on how early the character gets it and how many DLCs the player has installed.

S.P.E.C.I.A.L. distribution
Points allocated to S.P.E.C.I.A.L attributes affect their associated skills differently. For instance, the following attributes give these bonuses:
 * Strength only 1
 * Intelligence and Perception 3
 * Luck all, but only at 1/4 of the effect and rounded up (statistically roughly the same as affecting three stats)
 * Agility, Charisma, and Endurance 2 each

The most effective stat for maxing skills to 100 by level 50 is INT. Starting with an INT of 8 will bring you close to maxing out your skills, especially with decent luck and raising stats using perks.

Maxed skills
With all DLCs, it becomes fairly trivial to max out all your skills at 100.

At the base level, you need 1300 skill points for complete maximization (100 points for 13 skills). At level 1, you get 45 skill points for free (from your 3 Tag! skills), and an average character (5 in all SPECIAL stats) will have 15 as a base for all skills. This reduces the amount of skill points you need to 1060 (1300 - (45 + 15 x 13)).

For 49 levels at average intelligence, you get 612 skill points (12.5 x 49). Just with these base stats, this is enough to get all but 6 skills completely maxed out (remaining 448 / 85, rounding up).

Simply by taking Educated at level 4 leaves us with 356 skill points remaining to completely max out. Taking Comprehension at level 6 (and saving skill books until then) means that reading 89 skill books is enough to net you the remaining skill points (so long as you adapt your per-level skill points to the remaining skill books). As a note, the base game contains 53 skill book; Old World blues contains 16 skill books/recipes; Dead Money also contains 12; and Honest Hearts can contain anywhere from 0 to 8, 0 to 2 per workbench (and may require a bit of saving and reloading before entering caves). With diligence in finding skill books/recipes (all well-documented on this wikia) and a bit of reloading in Honest Hearts to generate all 8, you can max out all skills without any other special character effort.

With simple variations, the task of maxing out skills can become easier or harder. A character with Intelligence of 10 with Educated at level 4 and starting off with Skilled will be short only 408 skill points, not including skill points from initial character creation (which will yield at least 111: 45 from three Tag! skills and 22 from Repair/Medicine/Science, ignoring Luck). This character will need only very few skill books by comparison, about 42 if all other SPECIAL stats are left at 5.

All of the above also ignores the effect of implants from the New Vegas medical clinic, the special Old World Blues perks, and other perks, traits, equipment that can effectively make permanent alterations to your SPECIAL stats or skills. These can range from Tag!, which gives 15 skill points to a skill; getting an implant or taking Intense Training to increase Luck to an odd number, which yields 13 extra skill points; or even something like Night Person which yields up to 12 skill points (+2 Perception and Intelligence) at night.

In short, due to the increased level cap, extra content, and perks/traits from DLCs, the task of maxing out your skills is nowhere near as exacting as it once was, requiring incredibly specific SPECIAL scores or perk/trait selection. Even "dumb" characters (Intelligence of 1 and no special perks or traits) will be able to max out many skills.

Note that when taking Logan's Loophole, maxing out your skills becomes impossible due to the reduced level cap (unless the skilled trait glitch is used). Even with perfectly optimized SPECIAL scores, Skilled as the other trait, all possible implants, including the effects of completing Lonesome Road and Old World Blues, and the following perks: Comprehension, Educated, 10 Intense Trainings, Tag!, Solar Powered, and Walker Instinct (all perks that give you non-contradictory ways to increase your skills), you will be exactly 19 skill points shy of maxing out all your skills. Not to mention that such an exacting character will probably not be very fun to play and will be trying to cancel out one of the major benefits to Logan's Loophole (double-duration skill magazines).

Comprehension/Educated perks
Allowing for some variation due to S.P.E.C.I.A.L. point distribution and raising those stats by the Intense Training perk, you will normally end up at level 50 some 140 points short of maxed skills.

This assumes you buy all 7 implants pertaining to stats and the Lonesome Road extra point, find some 80 of the books, and do not take the Comprehension/Educated/Tag! perks or the above temporary perks, or Logan's Loophole.

Hence, taking both the Comprehension and Educated perks is definitely overkill, netting you some 80 points and 92 points respectively. Taking both makes for some accelerated skill-progression early and mid-game, but little effectively so.

You might consider taking both if you have a stat distribution giving you a low skill raise, i.e. high STR and low INT, but might as well make up for it with the Skilled trait. The latter may be a very good choice anyway as outlined here.

While the Comprehension perk depends on diligence in searching books, it might be preferable to Educated, as it will also make skill mags twice as effective on top of the bargain and net almost the same number of points as Educated.

With Comprehension those will give a major boost of +20 to the relevant skill and enable you, e.g. to get past some locks or computers otherwise out of your skill range by a large margin.

Some missing skill points at lvl 50 are far apart from tragic. For skills not used constantly (like weapons skills, survival or sneaking), but only in foreseeable occasions (such as barter, lockpick, science, repair, speech), there is always some lightweight apparel or chem at hand, giving those skills a boost for up to 10 points.