user3093: Does anyone know the function which dictates which three of these time-control categories any particular game would fall under?  For example, I know that a 3 0 is the quickest blitz game that can be played but I would be unsure whether or not a 2 3 (2 minutes on each persons clock with 3 second increments added) would be blitz or bullet.  I'm assuming there is a fairly simplistic formula I could plug these metrics into for a definitive answer but I have yet to stumble upon it.
Thanks ^_^

user3872: I do not think that there is a simple formula. It is similar to the paradox between defining heaps of sand or grains of sand. It is difficult to draw the line precisely. If a formula is necessary, I would define it by how much time is used. 
Assuming that the barriers between blitz and bullet(lightning) is 3 0. 
A time control can be written as (x,y), for example, (3,0) is the quickest time control for blitz. 
Let F(x,y)=2x+(4/3)y. 
The 4/3 was created by the expected time used in a game that last 40 moves(supposedly the average length of a game).
 F(2,3)=2(2)+(4/3)(3)=4+4=8 Therefore, (2,3) is blitz because it is greater than the boundary defined by F(3,0)=2(3)+0=6
The same can be done for standard chess, but a boundary must be specified.

user1201: There is no such globally accepted formula. Time controls are defined only by their formal definitions (as unhelpful as that sounds). Any further descriptive language, like "blitz" or "lightning" or "bullet", while they carry certain conventional connotations, do not have objective criteria. However, certain organizations may define these terms concretely within their own domains.

USCF
The USCF defines three time-control zones: Regular, Quick, and Blitz. Different sets of time controls fall into one (or more--it is possible for a game to count as both Regular and Quick, in which case the player's ratings in both categories are affected) of these categories. Determining the category is simple: calculate the [estimated] total playing time (TPT_U) as:
TPT_U = Minutes + SecondsPerIncrement

The TPT_U is then slotted into a zone as follows:
TPT_U > 65: Regular
30 ≤ TPT_U ≤ 65: Regular AND Quick
10 < TPT_U < 30: Quick
5 ≤ TPT_U ≤ 10: Blitz


FIDE
FIDE defines (as far as I can tell) two time-control zones beyond the standard FIDE time control: Rapid and Blitz. To determine which of these zones a time control falls within, calculate the [estimated] total playing time (TPT_F) as:
TPT_F = Minutes + SecondsPerIncrement

The TPT_F is then slotted into a zone as follows:
10 < TPT_F < 60: Rapid
TPT_F ≤ 10: Blitz


CHESS.COM
Chess.com defines three time-control zones: Standard, Blitz, and Bullet. To determine which of these zones a time control falls within, calculate the [estimated] total playing time in minutes (TPT_C) as:
TPT_C = Minutes + 2/3*SecondsPerIncrement

This assumes a forty-move game and is derived from the following expression (multiply the increment in seconds by forty, then convert to minutes):
TPT_C = Minutes + (40 * SecondsPerIncrement / 60)

The TPT_C is then slotted into a zone as follows*:
15 ≤ TPT_C: Standard
3 ≤ TPT_C < 15: Blitz
TPT_C < 3: Bullet

*I've had to extrapolate here, as the definition actually appears to leave a gap between 14 and 15 minutes. I've filled this gap in the manner I considered most likely to be accurate.

Examples
Base | Incr | TPT_U | TPT_F | TPT_C | USCF  | FIDE  | CHESS.COM
-----|------|-------|-------|-------|-------|-------|----------
 2   | 1    | 3     | 3     | 2.667 | N/A   | Blitz | Bullet
 3   | 0    | 3     | 3     | 3     | N/A   | Blitz | Blitz
 3   | 2    | 5     | 5     | 4.333 | Blitz | Blitz | Blitz
 5   | 0    | 5     | 5     | 5     | Blitz | Blitz | Blitz
 10  | 0    | 10    | 10    | 10    | Blitz | Blitz | Blitz
 10  | 1    | 11    | 11    | 10.67 | Quick | Rapid | Blitz
 14  | 3    | 17    | 17    | 16    | Quick | Rapid | Standard


3093: <p>Does anyone know the function which dictates which three of these time-control categories any particular game would fall under?  For example, I know that a 3 0 is the quickest blitz game that can be played but I would be unsure whether or not a 2 3 (2 minutes on each persons clock with 3 second increments added) would be blitz or bullet.  I'm assuming there is a fairly simplistic formula I could plug these metrics into for a definitive answer but I have yet to stumble upon it.</p>

