# Relief Staff Ranking

Let’s discuss relief pitching today.   Relief pitching is very important because starters seldom go a complete game and usually are pulled after 6 or 7 innings leaving 2 or 3 innings for the relief pitching to deal with.  We need a way to measure value of a relief squad because they usually make up 1/3 of the game for PITCH.  If there is a bad pitcher starting the relief staff could end up pitching most of the game.

Since WAA has additive properties we can simply add up the relievers’ WAA to compute the WAA for the entire relief staff.  This is exactly what is done for lineups and any group of players.  Here are the top 5 relief staffs in MLB as of yesterday.

TeamID WAA IP WinPct
CLE 5.65 99.8 0.755
CHA 5.17 102.5 0.727
NYA 4.33 104.3 0.687
BOS 4.16 106 0.677
CHN 3.46 135.3 0.615

Both Cubs and White Sox are in the top 5.  The Cubs have a very high number of relief innings pitched, almost 4 per game.  That could be a choice Joe Maddon makes to keep his relievers sharp — and according to the above table they are.

The WinPrct column is calculating using this property of WAA.  The formula is simply:

Win% =  0.5*WAA/(number of games played) + 0.5

For pitching number of games played is innings pitched divided by 9.  An average MLB game is not always 9 innings but that’s the constant used for over a century to compute ERA and it’s still good enough.

But what does WinPct represent?  It doesn’t mean that if CLE is ahead and they pull their starter they have a 0.755 chance of winning that game.   That percentage places  WAA in context and shows how far above average much like the WinPct listed with a team’s W-L record.   CLE, at 18-16 has a slightly above average team and the above table shows their relievers are carrying a lot of weight.

Edit: The WAA value measure  exactly describes a relief staff’s contribution to their team’s win loss record.  At 18-16 CLE has a real WAA=+2.   Their relief staff has a WAA=+5.65. If they had an average relief staff that 5.65 would be taken off the books and their real WAA so far this season would be -3 or -4 and CLE would be a sub 0.500 team.  Ranking for any player or any group of players is done through the weighted WAA measure — not WinPct.  It is possible for a relief staff to have a higher WinPct than a team with a higher WAA.    WinPct provides context to WAA,, nothing more.  We know exactly how much CLE relievers are carrying that team and it’s 5.65 wins.  The rest of CLE adds to WAA=-3.65.

Like win loss records, top batting averages, the long baseball season will average things out and the above high WinPct will converge closer to 0.500.   For example, here are the top three relief teams last season:

TeamID WAA IP WinPct
LAN 11.28 545.2 0.593
BAL 10.46 597.3 0.579
WAS 9.51 487.9 0.588

Top MLB teams hover around 0.600 in their win loss records too. Now let’s look at how the Cubs relief staff breaks down at a player level. Often this is Too Much Information (TMI) but right now it illustrates how we measure relief staff.

WAA Name_TeamID Pos IP
1.49 Mike_Montgomery_CHN PITCH 23.0
0.99 Carl_Edwards_CHN PITCH 15.3
0.42 Koji_Uehara_CHN PITCH 13.7
0.21 Hector_Rondon_CHN PITCH 13.7
0.19 Dylan_Floro_CHN PITCH 4.3
0.08 Miguel_Montero_CHN PITCH 1.0
0.04 Felix_Pena_CHN PITCH 5.0
0.04 Brian_Duensing_CHN PITCH 14.0
0.04 Pedro_Strop_CHN PITCH 11.7
-0.25 Rob_Zastryzny_CHN PITCH 4.0
-1.20 Justin_Grimm_CHN PITCH 14.3
TOTAL WAA=3.46 IP=135.3 WinPct=0.615

The above table shows the value of all relievers who pitched for CHN this season.  As the season progresses the active relief roster changes and the above number is not valid for use as a value indicator for a particular game.  The above is the accumulated value for a season.  When ranking a team on a seasonal basis we want all the numbers.  When evaluating on a daily or game basis, we want the current value.  Lineups and relief staff value can be quite different from seasonal value especially after trade deadline when playoff wannabes stock up on good players and discard their poor performers.  More on that later .  Until then….