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Weekend Report: Stats Demystified - EQR, RARP

on 06/21/2002


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.

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, throw-ins 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 17-24 more games using 4.5 to 5 PAs per game. Each missed game will add another 2 or 3 games onto that time frame.


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