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	<title>Comments on: Not To Be Mean, But, What About The Median?</title>
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		<title>By: Are The Yankees Actually Getting Younger? &#124; Bronx Baseball Daily</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247672</link>
		<dc:creator>Are The Yankees Actually Getting Younger? &#124; Bronx Baseball Daily</dc:creator>
		<pubDate>Fri, 01 Jan 2010 22:59:47 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247672</guid>
		<description>[...] Steve over at WasWatching had a slight problem with their methodology &#8211; and rightfully so.  As he said, &#8220;A few [...]</description>
		<content:encoded><![CDATA[<p>[...] Steve over at WasWatching had a slight problem with their methodology &#8211; and rightfully so.  As he said, &#8220;A few [...]</p>
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		<title>By: Evan3457</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247667</link>
		<dc:creator>Evan3457</dc:creator>
		<pubDate>Fri, 01 Jan 2010 04:09:01 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247667</guid>
		<description>The article is correct; no matter how you slice it, the 2009 staff is significantly younger than the 2005 staff. You can do it through weighting by innings pitched...perhaps it would be simpler to compare the ages of the pitchers with the same role for the first 10-11 pitchers on the staff, to avoid giving excessive weight to lightly used pitchers. So, here we go...

#1 Starter
2005: Randy Johnson, 41; 2009: C.C. Sabathia, 28

#2 Starter
2005: Mike Mussina, 36; 2009: A.J. Burnett, 32

#3 Starter
2005: Wang and Pavano, 27 (25 and 29); Andy Pettitte, 37

#4 Starter
2005: Brown and Wright, 34.5 (40 and 29); Joba Chamberlain, 23

#5 Starter
2005: Chacon, Small and Leiter, 33 (27, 33 and 39); 2009: Mitre, Wang, Hughes and Gaudin, 27 (28, 29, 26, and 23)

I don&#039;t see how one can possibly avoid the conclusion that the 2009 rotation was significantly younger, as a group, than the 2005 rotation.
==========================================
Closer

2005: Mariano, 35; 2009: Mariano 39

Primary Set-up Man
2005: Tom Gordon, 37; 2009: Phil Hughes 23

Top Lefty
2005: Felix Rodriguez 32; 2009: Phil Coke 26

Other set-up men
2005: Proctor and Sturze, 28 and 34; 2009: Robertson and Bruney 24 and 27

Long man
2005: Quantrill? Sturtze? 36 and 34; 2009: Alfredo Aceves: 26

The only slot in the bullpen where the 2009 Yankees are older is Mariano, who is 4 years older than himself in 2005. The Yankee pen was significantly younger at all other roles in 2009. As Mariano is apparently ageless, his extra 4 years is largely irrelevant.

==========================================
The rotation is a lot younger. The pen is a lot younger. Both were also a lot better. The article is correct and in no way deceptive. Regardless of the method used, this year&#039;s staff is both significantly younger and significantly better, and to the extent that Brian Cashman was able to bring about change, he deserves credit for it, not quibbling about methods of statistical analysis that can fairly be described as irrelevant.

