ADD OBP AND SLUGGING RATINGS TO FORM FIVE GROUPING
6 = BEST HITTERS
5 = ABOVE AVERAGE HITTERS
4 = AVERAGE HITTERS
3 = BELOW AVERAGE HITTERS
2 = WORST HITTERS (EXCLUDING PITCHERS)
0 = PITCHERS
HIGHER BAs WHEN PITCHER BATS NEXT ARE SIGNIFICANT
OTHER DIFFERENCES ARE NOT SIGNIFICANT
DIFFERENCES BY NEXT BATTER STRENGTH ARE NOT STATISTICALLY
HIGHER LEVELS WHEN PITCHER BATS NEXT ARE SIGNIFICANT
EXCEPT WHEN 6's BAT (TOO FEW PLAYS)
TENDENCY FOR MORE WALKS WHEN A WEAKER BATTER FOLLOWS (MANY OF THE DIFFERENCES SHOWN ARE STATISTICALLY SIGNIFICANT)
BASED ON (SB + CS)/(1B + BB + HBP)
MEASURES FREQUENCY OF STOLEN BASE ATTEMPTS WHEN
PLAYER REACHES FIRST BASE
COMPUTABLE FROM STANDARD DATA
THREE WAY CLASSIFICATION:
3 = FASTEST: 14.1% AND ABOVE
2 = MIDDLE: BETWEEN 4.8% AND 14.1%
1 = SLOWEST: LESS THAN 4.8% AND ALL PITCHERS
GRAPH SHOWS PERCENT FIRST TO SECOND (WHEN NO RUNNER
ON SECOND), SO LOWER IS BETTER
DIFFERENCES ARE SIGNIFICANT
GRAPH SHOWS PERCENT SECOND TO THIRD, SO LOWER IS
DIFFERENCES ARE SIGNIFICANT
GRAPH SHOWS PERCENT FIRST TO THIRD, SO LOWER IS
DIFFERENCES ARE SIGNIFICANT
MOST DIFFERENCES ARE SIGNIFICANT: BOTH FASTER BATTERS
AND FASTER RUNNERS ARE INVOLVED IN FEWER DOUBLE PLAYS
DIFFERENCES ARE SIGNIFICANT: FASTER BATTERS REACH
BASE MORE OFTEN ON ERRORS
BATTING HAND IS MORE IMPORTANT: SLOWEST RIGHT REACH
MORE ON ERRORS THAN FASTEST LEFT
STRENGTH OF FOLLOWING HITTER HAS ONLY SLIGHT EFFECT
ON BATTING PERFORMANCE
BATTING AND SLUGGING AVERAGES NOT AFFECTED
SLIGHTLY MORE WALKS WHEN WEAKER HITTERS NEXT
HIGHER BATTING AVERAGES AND
MORE NON- INTENTIONAL WALKS WHEN PITCHER FOLLOWS
FASTER BATTERS AND RUNNERS HAVE STATISTICALLY SIGNIFICANT
MORE LIKELY TO ADVANCE FURTHER ON HITS
AVOID SOME DOUBLE PLAYS
REACH BASE MORE OFTEN ON ERRORS
KEY QUESTION: WHAT ARE THE EFFECTS ON RUN SCORING
AND CONSTRUCTION OF BATTING ORDERS?
Introduction. This section provides explanations and additional information to accompany the overhead slides. In a sense, it is an article organized those slides.
For several years, I have been developing a so-called "Markov Chain" model of major league baseball. [I have given several talks and written several articles on the subject, so no further explanation is provided here.] One product of the model is a method for determining how many runs a lineup will score on the average over a large number of games and an associated model that finds the highest scoring batting order given the nine hitters.
Any mathematical model of a complex process incorporates simplifying assumptions. The most important one in my model is the assumption that players' batting performance is not affected by where in the order they hit or the lineup positions of the other players. Baseball lore contains statements like "if you put a weak hitter after a strong one, the strong hitter won't do well because he won't get anything to hit." I decided to do a study to see if that is indeed the case. Except for individual player egos and psychology (e.g. Barry Bonds did not want to lead off because he figured that a high RBI total would increase his pay, and it is hard to argue with him at this point), the possible effects caused by the strength of the next batter seemed to me to be the most likely reason my assumption on batting performance might not be correct.
