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Tuesday, July 27, 2010

SABR 101 - Bases

By Tangotiger, 04:31 PM

Triples and homeruns will advance all runners on base the maximum number of bases possible.  Runners on first base will advance three bases, runners on second base will advance two bases, and runners on third base will advance one base.

On average, there are 0.3 runners on 1B, 0.2 runners on 2B and 0.1 runners on 3B.  Therefore, the total number of bases advanced by the triples and homeruns is 0.3 times 3, plus 0.2 times 2, plus 0.1 times 1, or a total of 1.4 bases.  This is the base-advancement value of a triple and home run.

Doubles have the same base impact for runners on 3B and 2B.  For runners on 1B, 40% of the time, they will advance the runner three bases, and 60% of the time, it will be two bases, for an average of 2.4 bases.  Following the same calculation above, we have 0.3 times 2.4, plus 0.2 times 2, plus 0.1 times 1, or a total of 1.22 bases as the base-advancement value of a double.

For singles, they’ll advance the runner on 2B two bases 60% of the time and one base 40% of the time (average of 1.6 bases), and the runner on 1B will advance two bases 30% of the time and one base 70% of the time (average of 1.3 bases).  The calculation follows: 0.3 times 1.3, plus 0.2 times 1.6, plus 0.1 times 1.  That’s a base-advancement value of .81 bases for the single.

Walks advance all runners from first base one base.  The runner on 2B will advance only when there is also a runner on 1B (so the overall frequency is about .10).  And the runner on 3B will advance only when the bases are loaded (about 2% of the time).  So, we have: .3 x 1, plus .1 times 1, plus .02 times 1, equals .42 bases for the walk.

All these numbers are nicely rounded for ease of illustration.

Here’s the summary:
1.40 HR
1.40 3B
1.22 2B
0.81 1B
0.42 BB

This was based on having 0.60 runners on base per plate appearance.  If you have more runners, say 0.90, then all those numbers go up 50%.  If you have fewer runners, say 0.30, then all those numbers need to be cut down in 2.

Added to that is the number of bases the batter himself gets (4 for HR, 3 for 3B, 2 for 2B, 1 for 1B, BB).  Those numbers are independent to the run environment.  So, a HR gets 4 bases for the batter and 1.40 for the runners, or a total of 5.40 bases.  Here’s the summary of that:
5.40 HR
4.40 3B
3.22 2B
1.81 1B
1.42 BB

In this SABR 101 article (required reading) from Patriot, he shows some data I provided using actual data:
5.41 Home Run
4.46 Triple
3.23 Double
1.83 Single
1.39 Walk

You can see here how the theoretical pretty much matches the empirical.  This is how run scoring works in baseball. 

Given that there are 4 bases required to score a run, you can take the number of bases and divide by 4.  Taking the theoretical numbers, we have:

1.35 HR
1.10 3B
0.81 2B
0.45 1B
0.36 BB

That’s more or less the number of runs each event is worth.  All this is pretty standard for the regulars around here.  Hopefully, this brings all the new readers up to speed.


#1    skyjo      (see all posts) 2010/07/27 (Tue) @ 17:01

minor typo:

“On average, there are 0.3 runners on 1B, 0.2 runners on 2B and 0.1 runners on 1B. “

I assume should be:

“....and 0.1 runners on 3B.”


#2    Tangotiger      (see all posts) 2010/07/27 (Tue) @ 17:15

Thanks, fixed.


#3          (see all posts) 2010/07/27 (Tue) @ 18:15

Is there a similar simple “theoretical” (as opposed to empirical) way to derive the (negative) value of an out?  Would you simply divide average R/G by the average number of outs per game (slightly under 27)?


#4    dq      (see all posts) 2010/07/27 (Tue) @ 18:49

I love posts like this one.


#5    Eddo      (see all posts) 2010/07/27 (Tue) @ 19:20

Very cool.  This is a great primer/refresher.