Now, if you want to talk about differences in the defensive ability of the lineups of 2009 squad compared with its predecessor from four years before, and the impact that has on pitcher&#039;s records, you might start to have a point...</description>
		<content:encoded><![CDATA[<div class="comment-toolbar" style="text-align: right"><input type="button" value="Reply" onclick="CF_Reply('Evan3457');" /><input type="button" value="Quote" onclick="CF_Quote('co_247667','Evan3457');" /></div><span id="co_247667"><p>The article is correct; no matter how you slice it, the 2009 staff is significantly younger than the 2005 staff. You can do it through weighting by innings pitched&#8230;perhaps it would be simpler to compare the ages of the pitchers with the same role for the first 10-11 pitchers on the staff, to avoid giving excessive weight to lightly used pitchers. So, here we go&#8230;</p>
<p>#1 Starter<br />
2005: Randy Johnson, 41; 2009: C.C. Sabathia, 28</p>
<p>#2 Starter<br />
2005: Mike Mussina, 36; 2009: A.J. Burnett, 32</p>
<p>#3 Starter<br />
2005: Wang and Pavano, 27 (25 and 29); Andy Pettitte, 37</p>
<p>#4 Starter<br />
2005: Brown and Wright, 34.5 (40 and 29); Joba Chamberlain, 23</p>
<p>#5 Starter<br />
2005: Chacon, Small and Leiter, 33 (27, 33 and 39); 2009: Mitre, Wang, Hughes and Gaudin, 27 (28, 29, 26, and 23)</p>
<p>I don&#8217;t see how one can possibly avoid the conclusion that the 2009 rotation was significantly younger, as a group, than the 2005 rotation.<br />
==========================================<br />
Closer</p>
<p>2005: Mariano, 35; 2009: Mariano 39</p>
<p>Primary Set-up Man<br />
2005: Tom Gordon, 37; 2009: Phil Hughes 23</p>
<p>Top Lefty<br />
2005: Felix Rodriguez 32; 2009: Phil Coke 26</p>
<p>Other set-up men<br />
2005: Proctor and Sturze, 28 and 34; 2009: Robertson and Bruney 24 and 27</p>
<p>Long man<br />
2005: Quantrill? Sturtze? 36 and 34; 2009: Alfredo Aceves: 26</p>
<p>The only slot in the bullpen where the 2009 Yankees are older is Mariano, who is 4 years older than himself in 2005. The Yankee pen was significantly younger at all other roles in 2009. As Mariano is apparently ageless, his extra 4 years is largely irrelevant.</p>
<p>==========================================<br />
The rotation is a lot younger. The pen is a lot younger. Both were also a lot better. The article is correct and in no way deceptive. Regardless of the method used, this year&#8217;s staff is both significantly younger and significantly better, and to the extent that Brian Cashman was able to bring about change, he deserves credit for it, not quibbling about methods of statistical analysis that can fairly be described as irrelevant.</p>
<p>Now, if you want to talk about differences in the defensive ability of the lineups of 2009 squad compared with its predecessor from four years before, and the impact that has on pitcher&#8217;s records, you might start to have a point&#8230;</p>
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		<title>By: jay</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247664</link>
		<dc:creator>jay</dc:creator>
		<pubDate>Fri, 01 Jan 2010 01:03:58 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247664</guid>
		<description>I figured out the way NoMaas did their calculation. They weight the age of each pitcher by IP for each year. 

So it would be accurate to say that the contributions towards the total IP by Yankees pitchers from 2005 through 2009 has been by increasingly younger pitchers. Another way to say this is that we&#039;re getting more IP from relatively younger pitchers. Yet another way to say it is that the Yankees pitching staff has been getting younger. You could even go so far as to say that the article is correct.

I&#039;m not sure if this qualifies as &quot;inside the numbers.&quot;</description>
		<content:encoded><![CDATA[<div class="comment-toolbar" style="text-align: right"><input type="button" value="Reply" onclick="CF_Reply('jay');" /><input type="button" value="Quote" onclick="CF_Quote('co_247664','jay');" /></div><span id="co_247664"><p>I figured out the way NoMaas did their calculation. They weight the age of each pitcher by IP for each year. </p>
<p>So it would be accurate to say that the contributions towards the total IP by Yankees pitchers from 2005 through 2009 has been by increasingly younger pitchers. Another way to say this is that we&#8217;re getting more IP from relatively younger pitchers. Yet another way to say it is that the Yankees pitching staff has been getting younger. You could even go so far as to say that the article is correct.</p>
<p>I&#8217;m not sure if this qualifies as &#8220;inside the numbers.&#8221;</p>
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		<title>By: jay</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247663</link>
		<dc:creator>jay</dc:creator>
		<pubDate>Fri, 01 Jan 2010 00:48:15 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247663</guid>
		<description>&lt;blockquote&gt;Does it really mean the Yankees are getting younger? Maybe…but, maybe not. You have to look “inside the numbers” to be sure.&lt;/blockquote&gt;

I agree. You need to look &quot;inside the numbers&quot; (if you like that term.) A better way to say that you need to look &quot;inside the numbers&quot; is to say that you need to conceptually understand the statistical tools you are using. The mean is the average. The median is the middle number of a data set. We&#039;re trying to get an answer as to whether or not the Yankees pitchers have been getting younger, aren&#039;t we?

