Do Hitter's Get Their Expected RBIs?

This was originally published in By the Numbers, the statistical newsletter of the Society for American Baseball Research (SABR), February 2004.

For the most part, yes. If we assume hitter’s hit the same way with runners on base as they do all the time, they generally get about the number of RBIs we would expect based on how many base runners they are on when they bat and what bases they are on.

To calculate a hitter’s number of expected RBIs, I first computed how many runners were on first base when he batted, how many were on second base and how many were on third base. Then I computed how what his single, double, triple and homerun frequency. I then assumed he had the same frequency with runners on base as he did for all of his at bats. For example, if there were 2000 runners on first during the period (the data is explained below), and his homerun frequency is 3%, then we would expect him to get 60 RBIs for that case. Then we also assume that he hits homeruns 3% of the time when runners are on second base and third bases. The same is done for triples. Assume he hits triples with the same frequency as his overall triple rate and multiply that times how many base runners were on when he batted.

With singles and doubles, things are a little different. Of course runners on third and second will score on a double and a runner on third will score on a single. But I had to make assumptions about how often runners on first would score on a double and how often runners on second would score on a single. I assumed that 42.6% of runners scored from first on doubles and 63.4% scored from second. These were the major league averages for the years 1987-2000 that I got from John Jarvis’s website (http://knology.net/~johnfjarvis/stats.html).

Let’s look at an example. Jay Bell. Here is how many runners were on base when he batted, his hit frequencies, his expected RBIs in each case, and how many total RBIs we would have expected him to get (I had to adjust the numbers for at bats with runners on base I found at the CNN/SI site-this is explained in the section on the data below). This only includes RBIs from hits. RBIs from sacrifice flies and walks with the bases loaded are not included.

		AB with None On	AB with Runners on	AB with Runners on 1st	AB with Runners on 2nd	AB with Runners on 3rd	Situational
		4298	2921	1814	1396	708	Total
1B%	0.1773	0	N/A	0	156.93	125.54	282.47
2B%	0.054	0	N/A	41.75	75.42	38.25	155.41
3B%	0.0093	0	N/A	16.84	12.96	6.57	36.36
HR%	0.0266	114.31	77.69	48.25	37.13	18.83	296.21
		Expected RBI	Expected RBI	Expected RBI	Expected RBI	Expected RBI	770.45
							Grand Total

If Jay Bell had the same hit frequencies with runners on base as he did overall, we would expect him to get 770.45 RBIs. The N/A in the fourth column for singles, doubles and triples is there because those expected RBIs are shown in the next three columns. For homeruns, there is a total in both the “None on” and “Runners on” columns since any homeruns in those cases give one RBI for the hitter over and above any runners on base.

Bell gets 114.31 expected RBIs from his at bats with none on from homeruns since .0266*4298 = 114.31. He gets 156.93 expected RBIs with runners on 2nd from singles since 1396*.1773*.634 = 156.93. He gets 41.75 expected RBIs with runners on 1st from doubles since 1814*.054*.426 = 41.75. I assumed that all runners on 3rd score on singles and all runners on 2nd score on doubles. He gets 16.84 expected RBIs with runners on from triples since 1814*.0093 = 16.84. I assumed that all runners scored on triples.

Adding up all of the individual cases gives 770.45 expected RBIs. During the years 1987-2001, Jay Bell actually got 776 RBIs, with sacrifice flies and bases loaded walks excluded. Below is a list of the 61 players who had 6000 or more plate appearances from the years 1987-2001 and who also had data listed at the CNN/SI site. The totals are per 600 at bats, or about a full season.

