Productive Outs Don’t Help
in Assessing a Hitter’s Value
by Cyril Morong
From the ESPN website “A Productive Out, as defined and developed by ESPN The Magazine and the Elias Sports Bureau: when a fly ball, grounder or bunt advances a runner with nobody out; when a pitcher bunts to advance a runner with one out (maximizing the effectiveness of the pitcher's atbat), or when a grounder or fly ball scores a run with one out.”
(go back to my home page to see my study on how producitve outs are not important at the team level)
I also looked to see if including data on productive outs changes the statistical evaluation of individual hitters. The ESPN site lists 259 players with their productive outs for 2004.
To check this, I calculated the linear weights batting runs (BR, from Pete Palmer) for each player with Productive Outs (PO) data listed at the ESPN website. The values for this are
1B = .47
2B = .78
3B = 1.09
HR = 1.4
BB = .33
Out = .25
BB includes BB and HBP.
Then I adjusted their BR in the following manner: I gave them .167 BR for each PO. Why that number? I. used data from Tangotiger’s website (see link at the end of this study). Here is his run expectancy (RE) table:
RE 9902 0 1 2
Empty 0.555 0.297 0.117
1st 0.953 0.573 0.251
2nd 1.189 0.725 0.344
3rd 1.482 0.983 0.387
1st_2nd 1.573 0.971 0.466
1st_3rd 1.904 1.243 0.538
2nd_3rd 2.052 1.467 0.634
Loaded 2.417 1.65 0.815
If you go from a man on first and no outs to a man on second and 1 out, your RE falls from .953 to .725. But if the runner did not advance, RE falls to .573. So you are .152 better off if he is on second. So what does a PO do to RE? The table below shows this
Runners 
PO Value 
1 
0.152 
2 
0.258 
12 
0.496 
3 
0.134 
13 
0.101 
23 
0.080 
123 
0.016 
The “Runners” column shows the situation before the PO occurred. The PO value is for no outs in the first three cases and with one out in the rest. This fits the definition of a PO. So, if you have a man on second and one out instead of a man on first and one out, you are .152 better off in RE (.725.573). If you have a runner on third and one out instead of a runner on second and one out you are .258 better off (.983.725). The situations with a man on third are trickier. If you get a PO with runners on second and third (23) and one out, you end up with a man on third and two out. From the RE table, you go from 1.467 RE to .387. So you lose 1.08 RE. But a run did score, so you only lose .08, which is the PO value. If you get a PO with a runner on third and one out you end up with the bases empty and two outs and the RE falls .866 (.983 .117 = .866). But a run did score, so the PO has a value of .134 (1 .866).
Then I assume that all hitters got their POs with a given frequency. From data that I got from Tom Ruane (it is based on game from the 1980s and Tangotiger’s data is based on 19992002this is not a perfect situation, but it is the data I have) here are the frequencies of the above situations.
Runners 
Frequency 
PO Freq. 
1 
0.053 
0.42 
2 
0.019 
0.15 
12 
0.013 
0.10 
3 
0.012 
0.09 
13 
0.011 
0.09 
23 
0.011 
0.08 
123 
0.009 
0.07 
The first frequency column shows how often the runner situation occurs as a percentage of all baseout situations. The second one shows its frequency as a percent of all PO situations. Remember that if a situation has a man on third, it is for one out, keeping with the definition of POs. The PO situations occur about 12.76% of the time. And .053 is about 42% of 12.76.
Now, how does this translate into a value for POs? Multiply the RE change times the frequency in which it occurred and then add them all up to get a weighted average.
Runners 
Frequency 
PO Freq. 
PO Value 
Weight 
1 
0.053 
0.42 
0.152 
0.064 
2 
0.019 
0.15 
0.258 
0.038 
12 
0.013 
0.10 
0.496 
0.051 
3 
0.012 
0.09 
0.134 
0.012 
13 
0.011 
0.09 
0.101 
0.009 
23 
0.011 
0.08 
0.080 
0.007 
123 
0.009 
0.07 
0.016 
0.001 




0.167 
So it all adds up to.167.
So every player had a BR figure calculated. Then the value of their productive outs was calculated (PO*.167). That PO value got added to their BR. Then I found the correlation between BR and the BR with the PO value added in (the adjusted PO). The correlation was .9986. Almost a perfect 1to1 relationship. So, by that, looking at productive outs adds very little to what we know about a hitter’s value.
When I made the value of a PO .2, just in case I underestimated it, the correlation was still .998. I also tried an out value of .30 instead of .25 (the baseout data immplies .30). The correlation was still .984. With PO value = .2 and out value = .30, the correlation was still .9846.
With an out value of .167, only 9 players increased their BR by as much as 5 runs and the highest was Randy Winn (who had the most productive outs with 39), was at 6.513. If I made the value of a PO .2, 16 players increased their BR by 5 or more runs with Winn at 7.8. Since it takes 10, maybe 11 runs to make one more win, the PO value seems insignificant.