I stick by my question - what is the point of this post? To point out that by looking at the mean, we&#039;re looking at that mean? Why not do the analysis and see if the folks at NoMaas are correct or incorrect? It would probably take 15 minutes.</description>
		<content:encoded><![CDATA[<div class="comment-toolbar" style="text-align: right"><input type="button" value="Reply" onclick="CF_Reply('jay');" /><input type="button" value="Quote" onclick="CF_Quote('co_247663','jay');" /></div><span id="co_247663"><blockquote><p>Does it really mean the Yankees are getting younger? Maybe…but, maybe not. You have to look “inside the numbers” to be sure.</p></blockquote>
<p>I agree. You need to look &#8220;inside the numbers&#8221; (if you like that term.) A better way to say that you need to look &#8220;inside the numbers&#8221; is to say that you need to conceptually understand the statistical tools you are using. The mean is the average. The median is the middle number of a data set. We&#8217;re trying to get an answer as to whether or not the Yankees pitchers have been getting younger, aren&#8217;t we?</p>
<p>I stick by my question &#8211; what is the point of this post? To point out that by looking at the mean, we&#8217;re looking at that mean? Why not do the analysis and see if the folks at NoMaas are correct or incorrect? It would probably take 15 minutes.</p>
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		<title>By: Pat F</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247661</link>
		<dc:creator>Pat F</dc:creator>
		<pubDate>Thu, 31 Dec 2009 23:14:47 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247661</guid>
		<description>using the median isn&#039;t perfect either, and using the mean is a better route because having those &quot;older apples&quot; (actually, 6 of them, which is a ton) is a big part of a team being old, and the mean simply reflects that.  sure they really bring the mean up, but that&#039;s the whole idea of a mean.  having 6 really old players on a team means a team is really old unless everyone else is super young, which we know not to be the case.  of course, you don&#039;t need any numbers besides the ages of individual players to prove the point that the yankees are getting younger.  you can just take a quick glance at the ages of the five starters in 05 vs. 09 and the ages of each position player in 05 vs. 09 and see that the yankees are getting younger.  cashman is doing a tremendous job in this regard, and that&#039;s really all that matters.  because age is flexibility in baseball.  to quote rob neyer from the other day: 

But the only way the Yankees can fall into a habit of losing, someday, is by stockpiling too many players in their 30s with big long-term contracts. It&#039;s incredibly difficult to place a value on flexibility, but that value is real and important and Brian Cashman&#039;s awareness of that value is going to keep the Yankees on top for quite some time.&quot;