Name	Actual	Predicted	Difference
Tino Martinez	103.93	93.75	10.18
Jeff Bagwell	113.06	103.81	9.25
Frank Thomas	117.9	109.89	8.01
Wally Joyner	84.48	77.04	7.44
Robin Ventura	90.57	83.67	6.9
Dante Bichette	99.95	93.1	6.85
Harold Baines	94.28	87.51	6.77
Mark Grace	76.18	69.97	6.21
David Justice	103.19	96.99	6.21
B.J. Surhoff	75.98	70.02	5.96
Juan Gonzalez	123.21	117.78	5.43
Luis Gonzalez	87.5	82.46	5.05
John Olerud	87.83	83.08	4.76
Greg Vaughn	100.19	95.57	4.62
Paul O'Neill	94.8	90.19	4.6
Tony Gwynn	71.58	67.14	4.44
Travis Fryman	86.69	82.43	4.26
Gary Sheffield	98.15	94.06	4.08
Eric Karros	89.7	85.73	3.98
Jay Buhner	106.52	102.96	3.56
Bernie Williams	93.49	89.97	3.52
Barry Bonds	111.72	108.35	3.36
Ken Griffey Jr.	112.3	108.94	3.36
Mark McLemore	51.36	48.06	3.3
Kenny Lofton	55.16	51.87	3.29
Larry Walker	107.72	104.48	3.24
Jose Canseco	111.68	108.56	3.12
Andres Galarraga	102.89	99.77	3.12
Sammy Sosa	108.32	105.25	3.07
Ray Lankford	86.15	83.2	2.95
Delino DeShields	52.73	50.03	2.69
Will Clark	93.75	91.32	2.42
Todd Zeile	80.47	78.2	2.27
Mark McGwire	127.26	125.02	2.24
Matt Williams	99.05	96.96	2.1
Cal Ripken	79.41	77.61	1.81
Fred McGriff	100.76	99.09	1.67
Tim Raines	65.42	63.76	1.67
Edgar Martinez	97.8	96.44	1.36
Ken Caminiti	85.88	85.16	0.72
Jay Bell	64.5	64.04	0.46
Gregg Jefferies	66.3	65.95	0.36
Brady Anderson	63.65	63.36	0.3
Rafael Palmeiro	96.95	96.67	0.29
Chuck Knoblauch	51.53	51.75	-0.22
Tony Fernandez	60.07	60.45	-0.39
Ruben Sierra	89.29	89.83	-0.55
Ron Gant	86.37	87.04	-0.66
Roberto Alomar	71.11	71.86	-0.75
Marquis Grissom	60.58	61.59	-1.02
Bobby Bonilla	90.35	91.37	-1.02
Barry Larkin	68.58	70.52	-1.94
Devon White	64.56	66.5	-1.94
Steve Finley	66.49	68.46	-1.97
Dave Martinez	55.81	57.81	-2
Craig Biggio	59.81	61.86	-2.05
Omar Vizquel	47.01	49.76	-2.75
Rickey Henderson	55.4	58.45	-3.05
Benito Santiago	71.44	75.83	-4.39
Ellis Burks	93.29	99.86	-6.57
Wade Boggs	56.42	63.25	-6.83

Some observations. 47 of the 61 hitters (77%) were predicted to within 5 RBIs per 600 at bats. So this is reasonably accurate (the correlation between the actual RBIs and predicted RBIs is .987). But there are only 16 hitters who had fewer RBIs than expected. I expected about half the hitters to have more RBIs than expected and half to have less. A few RBIs come from groundouts and I don’t have data on those. But there are not many such cases.

Maybe my list of 61 players tends to be populated by very good hitters (who else would last so long?). They tend to bat in the middle of the order and the runners who are on base might be faster than average since they would be the 1 and 2 hitters. Also, these hitters may have more than average power. Maybe their singles and doubles go farther (and travel faster) than average, making it easier for runners to score.

Notice that the players who are above expectations also seem to be power hitters who hit in the middle of the order. The players who are negative tend to be players who batted at the top or bottom of the order. If they were at the top of the order, it might be partly because of their speed. So they may get more singles and doubles as a result of speed and the runners who are on already may not score. Also, if they have below average power, maybe their doubles and singles don’t go as far as they do for the power hitters, making it harder for runners to score.

But the bottom line is that the vast majority of hitters are predicted fairly well, and only one was off by more than 10 RBIs.

Alternate methods

The assumed runner advancement is for both leagues. I also tried using different figures for hitters from each league. For the AL, 64.5% of runners scored from 2nd on singles and 39.5% scored from 1st on doubles. For the NL, these were 62.3% and 45.7%, respectively. For any players who did not get at least 80% of their at bats in one league, I used a weighted average. The results of that analysis is the left-hand column. Then I not only used the league runner advance figures, but I also took into account the fact that, on average, batting average is higher with runners on base (and HR% is lower). The differences are not great. Email me for details. These results are in the right-hand column. In each case, I only give the difference between actual RBIs and expectations.

