How Much Does Having Runners on Base Improve a Hitter?

The Reds struggled quite a bit in 2014, as the offense scored 100 fewer runs than it did in 2013. The most obvious reason for the struggles was Joey Votto missing significant time. While Votto has the ability to hit for power, he is best known for taking a walk. There is a hidden advantage for players with high on base percentages — they make the hitters after them better by reaching base. Let’s look at how much a batter can expect to improve because of the previous hitters’ on-base percentages.

Lineup projection is a topic which has been discussed and debated at great length. Protection in baseball is normally thought of as the concept of a stud hitter needing a good batter up behind them so they won’t get pitched around. The concept was debunked in the “The Book” when it found unprotected sluggers were a bit more productive than the protected ones (.380 wOBA vs. .376 wOBA).

Another lineup phenomenon exists but is rarely ever mentioned. This situation is having runners on base when the player is up to bat. Batters have always hit better with men on base. The reasons could be many. The pitcher could be distracted by the runner. They may not pitch as well from the stretch. The defense has to adjust, and in covering a base may open a hole elsewhere. Instead of guessing why exactly this phenomenon occurs, let’s look for the magnitude of its effect.

For an example of this situation, let’s look at the already mentioned Joey Votto and also Jay Bruce . Votto played in only 62 games in 2014 while dealing with some leg issues. Bruce missed some time with a knee issue, but was able to play in 137 games. Votto has a career .417 OBP and has been on base quite a bit when Bruce has been at the plate in the past. Over Bruce’s career, he has a posted a .774 OPS with no runners on base (ROB) and a .801 with ROB, so he has historically done better with runners on base. When Votto was in the lineup in 2014, Bruce hit for an OPS of .751 (.237/.332/.419). When Votto was out of the lineup, his OPS was down to .600 (.208/.250/.350).

How much of that difference in production should be attributed to Bruce’s injury and how much to coming to bat fewer times with someone on base? Like it or not, it is time for math to find the possible effect.

In 2014, players hit .245/.303/.379 with no one on base and .259/.327/.397 with at least one runner on base. This works out to a 42 point increase in a player’s OPS. OPS may not be the perfect stat, but it will work as a coarse production change estimate. These 2014 numbers can be a little misleading because they are calculated from the overall league average and are not a gauge of how each individual hitter performed. The good hitters could all be concentrated on a few teams and they just naturally hit more often with ROB. To get rid of this possible bias, let’s take all the hitter seasons (minimum 100 plate appearances) from 2002 to 2014 and compare how the batters hit with and without ROB.

Here is what we see.

Note: The increases aren’t completely neutral since bad pitchers are more likely to have runners on base. Hitters may just seem to be performing better with runners on base, but all hitters do better with a supbar pitcher on the mound, allowing baserunners. The difference would be difficult to extract from the data, but would make the final effect even a bit smaller than we found here.

Stat: Average increase with ROB
AVG: +.012
OBP: +.024
SLG: +.007
WOBA: +.007

The average hitter will see a 31 point increase OPS with ROB. This value is close to Bruce’s career difference of 27 points. It’s tempting to say his season was torpedoed by Votto’s injury more than his own.

But just because a player is better with runners on doesn’t mean that changes on the team level trickle down and affect the player’s projection much. Think of all the different situations that happen in the course of a game. How often did the inning end or begin without Bruce hitting behind Votto even when Votto was healthy, for example?

Next, we need to calculate the number of times a hitter comes to bat with a runner on base. We can’t just take the OBP for the team, because the hitter could be leading off an inning. Also, there are numerous possibilities for runners to get on and off base before a hitter comes up.

Using some best fit lines with high correlations, I found a simple formula to determine how often a team hits with a ROB, given that the team’s OBP:

Team ROB% = Team OBP + 12%

To help find possible production changes in 2015, here are the 2014 values and the values projected by Steamer. The projected 2015 team OBP values change all the time as players are continually traded or signed this offseason. The most recent changes in production are shown here, but as you will see, they really don’t matter too much.