<p>Thanks ^_^</p>
 3872: <p>I do not think that there is a simple formula. It is similar to the paradox between defining heaps of sand or grains of sand. It is difficult to draw the line precisely. If a formula is necessary, I would define it by how much time is used. 
Assuming that the barriers between blitz and bullet(lightning) is 3 0. 
A time control can be written as (x,y), for example, (3,0) is the quickest time control for blitz. 
Let F(x,y)=2x+(4/3)y. 
The 4/3 was created by the expected time used in a game that last 40 moves(supposedly the average length of a game).
 F(2,3)=2(2)+(4/3)(3)=4+4=8 Therefore, (2,3) is blitz because it is greater than the boundary defined by F(3,0)=2(3)+0=6
The same can be done for standard chess, but a boundary must be specified.</p>
 1201: <p>There is no such globally accepted formula. Time controls are defined only by their formal definitions (as unhelpful as that sounds). Any further descriptive language, like "blitz" or "lightning" or "bullet", while they carry certain conventional connotations, do not have objective criteria. However, certain organizations may define these terms concretely within their own domains.</p>

<hr>

<h2>USCF</h2>

<p>The USCF <a href="http://www.uschess.org/docs/gov/reports/RulebookChanges.pdf" rel="noreferrer">defines</a> three time-control zones: <em>Regular</em>, <em>Quick</em>, and <em>Blitz</em>. Different sets of time controls fall into one (or more--it is possible for a game to count as <em>both</em> Regular and Quick, in which case the player's ratings in both categories are affected) of these categories. Determining the category is simple: calculate the [estimated] <em>total playing time</em> (<code>TPT_U</code>) as:</p>

<pre><code>TPT_U = Minutes + SecondsPerIncrement
</code></pre>

<p>The <code>TPT_U</code> is then slotted into a zone as follows:</p>

<pre><code>TPT_U &gt; 65: Regular
30 ≤ TPT_U ≤ 65: Regular AND Quick
10 &lt; TPT_U &lt; 30: Quick
5 ≤ TPT_U ≤ 10: Blitz
</code></pre>

<hr>

<h2>FIDE</h2>

<p>FIDE <a href="http://www.fide.com/fide/handbook.html?id=171&amp;view=article" rel="noreferrer">defines</a> (as far as I can tell) two time-control zones beyond the <a href="http://www.fide.com/component/handbook/?id=39&amp;view=category" rel="noreferrer">standard FIDE time control</a>: <em>Rapid</em> and <em>Blitz</em>. To determine which of these zones a time control falls within, calculate the [estimated] <em>total playing time</em> (<code>TPT_F</code>) as:</p>

<pre><code>TPT_F = Minutes + SecondsPerIncrement
</code></pre>

<p>The <code>TPT_F</code> is then slotted into a zone as follows:</p>

<pre><code>10 &lt; TPT_F &lt; 60: Rapid
TPT_F ≤ 10: Blitz
</code></pre>

<hr>

<h2>CHESS.COM</h2>

<p>Chess.com <a href="https://support.chess.com/customer/portal/articles/1444851-why-are-there-three-different-ratings-in-live-chess-" rel="noreferrer">defines</a> three time-control zones: <em>Standard</em>, <em>Blitz</em>, and <em>Bullet</em>. To determine which of these zones a time control falls within, calculate the [estimated] <em>total playing time</em> in minutes (<code>TPT_C</code>) as:</p>

<pre><code>TPT_C = Minutes + 2/3*SecondsPerIncrement
</code></pre>

<p>This assumes a forty-move game and is derived from the following expression (multiply the increment in seconds by forty, then convert to minutes):</p>

<pre><code>TPT_C = Minutes + (40 * SecondsPerIncrement / 60)
</code></pre>

<p>The <code>TPT_C</code> is then slotted into a zone as follows*:</p>

<pre><code>15 ≤ TPT_C: Standard
3 ≤ TPT_C &lt; 15: Blitz
TPT_C &lt; 3: Bullet
</code></pre>

<p>*I've had to extrapolate here, as the <a href="https://support.chess.com/customer/portal/articles/1444851-why-are-there-three-different-ratings-in-live-chess-" rel="noreferrer">definition</a> actually appears to leave a gap between 14 and 15 minutes. I've filled this gap in the manner I considered most likely to be accurate.</p>

<hr>

<h2>Examples</h2>

<pre><code>Base | Incr | TPT_U | TPT_F | TPT_C | USCF  | FIDE  | CHESS.COM
-----|------|-------|-------|-------|-------|-------|----------
 2   | 1    | 3     | 3     | 2.667 | N/A   | Blitz | Bullet
 3   | 0    | 3     | 3     | 3     | N/A   | Blitz | Blitz
 3   | 2    | 5     | 5     | 4.333 | Blitz | Blitz | Blitz
 5   | 0    | 5     | 5     | 5     | Blitz | Blitz | Blitz
 10  | 0    | 10    | 10    | 10    | Blitz | Blitz | Blitz
 10  | 1    | 11    | 11    | 10.67 | Quick | Rapid | Blitz
 14  | 3    | 17    | 17    | 16    | Quick | Rapid | Standard
</code></pre>
