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Weekend Report: Stats Demystified - ARP

on 08/23/2002


It's time for this column to get back to its roots, describing the "how and why" of complicated statistics. This week I tackle Michael Woolverton's reliever evaluation tools. These tools differ from most of the statistics I've reviewed previously because they are not context independent. Of course they are adjusted for park/league effects, but they focus on what is actually happening during the game when the reliever is pitching. The concepts behind Adjusted Runs Prevented (ARP) are pretty simple. Part of a reliever's job is to come in and strand the runners on base. Conventional run assignment places "blame" for those runs on the pitcher who let them on base. Without debating who deserves more blame for inherited runners scoring, it is sufficient to acknowledge that the reliever is partly responsible. He should be evaluated based on how he prevents runs in total, which includes stranding runners as well as not giving up his own runs.

The methodology is very simple for these statistics. In The Hidden Game of Baseball published in the early 80's the idea of run expectancy and base out situations was introduced. For those not familiar, the authors of the book took data from 1977 back into the 1960's to arrive at a contingency table. This is a fancy way of saying they determined how many runs on average could be expected to score for the remainder of an inning for any of the 24 base-out situations. Now the astute reader will quickly realize that such a contingency table is of much less relevance in today's offensive era. Woolverton's solution is to have a contingency table for each ballpark which neatly takes care of the park and league effects. Using this contingency table, it is easy to compare how well the reliever did at preventing runs compared to the average pitcher placed in the same situation.

Here is an excellent place to do a sample calculation. I don't have the actual tables, so I'll just use the conveniently provide generic ones Woolverton used on his recent base running article. Here's the situation: Jamey Wright pitches into the 5th inning and gives up a leadoff double, followed by a hit batter and a walk to load the bases with no one out. Royster finally notices something is going on and summons Ray King to face the lefty batter. At this point your intuition is telling you that getting out of the inning with only limited damage (a run or two) is probably a victory. You'd be right, as the expectation is 2.35 runs. Ray comes in and gets a quick strike. The batter then gets a fly ball to LF, which scores a run, but isn't deep enough to advance the runner to third. At this point Sammy Sosa steps up to bat and Royster, actually on top of the situation for once, decides to bring in Durocher. Jayson comes in to strike out Sammy and gets McGriff to pop out. To finish this calculation we need one more number which is the expectancy for runners on 1st and second with one out, which is 0.96. So how did Ray do? He entered the game with the expectation of 2.35 runs scoring and left with it at 0.96 for a positive difference of 1.39 runs saved. The exception is that he allowed a run to score so that gets subtracted from the total, still leaving him in positive territory of 0.39 runs saved.

Continuing our example Durocher stays in to work the next inning. He gives up a lead-off walk, followed by an IF single, a strikeout, and a double play grounder to end the inning. To come up with his total, we start first with the inning he entered the game. He came in with an expected 0.96 runs to score and didn't allow any. Since he finished the inning, he gets credit for preventing the full 0.96 runs. Only beginning and end points matter in the calculation, so the run expectancy after he struck out Sosa doesn't matter here. He then worked the next inning without allowing a run. What happened during the inning doesn't matter as long as no runs scored. The run expectancy at the start of an inning is 0.51 runs. So adding those two totals together gives you 1.47 runs saved - a very good outing. What would have happened if Royster had pulled Jayson after there were 2 men on and no outs? Following through is pretty simple. When that inning started 0.51 runs could be expected to score; when he left 1.51 runs could be expected to score, for a total of -1 run that inning. Combined with his previous total of 0.96 saved, he ends up costing the team 0.04 runs.

Woolverton uses these calculations to arrive at a plethora of numbers. These other statistics aren't particularly useful in assessing total player worth, but they do help provide a full picture of a pitcher. Separate calculation are made to isolate only the pitcher's effectiveness at stranding runners, and in how other relievers have dealt with that player's own runners left on These are Inherited runs prevented (IRP) and bequeathed runs saved (BRS), respectively. Positive IRP means the pitcher has chopped runs off of other pitchers' totals. A positive BRS means that pitcher was bailed out by his teammates more often than average. One of the more interesting calculations is the difference between the runs assigned the pitcher by conventional scoring, and the total attributed to him with this system. It provides a nice measure of those pitchers whose performance is being poorly measured conventionally.

Player of the Week

I went into Wednesday night's game with three candidates for Player of the Week: Sheets, Jose, and maybe just maybe Jimmy "don't call me Olson" Osting. Clearly Ben's start knocked him out of contention, while Jose's HR and continued hitting streak helped bolster a merely good week into real Player of the Week contention. This left me sitting in suspense for Jimmy's Thursday afternoon start. Ouch - what a let down. Jose Hernandez is my Player of the Week in the most anticlimactic of ways.


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