			ADJ FOR LEAGUE
ADJ FOR LEAGUE	PER600		AND ROB	PER600
Name	AB		Name	AB
Tino Martinez	10.29		Tino Martinez	9.76
Jeff Bagwell	9.1		Jeff Bagwell	8.55
Frank Thomas	8.15		Frank Thomas	7.63
Wally Joyner	7.45		Wally Joyner	6.56
Robin Ventura	6.93		Robin Ventura	6.34
Dante Bichette	6.81		Dante Bichette	6.05
Harold Baines	6.74		Harold Baines	6.02
David Justice	6.21		David Justice	5.74
Mark Grace	6.16		Mark Grace	5.21
B.J. Surhoff	6		Juan Gonzalez	5.16
Juan Gonzalez	5.58		B.J. Surhoff	5.13
Luis Gonzalez	4.9		Greg Vaughn	4.35
John Olerud	4.89		Luis Gonzalez	4.21
Greg Vaughn	4.66		John Olerud	4.13
Paul O'Neill	4.63		Paul O'Neill	3.83
Tony Gwynn	4.44		Travis Fryman	3.6
Travis Fryman	4.34		Gary Sheffield	3.57
Gary Sheffield	4.03		Eric Karros	3.41
Eric Karros	3.89		Tony Gwynn	3.38
Jay Buhner	3.64		Jay Buhner	3.32
Bernie Williams	3.61		Ken Griffey Jr.	3.09
Ken Griffey Jr.	3.43		Barry Bonds	2.9
Kenny Lofton	3.27		Jose Canseco	2.82
Mark McLemore	3.25		Bernie Williams	2.82
Barry Bonds	3.22		Sammy Sosa	2.76
Jose Canseco	3.16		Kenny Lofton	2.56
Larry Walker	3.1		Larry Walker	2.47
Andres Galarraga	3.1		Andres Galarraga	2.43
Sammy Sosa	3.01		Mark McLemore	2.42
Ray Lankford	2.85		Mark McGwire	2.29
Delino DeShields	2.76		Ray Lankford	2.21
Will Clark	2.42		Delino DeShields	1.99
Todd Zeile	2.23		Will Clark	1.59
Mark McGwire	2.21		Matt Williams	1.56
Matt Williams	2.05		Todd Zeile	1.49
Cal Ripken	1.84		Fred McGriff	1.19
Fred McGriff	1.67		Cal Ripken	1.19
Tim Raines	1.64		Tim Raines	0.82
Edgar Martinez	1.49		Edgar Martinez	0.68
Ken Caminiti	0.67		Ken Caminiti	-0.06
Jay Bell	0.43		Rafael Palmeiro	-0.19
Rafael Palmeiro	0.36		Brady Anderson	-0.19
Gregg Jefferies	0.35		Jay Bell	-0.27
Brady Anderson	0.34		Gregg Jefferies	-0.47
Chuck Knoblauch	-0.23		Chuck Knoblauch	-0.97
Tony Fernandez	-0.41		Ron Gant	-1.17
Ruben Sierra	-0.49		Ruben Sierra	-1.26
Ron Gant	-0.67		Tony Fernandez	-1.42
Roberto Alomar	-0.76		Marquis Grissom	-1.67
Marquis Grissom	-0.97		Roberto Alomar	-1.68
Bobby Bonilla	-1.07		Bobby Bonilla	-1.84
Barry Larkin	-1.9		Devon White	-2.64
Devon White	-1.94		Steve Finley	-2.68
Dave Martinez	-1.99		Barry Larkin	-2.74
Steve Finley	-2		Craig Biggio	-2.79
Craig Biggio	-2.04		Dave Martinez	-2.85
Omar Vizquel	-2.84		Rickey Henderson	-3.67
Rickey Henderson	-3.07		Omar Vizquel	-3.74
Benito Santiago	-4.38		Benito Santiago	-5.13
Ellis Burks	-6.56		Ellis Burks	-7.3
Wade Boggs	-6.84		Wade Boggs	-7.85

The results are similar to the first case, although some players have noticeably bigger (or smaller) differences between actual and expected RBIs.

I also looked at this issue with walks included. That is, for a player’s hit frequency, I used at bats + walks + HBP as the denominator. Of course, it also meant that there were more runners to drive in. The lists below are those three cases. Again, the results are similar what we have already seen. I just show the difference between actual RBIs and expectations per 660 plate appearances. RBIs from bases loaded walks are included but not RBIs from sacrifice flies. The column on the left makes no adjustment for what league a hitter was in. The one in the center does. The one on the right adjusts for league and the normally higher hit frequencies with runners on base (and lower HR%s with runners on).

