I'm starting work on the column early in the week so you'll have to wait until the end for my Player of the Week, I know the suspense is killing you. Last week I tortured everyone with an in depth discussion of how to calculate EQA. I mentioned a number of other stats briefly like EQR and RARP. So this week I'm going to expand that list to include EQR, RAR, RAP, and RARP. That seems like a lot, but after EQA they are all simple derivatives.
Starting with EQR, as I mentioned last week EQR is the last number before EQA. And to refresh, you get EQA from EQR by dividing by the number of outs the player has made and a couple of other numbers that scale it to look right (EQA = (0.2 * EQR / Out) ^ (0.4) like I said multiplying by .2 and raising everything to the .4 power only changes what the number looks like so that it resembles batting averages). This means that EQR is a direct measure of how many of the total league runs scored could be attributed to a particular individual. Because of how the system works an equivalent run is equal to a "real" run on the scoreboard for that particular era. The important distinction between EQA and EQR is that EQA allows you to compare players regardless of playing time differences, while EQR is very dependent on playing time.
As you might imagine having previously defined a league average hitter for EQA we could do the same with EQR. These calculations are where RAR, RAP, and RARP come into play. By dividing up performances by position it is easy to calculate the average offensive performance for each position. Taking this EQA you work backwards by now multiplying by the number of outs used by the player in question (and the other manipulations are reversed to I'll let you do the algebra). This tells you how many runs a league average hitter at that position would have scored given the same number of outs that the player used (RAP runs above position). A positive number means the player has created more runs than league average, and negative the opposite.
Pos 
AB 
H 
XB 
BB 
SB 
CS 
EQR 
BA 
OBA 
SA 
EQA 
P 
2116 
327 
107 
86 
1 
1 
26 
0.155 
0.188 
0.205 
0.097 
C 
7080 
1769 
909 
681 
31 
28 
813 
0.250 
0.316 
0.378 
0.247 
1B 
7548 
2028 
1381 
1030 
52 
38 
1193 
0.269 
0.357 
0.452 
0.284 
2B 
7603 
1995 
887 
740 
207 
73 
937 
0.262 
0.328 
0.379 
0.256 
3B 
7487 
1922 
1210 
782 
87 
46 
1002 
0.257 
0.327 
0.418 
0.264 
SS 
7749 
2033 
1045 
667 
170 
94 
961 
0.262 
0.321 
0.397 
0.256 
LF 
7653 
2059 
1351 
992 
153 
67 
1192 
0.269 
0.353 
0.446 
0.282 
CF 
7556 
2027 
1186 
830 
296 
95 
1102 
0.268 
0.341 
0.425 
0.274 
RF 
7565 
2077 
1420 
1023 
172 
82 
1245 
0.275 
0.361 
0.462 
0.289 
Oth 
6645 
1681 
1038 
773 
102 
49 
900 
0.253 
0.331 
0.409 
0.264 
That is the chart on the EQA page showing the league average production by position, SA is slugging average. They seem to like average instead of percent. As you can see the most offensive position by EQA is RF, followed by 1st base, and then LF. The EQR column shows the total number of equivalent runs from that position. OPS wise you can see the standards have gotten pretty high for those 3 positions. RF an .823, 1st an .809, and LF a .799. Remembering that those numbers include plate appearances by all of the players who batted while playing that position (That means EY's 1 game as a LF is included). Also a players RAP score is calculated for each position he has played.
RAP is pretty intuitive to understand, but the other two RAR and RARP are less intuitive because they involve the mythical "replacement level". Most of us are familiar with the replacement idea, players that are easily available as minor league free agents, waiver wire fodder, throwins on trades. A lack of good metrics to describe defense leaves judgement of replacement level to offense and pitching. So when someone says that player X is only a replacement level hitter take it with a little bit of care. Is the player also a Gold Glove middle IF? Or is he a slug of a first basemen? The middle IF could probably start on a playoff team, while the second looks a lot like Kevin Young. Now without having a copy of BaseballProspectus 2002 I can only assume the following. The numerical values used to calculate replacement level more or less reflect reality. Or, what BP says is replacement level by and large is replacement level. Overall a replacement level hitter is defined to have a .230 EQA. From there the calculation of RAR (runs above replacement) proceeds as it did for RAP using a .230 EQA for comparison instead of the position average. I don't find this number particularly useful because we already know there is great variability between positions in terms of hitting ability.
Instead when I want to know if a player is truly better than replacement level I look at RARP (runs above replacement position). But how to calculate what a replacement hitter for a given position is? BP uses the average EQA for the position multiplied by 0.8835. As I said before I believe BP has a good reason for the numbers it uses and in this case 0.8835 is very close too (and maybe the) difficulty adjustment used for turning a AAA EQA into a Major league equivalent (MIEQA). We already know the league average for the positions, and the multiplier, so once again we just perform the same procedure working backwards to calculate how many equivalent runs a replacement level player at that position would have created in the same number of outs. For convenience I'll calculate the replacement level EQAs quickly
Pos 
Replacement EQA 
C 
.218 
1b 
.251 
2b 
.226 
3b 
.233 
SS 
.226 
LF 
.249 
CF 
.242 
RF 
.255 
And to finish off I'll give some selected MIEQAs. Izzy .261, Rushford .255,
Josh Klimek .226, Scooter .281, Marcus Jensen .232.
It looks like the replacement level definition works pretty well.
Player of the Week
Alright at this point there is probably no suspense in who the player of the week is.
When he got 3 hits and made a game saving throw on Friday he had already shot up the list
earning major bonus points for having a web gem during a game I could actually watch.
Then he just kept on hitting, and by Tuesday I was just basically waiting to see if someone
else would do anything truly special (4 HR game, no hitter..) to unseat Tyler Houston as
my first player of the week (I feel better knowing that Toby already has nice front runner
for his next offensive player of the week, though said player does have a challenger or two potentially).
I doubt Tyler will continue to hit .329, but after last year's seemingly out of place BA maybe he's
figured out a way to make a bit more contact and can hit near .300, which will at least give him that
league average OBP he's been lacking. Jim Powell did some of the work last night about trying to figure out
when Houston will start qualifying for the batting title if he can keep this up, but appeared to get
cold feet about doing the algebra on air. Luckily for him I'll provide the numbers. Based on your
estimate of how many PAs per game he will get (also assuming no missed games) it will take him between 1724 more
games using 4.5 to 5 PAs per game. Each missed game will add another 2 or 3 games onto that time frame.
