https://en.formulasearchengine.com/index.php?title=Binary_moment_diagram&feed=atom&action=historyBinary moment diagram - Revision history2024-03-28T11:16:55ZRevision history for this page on the wikiMediaWiki 1.42.0-wmf.5https://en.formulasearchengine.com/index.php?title=Binary_moment_diagram&diff=12857&oldid=preven>Headbomb: Cleanup for Book:Data structures using AWB (7840)2011-09-21T03:16:27Z<p>Cleanup for <a href="/index.php?title=Book:Data_structures&action=edit&redlink=1" class="new" title="Book:Data structures (page does not exist)">Book:Data structures</a> using <a href="/index.php?title=Testwiki:AWB&action=edit&redlink=1" class="new" title="Testwiki:AWB (page does not exist)">AWB</a> (7840)</p>
<p><b>New page</b></p><div>{{Unreferenced|date=August 2007}}<br />
In [[baseball statistics]],<br />
'''Defense-Independent ERA''' ('''dERA'''), created by [[Voros McCracken]], projects what a pitcher's [[earned run average]] (ERA) would have been, if not for the effects of defense and luck on the actual games in which he pitched.<br />
<br />
==Method==<br />
Version 2.0 of dERA uses the following statistics:<br />
*[[Total batters faced|Batters Faced (BFP)]]<br />
*[[Home runs allowed|Home Runs Allowed (HR)]]<br />
*[[Base on balls|Total Walks Allowed (BB)]]<br />
*[[Intentional base on balls|Intentional Walks Allowed (IBB)]]<br />
*[[Strikeout|Strikeouts (K)]]<br />
*[[Hit by pitch|Hit Batsmen (HB)]]<br />
<br />
<br />
0) Multiply BFP by 0.0074 to get the number of intentional walks allowed (dIBB).<br />
<br />
1) Divide HB by BFP-IBB. Call this $HB. Then multiply $HB by BFP-dIBB. This number gives the DIPS number of Hit Batsmen (dHB). <br />
<br />
2) Divide (BB-IBB) by (BFP-IBB-HB), and call this number $BB. Multiply BFP by 0.0074, and call this dIBB.<br />
:2a) Then multiply $BB by (BFP-dIBB-dHB). Take this number and add IBB. This number is now the DIPS number of total walks allowed (dBB).<br />
<br />
3) Divide K by (BFP-HB-BB) and call this number $K. Remember this number for later.<br />
:3a) Multiply $K by (BFP-dBB-dHB). This gives the DIPS number of strikeouts (dK).<br />
<br />
4) Divide HR by (BFP-HB-BB-K) and call this number $HR. Remember this number for later.<br />
:4a) Multiply $HR by (BFP-dBB-dHB-dK). This gives the DIPS number of Home Runs (dHR).<br />
<br />
5) Calculate the number of 'Balls Hit in the Field of Play'. This is BFP-dHR-dBB-dK-dHB.<br />
<br />
6) Estimate hits per balls in the field of play ($H):<br />
:6a) Take the number 0.304396 and subtract 0.010830 if the pitcher is strictly a knuckleball pitcher. If not keep the 0.304396 number. <br />
:6b) Take the result from the last step and add 0.002321 if the pitcher is left-handed, if not keep the number from the above step.<br />
:6c) Take the $K figure from above and multiply it by 0.04782. Subtract this number from the number in 6b.<br />
:6d) Take the $HR figure from way above and multiply it by 0.08095. Subtract this number from the number in 6c.<br />
:6e) Whatever remains is the $H figure.<br />
<br />
7) To get the projected number of Hits Allowed (DIPS 'Hits Allowed', or dH), multiply $H by the number of balls hit in the field of play (BHFP).<br />
:7a) Add this number to dHR. This number is the DIPS total of Hits Allowed (dH).<br />
<br />
8) Take BFP-dBB-dHB-dK-dH and multiply that number by 1.048. Add dK to that number. Take that number and divide by 3. This is the DIPS total of Innings Pitched (dIP).<br />
<br />
9) Sum the following products:<br />
: (dH-dHR)*0.49674<br />
: dHR*1.294375<br />
: (dBB-dIBB)*0.3325<br />
: dIBB*0.0864336<br />
: dK*(-0.084691)<br />
: dHB*0.3077<br />
: (BFP-dHB-dBB-dK-dH)*(-0.082927)<br />
<br />
The sum of all of these is the DIPS total of earned runs (dER). <br />
<br />
10) Calculate ERA as usual: (9*dER)/dIP. This is the DIPS ERA (dERA).<br />
<br />
==Alternative formulation==<br />
<br />
:0) &nbsp; <math>\rm{dIBB=0.9926 \ IBB} \,</math><br />
:1) &nbsp; <math>\rm{dHB = HB \left ( \frac{BFP-dIBB}{BFP-IBB} \right )} \,</math><br />
:2) &nbsp; <math>\rm{dBB = (BB-IBB) \left ( \frac{BFP-dIBB-dHB}{BFP-IBB-HB} \right )+IBB} \,</math><br />
:3) &nbsp; <math>\rm{dK = K \left ( \frac{BFP-dIBB-dHB}{BFP-IBB-HB} \right )} \,</math><br />
:4) &nbsp; <math>\rm{dHR = HR \left ( \frac{BFP-dHB-dBB-dK}{BFP-HB-BB-K} \right )} \,</math><br />
<br />
==See also==<br />
*[[Earned run]]<br />
*[[Earned run average]]<br />
*[[Component ERA]]<br />
*[[Peripheral ERA|PERA]]<br />
*[[Nate Silver#PECOTA, QERA, and the "Secret Sauce"|QERA]]<br />
<br />
==External links==<br />
*[http://www.futilityinfielder.com/dips2.html Defense Independent Pitching Stats]<br />
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[[Category:Pitching statistics]]</div>en>Headbomb