			ADJUSTED			ADJUSTED FOR	ROB
NO ADJ	PER660		FOR LEAGUE	PER660		LEAGUE AND	PER660
Name	PA		Name	PA		Name	PA
Tino Martinez	9.11		Tino Martinez	9.24		Tino Martinez	8.8
Dante Bichette	7.11		Dante Bichette	7.06		Dante Bichette	6.84
Jeff Bagwell	6.78		Harold Baines	6.77		Harold Baines	6.28
Harold Baines	6.77		Jeff Bagwell	6.64		Jeff Bagwell	6.22
Mark Grace	6.16		Mark Grace	6.11		Mark Grace	5.59
B.J. Surhoff	5.87		B.J. Surhoff	5.91		B.J. Surhoff	5.41
Robin Ventura	5.62		Robin Ventura	5.67		Robin Ventura	5.19
Wally Joyner	5.61		Wally Joyner	5.62		Wally Joyner	5.08
Frank Thomas	5.41		Frank Thomas	5.55		Frank Thomas	4.72
Juan Gonzalez	4.2		Juan Gonzalez	4.37		Juan Gonzalez	4.06
David Justice	3.93		Paul O'Neill	3.95		David Justice	3.69
Paul O'Neill	3.92		David Justice	3.93		Jose Canseco	3.63
Luis Gonzalez	3.64		Travis Fryman	3.68		Greg Vaughn	3.55
Travis Fryman	3.58		Jose Canseco	3.62		Eric Karros	3.44
Jose Canseco	3.57		Greg Vaughn	3.54		Paul O'Neill	3.43
Greg Vaughn	3.5		Luis Gonzalez	3.51		Travis Fryman	3.36
Eric Karros	3.44		Eric Karros	3.37		Luis Gonzalez	3.16
Kenny Lofton	3.24		Kenny Lofton	3.24		Kenny Lofton	2.94
Tony Gwynn	3.22		Tony Gwynn	3.22		Tony Gwynn	2.47
Ken Griffey Jr.	2.75		Ken Griffey Jr.	2.85		Mark McLemore	2.34
Mark McLemore	2.72		Bernie Williams	2.81		Bernie Williams	2.28
Bernie Williams	2.71		Mark McLemore	2.69		Jay Buhner	2.24
Delino DeShields	2.47		Delino DeShields	2.54		Delino DeShields	2.19
Andres Galarraga	2.17		John Olerud	2.32		Ken Griffey Jr.	2.03
John Olerud	2.17		Jay Buhner	2.22		Sammy Sosa	1.87
Gary Sheffield	2.14		Andres Galarraga	2.16		Andres Galarraga	1.87
Jay Buhner	2.13		Gary Sheffield	2.09		Gary Sheffield	1.85
Sammy Sosa	2.1		Sammy Sosa	2.05		John Olerud	1.47
Matt Williams	1.1		Matt Williams	1.05		Matt Williams	0.91
Will Clark	0.95		Will Clark	0.94		Mark McGwire	0.46
Larry Walker	0.64		Cal Ripken	0.68		Will Clark	0.35
Mark McGwire	0.63		Mark McGwire	0.61		Cal Ripken	0.29
Cal Ripken	0.63		Larry Walker	0.52		Ray Lankford	0.28
Ray Lankford	0.6		Ray Lankford	0.51		Todd Zeile	0.24
Todd Zeile	0.51		Todd Zeile	0.49		Larry Walker	0.18
Fred McGriff	0.44		Fred McGriff	0.44		Fred McGriff	0.06
Barry Bonds	0.08		Barry Bonds	-0.07		Jay Bell	-0.45
Jay Bell	-0.21		Jay Bell	-0.22		Brady Anderson	-0.97
Edgar Martinez	-0.59		Edgar Martinez	-0.44		Chuck Knoblauch	-0.99
Chuck Knoblauch	-0.66		Chuck Knoblauch	-0.65		Edgar Martinez	-1.13
Brady Anderson	-0.73		Brady Anderson	-0.67		Tim Raines	-1.17
Tim Raines	-0.77		Tim Raines	-0.79		Barry Bonds	-1.32
Tony Fernandez	-0.96		Tony Fernandez	-0.98		Tony Fernandez	-1.44
Gregg Jefferies	-1.24		Gregg Jefferies	-1.24		Ron Gant	-1.45
Ruben Sierra	-1.33		Ruben Sierra	-1.25		Gregg Jefferies	-1.68
Ron Gant	-1.45		Ron Gant	-1.46		Ruben Sierra	-1.75
Ken Caminiti	-1.48		Ken Caminiti	-1.52		Ken Caminiti	-1.96
Roberto Alomar	-1.6		Roberto Alomar	-1.61		Roberto Alomar	-1.99
Rafael Palmeiro	-1.95		Rafael Palmeiro	-1.86		Rafael Palmeiro	-2.28
Marquis Grissom	-2.09		Marquis Grissom	-2.04		Marquis Grissom	-2.33
Steve Finley	-2.26		Steve Finley	-2.28		Steve Finley	-2.51
Bobby Bonilla	-2.69		Bobby Bonilla	-2.74		Devon White	-3.02
Devon White	-2.77		Craig Biggio	-2.76		Craig Biggio	-3.11
Craig Biggio	-2.77		Devon White	-2.76		Bobby Bonilla	-3.19
Omar Vizquel	-2.89		Omar Vizquel	-2.96		Omar Vizquel	-3.29
Barry Larkin	-3.62		Barry Larkin	-3.58		Barry Larkin	-3.95
Dave Martinez	-3.72		Dave Martinez	-3.71		Dave Martinez	-4.06
Rickey Henderson	-5.14		Rickey Henderson	-5.16		Rickey Henderson	-5.32
Benito Santiago	-5.34		Benito Santiago	-5.32		Benito Santiago	-5.6
Ellis Burks	-7.1		Ellis Burks	-7.09		Ellis Burks	-7.17
Wade Boggs	-8.64		Wade Boggs	-8.63		Wade Boggs	-9.3

Again, the results are similar to the analysis based on at bats only.