Team	2014 OBP	2015 pOBP	Diff	2014 pROB%	2015 pROB%	AVG	OBP	SLG	OPS
BOS	0.316	0.340	0.024	0.436	0.460	0.00029	0.00058	0.00017	0.00074
CHC	0.300	0.319	0.019	0.420	0.439	0.00023	0.00046	0.00013	0.00059
SDP	0.292	0.311	0.019	0.412	0.431	0.00023	0.00046	0.00013	0.00059
SEA	0.300	0.317	0.017	0.420	0.437	0.00020	0.00041	0.00012	0.00053
CIN	0.296	0.312	0.016	0.416	0.432	0.00019	0.00038	0.00011	0.00050
TEX	0.314	0.329	0.015	0.434	0.449	0.00018	0.00036	0.00011	0.00047
SFG	0.311	0.323	0.012	0.431	0.443	0.00014	0.00029	0.00008	0.00037
ARI	0.302	0.311	0.009	0.422	0.431	0.00011	0.00022	0.00006	0.00028
COL	0.327	0.336	0.009	0.447	0.456	0.00011	0.00022	0.00006	0.00028
NYY	0.307	0.316	0.009	0.427	0.436	0.00011	0.00022	0.00006	0.00028
STL	0.320	0.329	0.009	0.440	0.449	0.00011	0.00022	0.00006	0.00028
ATL	0.305	0.313	0.008	0.425	0.433	0.00010	0.00019	0.00006	0.00025
MIL	0.311	0.319	0.008	0.431	0.439	0.00010	0.00019	0.00006	0.00025
WSN	0.321	0.329	0.008	0.441	0.449	0.00010	0.00019	0.00006	0.00025
CHW	0.310	0.317	0.007	0.430	0.437	0.00008	0.00017	0.00005	0.00022
HOU	0.309	0.315	0.006	0.429	0.435	0.00007	0.00014	0.00004	0.00019
NYM	0.308	0.314	0.006	0.428	0.434	0.00007	0.00014	0.00004	0.00019
TOR	0.323	0.329	0.006	0.443	0.449	0.00007	0.00014	0.00004	0.00019
CLE	0.317	0.320	0.003	0.437	0.440	0.00004	0.00007	0.00002	0.00009
PHI	0.302	0.305	0.003	0.422	0.425	0.00004	0.00007	0.00002	0.00009
LAA	0.322	0.324	0.002	0.442	0.444	0.00002	0.00005	0.00001	0.00006
MIA	0.317	0.319	0.002	0.437	0.439	0.00002	0.00005	0.00001	0.00006
OAK	0.320	0.322	0.002	0.440	0.442	0.00002	0.00005	0.00001	0.00006
TBR	0.317	0.318	0.001	0.437	0.438	0.00001	0.00002	0.00001	0.00003
BAL	0.311	0.311	0.000	0.431	0.431	0.00000	0.00000	0.00000	0.00000
KCR	0.314	0.314	0.000	0.434	0.434	0.00000	0.00000	0.00000	0.00000
DET	0.331	0.329	-0.002	0.451	0.449	-0.00002	-0.00005	-0.00001	-0.00006
MIN	0.324	0.321	-0.003	0.444	0.441	-0.00004	-0.00007	-0.00002	-0.00009
PIT	0.330	0.327	-0.003	0.450	0.447	-0.00004	-0.00007	-0.00002	-0.00009
LAD	0.333	0.325	-0.008	0.453	0.445	-0.00010	-0.00019	-0.00006	-0.00025

The Red Sox, who are predicted to see the largest bump in OBP in 2015, won’t even see a boost of one OPS point solely because of the increase in the amount of runners on base. The effect exists but it is too small to really matter.  Going one step further, if a player went from the team with the lowest OBP (2014 Padres, .292 OBP) to the team with the highest OBP (2015 Red Sox, .340 OBP), they would only like see an increase of about 1.5 points of OPS. The runners on base effect exists, but it is just not a large enough to really matter.

Going back to Jay Bruce. His ~150 point drop in OPS wasn’t because Votto was out of the lineup. It was probably from his banged up knee. Using some injury data I have compiled, a player should expect to experience a 37 point drop in OPS during a season when they are on the DL for a knee injury. The good news is that hitters with knee injuries are likely to get back to their pre-injury production levels the next season.

Hitters historically produce better when other runners are on base. A player could expect to see his stats improve if he moved to a high OBP team. The same could be expected for a player on a team which upgrades its overall lineup. The problem is that even the largest changes in team OBP don’t make much of a difference on the player level.

The biggest possible change for a player going from a low OBP team to a high OBP team would change his OPS by less than two points. Most of the time the change would be less than half a point. Just like protection after a batter, having a team with a high OBP and therefor a higher ROB% doesn’t lead to player over- or under-producing their projections.