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	<title>Tom Flesher &#187; Brooks Kieschnick</title>
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		<title>Tom Flesher &#187; Brooks Kieschnick</title>
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		<title>Micah Owings and Cobb-Douglas Production</title>
		<link>http://tomflesher.com/2010/07/22/micah-owings-and-cobb-douglas-production/</link>
		<comments>http://tomflesher.com/2010/07/22/micah-owings-and-cobb-douglas-production/#comments</comments>
		<pubDate>Thu, 22 Jul 2010 13:34:05 +0000</pubDate>
		<dc:creator>tomflesher</dc:creator>
				<category><![CDATA[Baseball]]></category>
		<category><![CDATA[Economics]]></category>
		<category><![CDATA[Brooks Kieschnick]]></category>
		<category><![CDATA[Cobb-Douglas function]]></category>
		<category><![CDATA[David Ortiz]]></category>
		<category><![CDATA[Micah Owings]]></category>
		<category><![CDATA[Reds]]></category>
		<category><![CDATA[run production]]></category>

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		<description><![CDATA[Micah Owings, who is one of the best two-way players in baseball since Brooks Kieschnick, was sent down to the minors by the Cincinnati Reds yesterday. As big a fan as I am of Micah (really, look at the blog), I think this was probably the right decision. Owings was being used as a long [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=tomflesher.com&#038;blog=20518139&#038;post=386&#038;subd=tomflesher&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p><strong><a href="http://www.baseball-reference.com/players/o/owingmi01.shtml?utm_source=direct&amp;utm_medium=linker&amp;utm_campaign=Linker">Micah  Owings</a></strong>, who is one of the best two-way players in baseball since Brooks Kieschnick, was <a href="http://news.cincinnati.com/article/20100721/SPT04/307210081/1062/SPT/Owings-out-Fisher-back">sent down to the minors </a>by the Cincinnati Reds yesterday. As big a fan as I am of Micah (really, look at the blog), I think this was probably the right decision.</p>
<p>Owings was being used as a long reliever. For a big-hitting pitcher like Micah, that&#8217;s death to begin with. Relievers need to be available to pitch, so the Reds couldn&#8217;t get their money&#8217;s worth from Owings as a pinch hitter, since he wouldn&#8217;t be available to re-enter the game as a pitcher unless they used him immediately. They also weren&#8217;t getting their money&#8217;s worth as a pitcher, since, as Cincinnati.com notes, the Reds&#8217; starting pitching was doing very well and so long relief wasn&#8217;t being used very often.</p>
<p>Letting Owings start in AAA will give him the best possible outcome &#8211; he&#8217;ll have regular opportunities to pitch, so he won&#8217;t rust, and he&#8217;ll get to bat at least some of the time. Owings needs to be cultivated as a batter because that&#8217;s where his comparative advantage is. I doubt he&#8217;ll ever be at the top of the rotation, but he could be a competent fifth starter. If he pitches often enough to get there, he&#8217;ll add significant value to the team in terms of his OBP above the expected pitcher. He&#8217;ll get on base more, so he&#8217;ll both advance runners and avoid making an out.</p>
<p>A baseball player is a factory for producing run differential. He does so using two inputs: defensive ability (pitching and fielding) and offensive ability (batting). In the National League, if a player can&#8217;t hit at all, he&#8217;s likely to produce very little in the way of run differential, but at the same time, if he&#8217;s a liability on defense, he&#8217;s not likely to be very useful either. Defense produces marginal runs by preventing opposing runs from scoring, and offense produces marginal runs by scoring runs. Having either one set to zero (in the case of a pitcher who can&#8217;t hit at all) or a negative value (an actively bad pitcher) would negatively affect the player&#8217;s run production. This is similar to a factory situation where labor and equipment are used to produce goods, and that situation is usually modeled using a <a href="http://en.wikipedia.org/wiki/Cobb%E2%80%93Douglas">Cobb-Douglas production function</a>:</p>
<p><img src='http://s0.wp.com/latex.php?latex=Y+%3D+K%5E%7B%5Calpha%7D+%5Ctimes+L%5E%7B1+-+%5Calpha%7D&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='Y = K^{&#92;alpha} &#92;times L^{1 - &#92;alpha}' title='Y = K^{&#92;alpha} &#92;times L^{1 - &#92;alpha}' class='latex' /></p>
<p>with Y = production, z = a productivity constant, K = equipment and technology, L = labor input, and <img src='http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='&#92;alpha' title='&#92;alpha' class='latex' /> is a constant between 0 and 1 that represents relatively how important the input is. K might be, for example, operating expenses for a machine to produce widgets, and L might be the wages paid to the operators of the machine. This function has the nice property that if we think both inputs are equally important (that is, <img src='http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='&#92;alpha' title='&#92;alpha' class='latex' /> = .5) then production is maximized when the inputs are equal.</p>
<p>In general, production of run differential could be modeled using the same method. For example:</p>
<p><img src='http://s0.wp.com/latex.php?latex=RD+%3D+P%5E%7B%5Calpha%7D+%5Ctimes+F%5E%7B%5Cbeta%7D+%5Ctimes+B%5E%7B1+-+%5Calpha+-+%5Cbeta%7D&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='RD = P^{&#92;alpha} &#92;times F^{&#92;beta} &#92;times B^{1 - &#92;alpha - &#92;beta}' title='RD = P^{&#92;alpha} &#92;times F^{&#92;beta} &#92;times B^{1 - &#92;alpha - &#92;beta}' class='latex' /></p>
<p>where P = pitching contribution, F = fielding contribution, B = batting contribution, and <img src='http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='&#92;alpha' title='&#92;alpha' class='latex' /> and <img src='http://s0.wp.com/latex.php?latex=%5Cbeta&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='&#92;beta' title='&#92;beta' class='latex' /> are both between 0 and 1 and would vary based on position. For example, <strong><a href="http://www.baseball-reference.com/players/o/ortizda01.shtml?utm_source=direct&amp;utm_medium=linker&amp;utm_campaign=Linker">David Ortiz</a></strong> is a designated hitter. His pitching ability is totally irrelevant, and so is his fielding ability outside of interleague games. The DH&#8217;s <img src='http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='&#92;alpha' title='&#92;alpha' class='latex' /> would be 0 and his <img src='http://s0.wp.com/latex.php?latex=%5Cbeta&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='&#92;beta' title='&#92;beta' class='latex' /> would be very close to 0. On the other hand, an American League pitcher would have an <img src='http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='&#92;alpha' title='&#92;alpha' class='latex' /> very close to 1 since pitcher fielding is not as important as pitching and his hitting is entirely inconsequential in the AL. Catchers would have <img src='http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='&#92;alpha' title='&#92;alpha' class='latex' /> at 0 but <img src='http://s0.wp.com/latex.php?latex=%5Cbeta&amp;bg=ffffff&amp;fg=666666&amp;s=0' alt='&#92;beta' title='&#92;beta' class='latex' /> much higher than other positions.</p>
<p>The upshot of this method of modeling production is that it shows Owings can make up for being a less than stellar pitcher by helping his team score runs and be a considerably better investment than a pitcher with a slightly lower ERA but no run production.</p>
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