May 13, 2008

Prospectus Toolbox

Stranded!

by Derek Jacques

I feel the need to re-introduce myself, or at least my column, since this space has been pretty quiet in 2008-I've spent a lot of time so far running around explaining legal concepts and covering live events for Baseball Prospectus-and I'm hoping this will be the beginning of a more regular schedule. Prospectus Toolbox is a column dedicated to new readers, or veteran readers who might not be familiar with all the acronyms and numbers that we tend throw around rather casually on this website. The focus is meant to be high on simple language and explanations and low on any form of math you'd have learned after middle school-because, really, you shouldn't need to be Stephen Hawking to comprehend the work that we do here, or to have it increase your enjoyment of baseball.

Since the best way to figure out what people want to learn more about is to listen to their questions, you'll find that this column-by design-leans more on reader mail than anyone else's. You're encouraged to use the links at the bottom of the page to send me questions or comments, particularly if you feel that there is something that isn't covered in our glossary. Sadly, I don't answer every email I receive, but I do read all of them, and a fair number wind up getting published.

Anyway, on to this week's question, from reader J.B.:

Does the 'Left on Base' Statistic have any correlation to a team's offensive success or failure?

Some statistics carry more of an emotional charge than others, and baserunners left on base (LOB or BLOB, as it's referred to in our glossary) incites emotions on the level of the home run or the strikeout. It's hard to find a more frustrating (or, if you're rooting for the team on defense, exhilarating) moment in a game than when a batter comes to the plate with the bases loaded, and fails to bring any of those runners home. Keeping track of how many runners an individual batter strands on base is a popular enough hobby that many scorecards dedicate a space just for keeping a running tally. At the same time, games in which either or both teams strand a lot of runners tend to be long, frustrating bores.

Before we take on J.B.'s question, a quick explanation of what he's asking for. Correlation is a very basic statistical tool that examines the relationship between two sets of numbers. You can have positive correlation between the two sets-if the values in one set go up, the values in the other will also rise, if they go down, the values in the other set will also fall (for example, your age and the date). Negative correlation means that as one value rises, the other falls (for example, the number of miles you've driven between trips to the gas station and the amount of fuel left in your tank). The correlation coefficient runs on a spectrum between 1 and -1, with strong relationships at either side of the spectrum, weakening as you approach the middle. A correlation coefficient of 0 means that the two sets of numbers are basically random with respect to each other.

Now, it's important to remember that correlation is a what, not a why. Just because two sets of numbers are correlated, it doesn't mean that one necessarily causes the other. Correlation sometimes suggests the nature of a relationship, but it never proves it.

The reason that J.B.'s question is interesting is because LOB has such negative connotations, that you'd probably expect a strong negative relationship to run scoring. After all, if you're leaving a lot of runners on base, by definition your team is losing out on scoring opportunities. To get an idea of whether this expectation holds water, let's look at the Team LOB leaderboard for last year, along with a couple of other statistics we usually relate to a team's offensive success or failure: Runs and Times on Base (TOB).

    Team    R     TOB    LOB
 1   PHI   892   2289   1295
 2   BOS   867   2314   1291
 3   OAK   741   2143   1258
 4   COL   860   2271   1250
 5   NYA   968   2371   1249
 6   CLE   811   2174   1216
 7   ATL   810   2145   1205
 8   LAN   735   2096   1200
 9   NYN   804   2146   1196
10   FLO   790   2107   1192
11   CHN   752   2070   1190
12   HOU   723   2058   1181
13   CIN   783   2098   1170
14   SLN   725   2073   1168
15   TBA   782   2098   1166
16   WAS   673   1992   1163
17   SDN   741   2014   1153
18   BAL   756   2076   1152
19   DET   887   2182   1148
20   SFN   683   1978   1141
21   SEA   794   2080   1127
22   MIN   718   2020   1120
23   PIT   724   1997   1119
24   MIL   801   2032   1117
25   TOR   753   2014   1112
26   ANA   822   2125   1100
27   TEX   816   2019   1092
28   ARI   712   1939   1090
29   KCA   706   1964   1089
30   CHA   693   1925   1074

Looking at this list, you see some evidence against the idea that LOB hurt your offense. Looking at the top five teams at leaving men stranded on the bases, you find four of the five top scoring offenses of 2007� and you find the Oakland A's, the tied-for-nineteenth-best-offense in the game. Just as you're tempted to draw the opposite conclusion, there are odd little bits of data-for example, the worst offense in the game (the Nationals) producing more LOB than the third-best offense (the Tigers). Is this all just random?

To answer the question, we'll want to look at a larger sample of data. So I asked the amazing Bil Burke to give me the LOB totals for each team since 1971, and from that sample I omitted strike-shortened seasons such as 1981, 1994, and 1995, as well as the current season. That leaves us with some 918 data points from which to calculate the correlation between team Runs scored and team LOB. The coefficient of correlation was 0.52, which is a pretty strong positive correlation between these two statistics. Two other correlations between the statistics presented above suggest a reason that we see this relationship between LOB and Runs scored. The coefficient of correlation between LOB and TOB was 0.72, and between TOB and runs it was an extremely high 0.91. Each of these relationships makes a bit of sense: the more runners you put on base, the more likely some are to get stranded there, and the more runners you put on base, the more likely you are to score runs. Put it all together and the data suggests that a high number of runners left on base, while frustrating and annoying, may not be a sure sign that your team's offense is broken or even in bad shape. It might actually be a good thing.

Notes:

• For a statistic that's well known, and a fixture in the box scores, it's very hard to find databases that include Team LOB totals. They're nowhere to be found in our sortable stats, and I couldn't find them on MLB.com, ESPN, Retrosheet, or Baseball Reference.
• According to Wikipedia, tracking Team LOB in the box score is an accounting step to make sure that every plate appearance in a game is accounted for (since every PA ultimately results in the batter scoring a run, being put out, or being left on base). This explains one of LOB's shortcomings as a measure of futility-the fact that baserunners eliminated on double plays aren't counted against the offense.
• We're just dealing with Team LOB here, not individual batter LOB. While I haven't been able to find databases listing individual LOB, either, our RBI Opportunities report does a similar job, only better. The Others Batted In Percentage (OBI%) statistic shows how effective (or ineffective) a batter has been at driving in the runners on base before him. If you wanted to talk about totals of runners not brought around to score, you could simply subtract OBI from a batter's Runners On Base (ROB). We'll end this edition with a current top five in this metric, which I'll call Runners Not Plated (RNP):

  
  Rk  Player            RNP
   1  Troy Glaus        116
   2  Bobby Crosby      111
   3  Dustin Pedroia    110
   4  David Ortiz       109
  T5  Garrett Atkins    108
  T5  Albert Pujols     108
  

Derek Jacques is an author of Baseball Prospectus. 
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