Another simplifying assumption in my model is that runner advancement on hits and outs, double plays, and batters reaching on errors all take place according to major league averages. Although, I doubt that this assumption has much of an effect when comparing two batting orders, there are obviously differences among players according to their speeds and base running abilities. In order to improve the model, I decided to collect the necessary data to account for these differences.
This talk reports on the primary results of these two investigations. The source of the data is the Project Scoresheet database, which currently contains play-by-play data for every major league game in the 1984-92 seasons. My objective was to obtain statistically meaningful results, which requires large numbers of plays, which in turn means broad groupings of players.
The page numbers referenced below are those of the
slide copies that appear earlier.
Page 1: Classification of Batters. Many studies have shown that run creation can be modeled as a function of two types of baseball events: 1) getting on base, and 2) advancing on the bases. The first is measured by on base percentage (OBP), and the second corresponds to slugging average (SA). Consequently, I decided to use these two measures when classifying batters by ability. Each player is classified by his one season performance, so the same player may have different ratings in different years. In order to get broad groupings, I divided all regular and semi-regular (at least 200 plate appearances) position players into three approximately equal groups for each of OBP and SA. Players with fewer than 200 plate appearances probably are, on the average, weaker hitters, so the overall distribution of players may have more 1s. However, better hitters tend to get more playing time, so the number of plate appearances will be distributed more uniformly.
Obviously, there will be hitters near the dividing points with different ratings and similar abilities. Keep in mind the ratings are for the purposes of forming broad groupings, not for evaluating individual players. The averages for the rating groups show that considered as groups, there are distinct differences in hitting ability among the groups.
The 3,2,1 ratings serve to provide labels. No claim is made that the 3s are 50% better than the 2s. Pitchers are put into their own separate group (rating = 0).
There are nine groups if we use all possible combinations
of the OBP and SA ratings. This seems to be too many, so I decided
to add the OBP and SA ratings to obtain five groups (2,3,4,5,6)
plus the pitchers. I do not claim that a 3 in OBP is somehow
equal to a 3 in SA in batting ability. The addition is done to
obtain an appropriate number of groups. It should be noted that
high OBP and high SA are not independent. There are exceptions,
but players who are above average in one category are often above
average in the other. I think the qualitative descriptions in
the overhead slide are justified.
Definition of Next Batter.
In most cases this is obvious, but two special cases are worth
discussing. If a player is the last batter of the game for his
team, the next scheduled batter is used as the next batter for
the purposes of this study. If a batter is the last batter in
an inning, the first batter of the next inning is considered the
next batter, whether or not he was in the lineup at the end of
the previous inning (i.e. he may be a pinch hitter or have entered
the game on defense). There are relatively few such cases, so
this decision is probably not crucial. In effect, I am assuming
that the opposition and batter acted as if they knew there would
be a substitution. While this is not likely to be true in all
cases, making the opposite assumption that they acted as if the
scheduled next batter would actually hit suffers from the same
problem. No definition can be perfect since in some cases, who
bats next depends on what the previous batter does.
Total Plate Appearances.
The tables show the distribution of plate appearances by batter
strength and next batter strength for each league and in total.