http://espn.go.com/blog/sweetspot/post/_/id/1885/yanks-fine-without-superstar-lf</description>
		<content:encoded><![CDATA[<div class="comment-toolbar" style="text-align: right"><input type="button" value="Reply" onclick="CF_Reply('Pat F');" /><input type="button" value="Quote" onclick="CF_Quote('co_247661','Pat F');" /></div><span id="co_247661"><p>using the median isn&#8217;t perfect either, and using the mean is a better route because having those &#8220;older apples&#8221; (actually, 6 of them, which is a ton) is a big part of a team being old, and the mean simply reflects that.  sure they really bring the mean up, but that&#8217;s the whole idea of a mean.  having 6 really old players on a team means a team is really old unless everyone else is super young, which we know not to be the case.  of course, you don&#8217;t need any numbers besides the ages of individual players to prove the point that the yankees are getting younger.  you can just take a quick glance at the ages of the five starters in 05 vs. 09 and the ages of each position player in 05 vs. 09 and see that the yankees are getting younger.  cashman is doing a tremendous job in this regard, and that&#8217;s really all that matters.  because age is flexibility in baseball.  to quote rob neyer from the other day: </p>
<p>But the only way the Yankees can fall into a habit of losing, someday, is by stockpiling too many players in their 30s with big long-term contracts. It&#8217;s incredibly difficult to place a value on flexibility, but that value is real and important and Brian Cashman&#8217;s awareness of that value is going to keep the Yankees on top for quite some time.&#8221;</p>
<p><a href="http://espn.go.com/blog/sweetspot/post/_/id/1885/yanks-fine-without-superstar-lf" rel="nofollow">http://espn.go.com/blog/sweetspot/post/_/id/1885/yanks-fine-without-superstar-lf</a></p>
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		<title>By: Steve Lombardi</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247660</link>
		<dc:creator>Steve Lombardi</dc:creator>
		<pubDate>Thu, 31 Dec 2009 22:05:35 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247660</guid>
		<description>&lt;b&gt;jay&lt;/b&gt; wrote:
&lt;blockquote&gt;I’m not sure what the intent of this post is. &lt;/blockquote&gt;

Same point as I&#039;ve made in the past - that, yes, 2+2 = 4.  But, unless you really know that 2 is &quot;2&quot; then you can&#039;t assume what you see is true.

And, if someone says:

Average age of Yankee pitchers 
2005: 34.2
2009: 29.3

Does it really mean the Yankees are getting younger?  Maybe...but, maybe not.  You have to look &quot;inside the numbers&quot; to be sure.</description>
		<content:encoded><![CDATA[<div class="comment-toolbar" style="text-align: right"><input type="button" value="Reply" onclick="CF_Reply('Steve Lombardi');" /><input type="button" value="Quote" onclick="CF_Quote('co_247660','Steve Lombardi');" /></div><span id="co_247660"><p><b>jay</b> wrote:</p>
<blockquote><p>I’m not sure what the intent of this post is. </p></blockquote>
<p>Same point as I&#8217;ve made in the past &#8211; that, yes, 2+2 = 4.  But, unless you really know that 2 is &#8220;2&#8243; then you can&#8217;t assume what you see is true.</p>
<p>And, if someone says:</p>
<p>Average age of Yankee pitchers<br />
2005: 34.2<br />
2009: 29.3</p>
<p>Does it really mean the Yankees are getting younger?  Maybe&#8230;but, maybe not.  You have to look &#8220;inside the numbers&#8221; to be sure.</p>
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		<title>By: Steve Lombardi</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247659</link>
		<dc:creator>Steve Lombardi</dc:creator>
		<pubDate>Thu, 31 Dec 2009 22:03:12 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247659</guid>
		<description>&lt;b&gt;MJ&lt;/b&gt; wrote:
&lt;blockquote&gt;I don’t know where the data comes from that yields a 29.3 average age for the pitchers. When I take the ages from B-R.com, I get an average of 28.1 and a median of 27.5.
&lt;/blockquote&gt;

I would bet B-R.com does some weighting based on PT.  Think about it - say your team calls up 15 pitchers after 9/1 - and they&#039;re all 20 years old and face just one batter each in September.  Would you really use a straight average to get average team age, and give those 15 the same weight as the other pitchers?  Makes no sense.

