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		<id>https://en.formulasearchengine.com/w/index.php?title=Versine&amp;diff=5547</id>
		<title>Versine</title>
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		<updated>2013-11-30T23:30:43Z</updated>

		<summary type="html">&lt;p&gt;184.65.5.24: /* History and applications */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Secondary average&#039;&#039;&#039;, or &#039;&#039;&#039;SecA&#039;&#039;&#039;, is a [[baseball statistics|baseball statistic]] that measures the sum of extra bases gained on hits, walks, and stolen bases (less times caught stealing) depicted per at bat.&amp;lt;ref name=abstract&amp;gt;James, Bill. &#039;&#039;The Bill James Historical Baseball Abstract&#039;&#039;. New York: Villard Books, 1988.&amp;lt;/ref&amp;gt;  Created by [[Bill James]], it is a [[sabermetrics|sabermetric]] measurement of hitting performance that seeks to evaluate the number of bases a player gained independent of [[batting average]]. Unlike batting average, which is a simple ratio of base [[hit (baseball statistics)|hit]]s to [[at bats]], secondary average accounts for power ([[extra base hit]]s), plate discipline ([[base on balls|walks]]), and speed ([[stolen base]]s minus times caught stealing).&amp;lt;ref name=career&amp;gt;&amp;quot;Career Leaders for Secondary Average.&amp;quot; [http://www.baseball-almanac.com/hitting/hisecavg1.shtml &#039;&#039;Baseball Almanac&#039;&#039;]. Baseball-Almanac. 2013. Web. 11 Nov. 2013.&amp;lt;/ref&amp;gt; Secondary averages have a higher [[variance]] than batting averages.&lt;br /&gt;
&lt;br /&gt;
==Formula==&lt;br /&gt;
The formula to calculate secondary average is:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;SecA = \frac{BB+(TB-H) + (SB-CS)}{AB}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
*&#039;&#039;BB&#039;&#039; = [[bases on balls]]&lt;br /&gt;
*&#039;&#039;TB&#039;&#039; = [[Total bases]]&lt;br /&gt;
*&#039;&#039;H&#039;&#039; = [[Hit (baseball statistics)|Hits]]&lt;br /&gt;
*&#039;&#039;SB&#039;&#039; = [[Stolen base]]s&lt;br /&gt;
*&#039;&#039;CS&#039;&#039; = [[Caught stealing]]&lt;br /&gt;
*&#039;&#039;AB&#039;&#039; = [[At bats]]&lt;br /&gt;
&lt;br /&gt;
The resulting number rounded to the thousandth place is a player&#039;s secondary average.  Variations to the formula exist, with some statisticians not counting caught stealing while others multiply caught stealing to increase its significance/negative effects.&lt;br /&gt;
&lt;br /&gt;
==Relation to batting average==&lt;br /&gt;
&lt;br /&gt;
Although they share no [[correlation]], overall league averages for secondary average are inclined to correspond with league batting averages, which allows for a viable reference point for secondary average in comparison to batting average.&amp;lt;ref name=abstract /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A player can possess a low batting average yet still be a valuable offensive contributor if he has a high secondary average.&amp;lt;ref name=bbook&amp;gt;James, Bill. &#039;&#039;The Baseball Book 1990&#039;&#039;. New York: Villard Books, 1990.&amp;lt;/ref&amp;gt;  However, a low secondary average is not necessarily an indicator of a poor hitter.  [[Ichiro Suzuki]] is an example of a hitter who relies on batting average for most of his offensive production.&amp;lt;ref name= Grochowski&amp;gt;Grochowski, John. [http://www.suntimes.com/sports/14618694-574/baseball-by-the-numbers-adam-dunn-shows-his-value-in-secondary-average.html &amp;quot;Baseball by the Numbers: Adam Dunn Shows His Value in Secondary Average.&amp;quot;] &#039;&#039;Chicago Sun-Times&#039;&#039;. Sun-Times Media, LLC, 20 Aug. 2012. Web. 11 Nov. 2013.&amp;lt;/ref&amp;gt;  Furthermore, batting average and secondary average are not mutually exclusive; a player can have a high batting average as well as a high secondary average.  The table below shows the leaders in both batting average and secondary average for the 2013 season (bold indicates leader in both categories).&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Batting Average !! Secondary Average&lt;br /&gt;
