Fallout: New Vegas skills

Background
Fallout: New Vegas shares a similar skill set to its predecessor, Fallout 3, but with several differences. The primary weapons skills have been revamped, with Small Guns and Big Guns having been combined into the Guns skill, which now covers all conventional firearms. Weapons using explosive ordinance (missiles and grenades, for instance) are now covered by Explosives. New throwing weapons, such as the throwing spear, have been added, and are categorized as Melee Weapons. The Survival skill has also been added to the roster. It allows for crafting of various items, such as food, stimpaks, and poisons to augment the effectiveness of weapons.

Unlike Fallout 3, the base game will not give the player enough points to max out every skill, even accounting for 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. However, with two or more DLCs installed, 10 Intellingence, 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, which 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. Like skill books, magazines are consumed once used, and more need to be collected to maintain the effect.

Effect of skills
Skills can be largely thought of as either "combat" or "non-combat": "combat" meaning skills that influence the effectiveness of weapons (also which skills Good Natured penalizes). Combat skills would be Energy Weapons, Explosives, Guns, Melee Weapons, and Unarmed. Having a higher score in any of these skills primarily allows for two things:
 * 1) Meet minimum weapon requirements. Not meeting one results in drastically reduced V.A.T.S accuracy and increased weapon wobble for range weapons. For melee/unarmed, this results instead in a slower rate of attack for melee/unarmed (as they have a 95% chance to hit in V.A.T.S. regardless).
 * 2) Increase the damage done by a weapon. A score of 100 does 100% of the listed base damage on individual weapon pages, whereas a hypothetical score of 0 (impossible by normal game rules) does a baseline of 50% weapon damage. The scaling from 0 to 100 is linear, so a score of 50 would do 75% of base weapon damage.

Non-combat skills have varying specific uses. See individual skill pages for more details. However, certain non-combat skills, specifically ones that tend to have more limited application on their own, tend to be used more frequently as skill checks during dialogue (the main purpose of Speech in fact). Of note, Barter tends to be used as a back-up to Speech skill checks in some conversations. Combat skills do occasionally get used in dialogue skill checks, though not nearly as frequently. Moreover, unlike past Fallout games, New Vegas uses the idea of uncontested rolls; that is, instead of a probability of success based on your skill score and the difficulty of the check, there is a minimum threshold to meet, which results in either an uncontestable success or failure.

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 will tag three skills, instantly adding 15 points to each one. When leveling up, the character will distribute ten skill points plus a number equal to half their Intelligence, totaling 15 at maximum IN. The Educated perk grants two additional skill points per level if chosen. Assuming the player has an Intelligence of ten from level 1 and takes the Educated perk at level 4, a maximum of 487 skill points can be distributed without any DLC. Each DLC raises the level cap by 5, thus adding a possible maximum of 5 x 15 = 75 points (or 5 x 17 = 85 points with Educated) to the total available.

Skill Points available with a starting INT of 10 and with / without Educated:

Base game: 487 / 435

One DLC: 572 / 510

Two DLC: 657 / 585

Three DLC: 742 / 660

Four DLC: 827 / 735

It can be seen from the above figures that the Educated perk confers an advantage relative to the number of DLCs / levels, so that a player with three DLCs and Educated actually has more skill points to distribute than a player with four DLCs but without Educated.

Videos

 * This Video will show how to set your SPECIALS to get Max Skills and double set of perks at level 30, 35, 40, and 45.