AMERICAN LEAGUE Next Batter 0 2 3 4 5 6 Total ------------------------------------------------------ Batter 0 6 4 1 6 5 22 Strength 2 3 51908 32092 32012 27108 23067 166190 3 8 37344 26295 28661 20543 27748 140599 4 5 34946 28742 32803 31071 32806 160373 5 3 25159 26309 33838 30433 33970 149712 6 3 18243 27039 32610 39254 46225 163374 Total 22 167606 140481 159925 148415 163821 780270 NATIONAL LEAGUE Next Batter 0 2 3 4 5 6 Total ------------------------------------------------------ Batter 0 8402 8837 11042 8479 6979 43739 Strength 2 26594 42494 22186 24970 14943 16553 147740 3 8638 27670 17438 22954 15831 20098 112629 4 6547 31831 24049 28659 21449 23428 135963 5 1983 20067 19851 24694 19702 21204 107501 6 721 18417 19790 22884 26405 28324 116541 Total 44483 148881 112151 135203 106809 116586 664113 TOTAL MAJOR LEAGUES: 1984-92 Next Batter 0 2 3 4 5 6 Total ------------------------------------------------------ Batter 0 8408 8841 11043 8485 6984 43761 Strength 2 26597 94402 54278 56982 42051 39620 313930 3 8646 65014 43733 51615 36374 47846 253228 4 6552 66777 52791 61462 52520 56234 296336 5 1986 45226 46160 58532 50135 55174 257213 6 724 36660 46829 55494 65659 74549 279915 Total 44505 316487 252632 295128 255224 280407 1444383
The few cases where strong hitters (5,6) are followed by a pitcher
are most likely due to part-time players or late season call-ups
who had very good performance statistics for the year. We see
that in general weak hitters tend to be followed by weak hitters
and strong hitters by strong hitters. Of course, there only so
many strong hitters to bat, so there are plenty of cases where
weak and strong hitters are adjacent in the lineup. Note that
over half the time pitchers are preceded by 2s.
Page 2: Batting Average. The best way to compare quickly the differences and similarities of performance levels is by a graph. The six batting strength groupings appear along the x-axis. Each batter strength group has six bars, one for the batting average of batters of the indicated strength when followed by each of the six strengths. (There are only five bars for the pitchers because pitchers never follow pitchers.)
In each case, the bar for the batting average when the pitcher bats next is higher than the other five bars for the same batting strength. These differences are statistically significant. One possible explanation for this difference is that pitchers don't want to walk the number eight hitter, who is usually a weak hitter, and give the pitcher a chance to bunt. Consequently, they throw more in the middle of the strike zone. However, as we shall see, non-intentional walks are also higher when the pitcher bats next, and slugging average is not affected. Another possible explanation is that the number eight hitters are more selective and more willing to walk.
The heights of the bars in each group when non-pitchers bat next
are about the same and there are no patterns to the differences.
Statistically, the differences are not significant. Hence, we
conclude that batting average is not affected by the strength
of the next batter, except when the pitcher bats next.
Page 3: Slugging Average. The heights of the bars in each
batter strength group are not much different, nor are there patterns
such as the bars getting taller as the next hitter gets stronger.
In general, the differences in slugging averages graphed are
not statistically significant.
Page 4: Non-intentional Walks per Plate Appearance. There are two significant effects for non-intentional walks. The first is that they are significantly more likely when the pitcher bats next. This is likely due to a combination of "unintentionally intentionally" walking the number eight hitter and greater selectivity on the part of the number eight hitters.
The second effect is a noticeable pattern of fewer walks of batters
rated 4 and higher in front of stronger hitters. This effect
becomes more pronounced as batter strength increases. Not all
of the differences are statistically significant and the pattern
is not perfect, but the effect is clear from the graph.
Page 5: Classification of Runners. Now we turn to the
effects of faster and better runners. As was the case for batting
ability, we need a measure of running ability in order to make
the classification. There are several sources of speed ratings,
but I wanted to use "standard" data, the type that can
be found in the Baseball Guide, for example. That pretty much
means using stolen bases. One commonly computed and discussed
statistic is stolen base percentage: SB/(SB+CS).
Its drawback is that some players have high percentages, but
very few steal tries (e.g. 4 of 5, 2 of 2). Also, many fast runners
attempt a lot of stolen bases, but are not particularly good at
it. My solution is to compute an approximation to how often a
player tries to steal when he has a chance (i.e. reaches first):
This statistic is far from perfect. Not all steal tries are
of second, and the runner may be blocked by a runner on second.
Also, some fast and good runners just don't try to steal very
much. My contention is that the top group consists, on the whole,
of much better runners than the middle group, which is turn contains
much better runners than the bottom group. Examination of the
players in each group (not shown here) bears out this assertion.
Page 6: Advancement on Singles (1). The graphs shown on this and the following pages are somewhat different from those illustrating batting effects. It is more convenient to show the percent of runners who stop at second, so a lower percentage indicates better base running. Hit location affects the chances of advancing beyond second, but the Project Scoresheet database does not have hit location for all plays. Instead, I used batter handedness as a surrogate for hit location. The number of outs can also affect whether the runner tries for an extra base, so that is also part of the grouping. The x-axis shows six groupings by batter hand and number of outs. Each has three bars, corresponding to runner on first speed. Since a slow runner on second can prevent a fast runner on first from going to third, only the cases where second base is open are tabulated.