|-&lt;br /&gt;
| 1. &#039;&#039;&#039;Miguel Cabrera (.348)&#039;&#039;&#039; || 1. Chris Davis (.476)&lt;br /&gt;
|-&lt;br /&gt;
| 2. Michael Cuddyer (.331) || 2. &#039;&#039;&#039;Mike Trout (.465)&#039;&#039;&#039;&lt;br /&gt;
|-&lt;br /&gt;
| 3. Joe Mauer (.324) || 3. &#039;&#039;&#039;Miguel Cabrera (.456)&#039;&#039;&#039;&lt;br /&gt;
|-&lt;br /&gt;
| 4. &#039;&#039;&#039;Mike Trout (.323)&#039;&#039;&#039; || 4. Edwin Encarnacion (.428)&lt;br /&gt;
|-&lt;br /&gt;
| 5. Chris Johnson (.321) || 5. Paul Goldschmidt (.427)&lt;br /&gt;
|-&lt;br /&gt;
| 6(t). Freddie Freeman (.319) || 6. Joey Votto (.423)&lt;br /&gt;
|-&lt;br /&gt;
| 6(t). Yadier Molina (.319) || 7. David Ortiz (.409)&lt;br /&gt;
|-&lt;br /&gt;
| 8(t). Jason Werth (.318) || 8. Giancarlo Stanton (.407)&lt;br /&gt;
|-&lt;br /&gt;
| 8(t). Matt Carpenter (.318) || 9. Jose Bautista (.403)&lt;br /&gt;
|-&lt;br /&gt;
| 10. Andrew McCutchen (.317) || 10. Shin-Soo Choo (.390)&amp;lt;ref&amp;gt;[http://espn.go.com/mlb/stats/batting/_/sort/secondaryAvg/type/sabermetric/order/true &amp;quot;MLB Player Batting Stats-2013.&amp;quot;] &#039;&#039;ESPN&#039;&#039;. ESPN Internet Ventures, n.d. Web. 11 Nov. 2013.&amp;lt;/ref&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
==Benefits for player evaluation==&lt;br /&gt;
&lt;br /&gt;
Secondary average operates under the principle that batting average is an incomplete indicator of a hitter&#039;s ability since batting average does not account for power, plate discipline, and speed.  According to Scott Gray (working with Bill James), &amp;quot;Secondary average is a much better indicator of offensive ability than batting average&amp;quot;.&amp;lt;ref&amp;gt;Gray, Scott. &#039;&#039;The Mind of Bill James: How a Complete Outsider Changed Baseball&#039;&#039;. New York: Doubleday, 2006. Print.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Since secondary average evaluates a player&#039;s offensive contribution independent of batting average, it can identify players who have low batting averages yet are still productive offensively.  For example, in 1990, Bill James identified [[Eric Davis]] as the most productive batter with a career average below .275; in spite of his low batting average, Davis had a career secondary average of .504, which was the highest of any active player at the time.&amp;lt;ref name=bbook /&amp;gt;  Batting average was not a great indicator of his true offensive value; secondary average was able to demonstrate his value more effectively.&lt;br /&gt;
&lt;br /&gt;
[[Adam Dunn]] is an example of a current player who has a low batting average but an excellent secondary average, resulting from his high walk totals and power numbers.&amp;lt;ref name=Grochowski /&amp;gt;  Although Adam Dunn only has a career .238 batting average,&amp;lt;ref&amp;gt;[http://www.baseball-reference.com/players/d/dunnad01.shtml &amp;quot;Adam Dunn&amp;quot;] &#039;&#039;Baseball-Reference.com&#039;&#039;. Sports Reference LLC, n.d. Web. 11 Nov. 2013.&amp;lt;/ref&amp;gt; he has a career .456 secondary average, ranking him 12th all-time.&amp;lt;ref name=career /&amp;gt; As &#039;&#039;Chicago Sun-Times&#039;&#039; reporter John Grochowski demonstrated, Adam Dunn&#039;s offensive value is more apparent when secondary average is accounted for.&amp;lt;ref name=Grochowski /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{Reflist}}&lt;br /&gt;
&lt;br /&gt;
{{Baseball statistics}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Batting statistics]]&lt;/div&gt;</summary>
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