#6    dave smyth      (see all posts) 2010/07/27 (Tue) @ 19:45

Tango, why not finish the presentation by analyzing the out value (absolute, not LW) in terms of bases lost.


#7    Tangotiger      (see all posts) 2010/07/27 (Tue) @ 23:41

David, that’ll be part of a SABR 101 - Outs post.


#8          (see all posts) 2010/07/28 (Wed) @ 00:27

It was a nice refresher at any rate.


#9    spinner      (see all posts) 2010/07/28 (Wed) @ 13:49

Well, for starters, runners on second and third base will sometimes NOT advance at all on a single!


#10    Thijs      (see all posts) 2010/07/28 (Wed) @ 16:42

For someone who is not all that familiar with SABR, this is awesome. Finally I know how you guys value hits and walks. (I assume HBP’s are valued the same as walks?) Thanks from overseas!


#11    Tangotiger      (see all posts) 2010/07/28 (Wed) @ 16:51

Craig/David: hopefully the SABR 101 and SABR 111 threads on outs handles your question.  If not, you can elaborate there.


#12          (see all posts) 2010/07/28 (Wed) @ 17:06

I’m curious but how come you don’t use these values (1.35 HR, 1.10 3B, 0.81 2B, 0.45 1B, 0.36 BB, 0.36 BB) in the wOBA calculation?  More importantly, why is the recasting of the values to make them relative to outs preferable to using the actual values and calculating the runs created per PA?


#13          (see all posts) 2010/07/28 (Wed) @ 17:44

Slightly off to the side:  is it worthwhile to note the difference in base advancement between 1B fielded by an outfielder, versus 1B fielded by an infielder?


#14    Tangotiger      (see all posts) 2010/07/28 (Wed) @ 17:51

Polo: your first question is answered here:

http://www.insidethebook.com/ee/index.php/site/article/sabr_111_base_values/

***

Doctor: sure, some analysts do that, notably MGL.


#15    Gooseman      (see all posts) 2010/07/30 (Fri) @ 11:16

This all seems very nice, but was it checked against actual data?

If I take the runs each event is worth, and the average team MLB data from ESPN for 2009 singles, doubles, triples, HR and BB (BB + HBP + IB), it predicts that the average team should have scored 1162 runs in 2009.  The average team actually scored 747 runs!  That’s an overestimation of 156%.

Same for 2008 and 2007 data (since the number of each events and actual runs is nearly identical for each year).

Am I missing something important?  After all, I would have guessed that the formula should underestimate the runs scored due to not accounting for bases gained due to errors, stolen basis and sacrifices.  But the opposite appears to true, and in a huge way.

Thanks -

Gooseman


#16    Tangotiger      (see all posts) 2010/07/30 (Fri) @ 11:32

Goose: you are definitely missing something important: the outs.

You probably came in through Neyer’s blog.  You need to read the whole series:

http://www.insidethebook.com/ee/index.php/site/article/sabr_101_111_bases_and_outs/


#17    dave smyth      (see all posts) 2010/07/30 (Fri) @ 11:34

Gooseman, the 1162 is what is called the ‘plus’ runs. To get the actual total you have to subtract the lost runs on batting outs, which is approx. 0.1 * (AB-H)


#18    Gooseman      (see all posts) 2010/07/30 (Fri) @ 12:07

Cool thanks, folks.  And I did come in from Neyer’s blog.

So simply put, runners left on base is the majority of what’s left out.  In fact, if I take the ratio (from the Outs 101 article) of runners scoring to runners left on base (4.7 to 7.3), and multiply that times the number of runs predicted by the run values above, I get numbers that are within 1% of the actual number of runs scored.  I guess that must mean a few other things cancel each other out (like errors, and...)

That seems like a simple addition to the formula, and gives a more accurate picture of the number of runs each event is worth, right?

Thanks for the fast responses -

Gooseman


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