That said, I stick by my point - having those 6 really old timers covering all those innings in 2005 makes the &quot;average age&quot; - no matter how B-R.com calc&#039;s it, look worse than it really is...</description>
		<content:encoded><![CDATA[<div class="comment-toolbar" style="text-align: right"><input type="button" value="Reply" onclick="CF_Reply('Steve Lombardi');" /><input type="button" value="Quote" onclick="CF_Quote('co_247659','Steve Lombardi');" /></div><span id="co_247659"><p><b>MJ</b> wrote:</p>
<blockquote><p>I don’t know where the data comes from that yields a 29.3 average age for the pitchers. When I take the ages from B-R.com, I get an average of 28.1 and a median of 27.5.
</p></blockquote>
<p>I would bet B-R.com does some weighting based on PT.  Think about it &#8211; say your team calls up 15 pitchers after 9/1 &#8211; and they&#8217;re all 20 years old and face just one batter each in September.  Would you really use a straight average to get average team age, and give those 15 the same weight as the other pitchers?  Makes no sense.</p>
<p>That said, I stick by my point &#8211; having those 6 really old timers covering all those innings in 2005 makes the &#8220;average age&#8221; &#8211; no matter how B-R.com calc&#8217;s it, look worse than it really is&#8230;</p>
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		<title>By: shaked</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247656</link>
		<dc:creator>shaked</dc:creator>
		<pubDate>Thu, 31 Dec 2009 18:32:20 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247656</guid>
		<description>[7] I see that now.  I browsed through comments prior to typing that up, but I must have glossed over your suggestion.  I would imagine this would give us a clear picture of age.  I believe it is also possible to calculate median in this manner.</description>
		<content:encoded><![CDATA[<div class="comment-toolbar" style="text-align: right"><input type="button" value="Reply" onclick="CF_Reply('shaked');" /><input type="button" value="Quote" onclick="CF_Quote('co_247656','shaked');" /></div><span id="co_247656"><p>[7] I see that now.  I browsed through comments prior to typing that up, but I must have glossed over your suggestion.  I would imagine this would give us a clear picture of age.  I believe it is also possible to calculate median in this manner.</p>
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		<title>By: jay</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247655</link>
		<dc:creator>jay</dc:creator>
		<pubDate>Thu, 31 Dec 2009 18:12:56 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247655</guid>
		<description>[6] I agree that&#039;s the best way to do this. This is what I was suggesting in [2].</description>
		<content:encoded><![CDATA[<div class="comment-toolbar" style="text-align: right"><input type="button" value="Reply" onclick="CF_Reply('jay');" /><input type="button" value="Quote" onclick="CF_Quote('co_247655','jay');" /></div><span id="co_247655"><p>[6] I agree that&#8217;s the best way to do this. This is what I was suggesting in [2].</p>
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		<title>By: shaked</title>
		<link>http://waswatching.com/2009/12/31/not-to-be-mean-but-what-about-the-median/comment-page-1/#comment-247653</link>
		<dc:creator>shaked</dc:creator>
		<pubDate>Thu, 31 Dec 2009 17:14:17 +0000</pubDate>
		<guid isPermaLink="false">http://waswatching.com/?p=20262#comment-247653</guid>
		<description>To go a step further, a weighted average based on total innings pitch would likely be the &quot;most&quot; accurate measure.  I am not sure how the original data was used, but if you weighted the innings of each starter as a percentage of the total, you could get a more accurate mean or median.  So that 24 year old that had no impact will not have much of an impact on the total.

Again, I have no clue how this data was originally constructed, but for argument&#039;s sake, using weights would be the most accurate.  So a 41 year old Randy Johnson would represent 10-15% of the total innings and therefore 10-15% of the &quot;average age&quot; and not just be a generic number.</description>
		<content:encoded><![CDATA[<div class="comment-toolbar" style="text-align: right"><input type="button" value="Reply" onclick="CF_Reply('shaked');" /><input type="button" value="Quote" onclick="CF_Quote('co_247653','shaked');" /></div><span id="co_247653"><p>To go a step further, a weighted average based on total innings pitch would likely be the &#8220;most&#8221; accurate measure.  I am not sure how the original data was used, but if you weighted the innings of each starter as a percentage of the total, you could get a more accurate mean or median.  So that 24 year old that had no impact will not have much of an impact on the total.</p>
<p>Again, I have no clue how this data was originally constructed, but for argument&#8217;s sake, using weights would be the most accurate.  So a 41 year old Randy Johnson would represent 10-15% of the total innings and therefore 10-15% of the &#8220;average age&#8221; and not just be a generic number.</p>
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