The differences in the graph are both significant
and expected. There is better advancement on singles by left
handed batters, faster runners advance to third more often, and
the number of outs affects the advancement: runners are slightly
more likely to go to third as the number of outs increases. What
may be surprising is that in all cases but one, more than half
of the time the runner stops at second. (Infield singles are
included in the tabulation.)
Page 7: Advancement on Singles (2).
This graph is similar to the previous one, and the conclusions
are much the same. It is interesting to note that more than 80%
of time, runners score from second on two-out singles. Also,
it is slightly harder to score when a right handed batter singles,
probably due to having to wait to see if some hits will go through
into left field.
Page 8: Advancement on Doubles. This graph and the effects are similar to those for advancement on singles. However, there is virtually no difference between left and right handed batters, which is not surprising.
The advancement on hits effects shown probably are
no surprise to most of you. I doubt that the next two topics
have been quantified as they are here.
Page 9: Avoiding Double Plays. The graph shows the percent of time a ground into double play (GIDP) occurs when there is a runner on first only, which is the purest situation to analyze, with none or one out. The x-axis groups are determined by batter handedness and batter speed. Hitting into double plays probably depends most on whether the batter tends to hit the ball in the air or on the ground or not all (i.e. strikes out), but this information is not part of the standard data in the Project Scoresheet database. I think it is fair to assume the distribution of flyball vs. groundball hitters is more or less the same by batter hand and batter speed.
Almost all of the differences in the graph are statistically
significant. Not surprisingly, we see that right handed batters
ground into DPs more frequently than lefties. For this reason,
runner speed makes a greater difference when the hitter bats right.
Except for the fastest left handed batters, the reductions in
GIDPs due to faster batters are not as great those due to faster
runners. This suggests that more double plays are foiled by being
broken up at second than by the batter just beating the throw.
Page 10: Batter Safe on Error. To avoid complications due to base runners, only situations with no one on are considered. The graph shows the percentages of these in which the batter reaches due to an error (no hit is scored on the play) by batter hand and batter speed. We see that faster batters do reach more frequently on errors. While this may not be a surprise, before doing this study, I wasn't so sure. Infielders tend to play a little closer in for faster batters, so they may not get to as many balls and have slightly fewer chances to make errors. Also, official scorers might base the hit/error decision on a close call on the speed of the batter. Perhaps the advantage results from infielders rushing their throws when the batter is speedy.
Note, however, that batter handedness is more important
than batter speed. The slowest right handed batters reached on
errors more frequently than the fastest lefties. This shows that
the longer throws from the left side of the infield provide are
more significant than the advantage the left handed batter has
getting to first.
Page 11: Conclusions. I am in the process of revising my basic run scoring Markov model, and the data shown above will be incorporated.
My conclusion is that the basic assumption that batting performance is not affected by the strength of the following hitter is still valid. Leaving aside the effects when the pitcher bats next (which affects one batter per team in one league and usually not for the whole game), we see that batting and slugging averages are not affected, but strong hitters draw slightly more walks when followed by weak hitters. Additional walks lead to additional runs even when weaker hitters follow. (Note that Barry Bonds is one of the league leaders in runs scored while batting fifth. Getting on base, which means not making outs, is critical to scoring.) My revised model will account for these additional walks.
There is no doubt that the advantages of faster runners are real, which is hardly a surprise. What is new, is that some of these have now been quantified and can be incorporated into mathematical models.
Statistical significance is useful for telling us
that something not due to random fluctuations is taking place,
but it is far from the whole story. Many of the statistically
significant differences are small, especially the chances of reaching
on an error. The important issue is how much these differences
effect run scoring. My revised models will be able to answer
that question. I hope to present some of the answers next year
in Arlington, Texas. See you there!
I am always looking for feedback, comments, methods
for improving my analysis and models, and research ideas. Please
feel free to contact me.
1018 N. Cleveland St.
Arlington, VA 22201