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When we first started cranking out the Baseball Prospectus a few years ago,
our goal was to produce a top-notch baseball guide. We want to produce
something which gives fans a solid grasp of the abilities and accomplishments
of the players at both the major league and minor league levels. While we
sought from the start to craft a book that people would enjoy reading, we also
seek to crank out the best available statistical tools for player analysis. For
us to continue to put out a top-notch book, we have to make sure that we’re
using top-notch numbers.

That said, few of the statistical concepts you’ll find in the book are wholly
original. Do you want to use hitting statistics to estimate runs scored? Well,
Bill James and Pete Palmer did that a long time ago, and there are books out
there now that use their methods, particularly Palmer’s Total Baseball. Do you
want to convert minor league statistics to major league equivalents? Again,
these can be found in the STATS Minor League Handbook. Evaluations of fielding
statistics? Total Baseball, again.

What then do the Davenport Translations (or DTs, conceptually similar to James’
MLEs) and Equivalent Average (which measures run production from batting stats)
offer that these older tools don’t? First off, these tools are not simply
copies of earlier works, but independent attempts to measure the same problems.
There is never anything wrong with having more than one option to get your
result. The argument has been made that the older methods, by virtue of their
being older, should have priority, an idea whose reductio ad absurdum would be
to consider runs scored per game played the ultimate measure of individual
accomplishment, like it was in the 1860s.

I could allow myself to make a similar but opposite argument: the earlier
statistics should be cast aside because they don’t do their job as well as the
ones you’ll find in the Baseball Prospectus. I don’t seriously believe that
this should be done, of course. But the truth is, the BP analysis stats are
better than their counterparts. We haven’t played this up more in our books so
far, for which the fault is probably mine. But validation tests make for pretty
boring reading, and take up space that I preferred to use on outlining a
totally new fielding approach, as well as on more players, more players, and
some more players. So, here on the webpage, I’ll tackle some of those issues.

For this article, I am going to look at how the statistics for a player compare
from one year to the next: the goal being to show, as James said ten years ago,
that minor league statistics, properly interpreted, are just as useful as major
league statistics for projecting future performance. This
is still true, and DTs for minor league performance pass the test of being just
as useful as major league statistics, and beyond that, DTs do this better than
the MLEs put out by STATS.

Chalking The Baselines

The first order of business is to determine just how variable major league
performances themselves are.

Table 1 shows the changes for major league players. The players used are those
who had at least 150 AB in any of the 1990 through 1996 seasons, and had 150 AB
again the next season (i.e., 1991-1997). The second column is the number of
players in that specific age range. The stats used are batting average (BA);
walk rate (WR), calculated as walks per AB+BB; and isolated power (ISO), which
is slugging average minus batting average. “Net” is the error score for the
player, and is equal to two times the BA error, plus the walk rate error, plus
the isolated power error, all in absolute values. This is proportionally
correct for each portion covered; it is essentially on-base percentage plus
slugging percentage, with the batting average pulled out as a separate entry.
All statistics are the translated, not real, ones. Since there are over 1700
players included, what I’ve done is summarize the statistics by age; this
refers to the player’s age in the first year of the pair.

```        Average change  Standard deviation
Age     N  BA  WR ISO Net   BA WR ISO Net
20-     6 -13   8 - 7  93   26 17 37 49
21     16 -12   7   5 125   43 19 43 56
22     39  12   1   9 122   41 30 46 68
23     54 - 6   1   3 106   32 25 44 52
24    130   1   3   9 113   35 25 44 55
25    165   3   6   3 111   35 26 46 57
26    185 - 6 - 3   1 111   32 24 53 59
27    196 - 1   3   1 114   35 24 47 58
28    173 - 1   2 - 1 111   33 25 50 62
29    168 - 4 - 4 - 4 117   36 26 49 63
30    159   2   0   2 110   36 26 45 58
31    130 - 7 - 1 -11 113   35 27 46 62
32     95 - 5   2 - 7 118   35 24 50 53
33     69 -10   4 - 6 118   36 26 42 56
34     50 - 4 -13 -20 108   29 27 45 47
35     33   1   0  13 115   34 29 46 65
36     26   3   1 -21 106   26 32 46 45
37     19 -27 - 9 -21 103   24 20 29 53
38+    22 - 7   2 -13 133   44 26 44 63

All  1745 - 2   0 - 1 113   35 26 48 58 All players 1990-97
94-96 761 - 2   0 - 4 113   35 26 47 58 All players 1994-97
19-26 605 - 1   2   4 112   35 25 48 58 Players aged 19-26 in 1990-96
```

Take-home lessons:

1. Demographically, there is a large, broad peak of players aged 25-30, with
rapid declines on either side. Perhaps not coincidentally, the 31-32 is the
first transition featuring large dropoffs in performance, although some might
argue that for the 29-30 transition.

2. The predictability of the various stats is relatively independent of age,
although standard deviations for slugging percentage are slightly higher during
the 26-29 peak.

3. Neither the 1994-1996 subset nor the age 19-26 are more variable than the
overall set, although the slugging average means differ somewhat.

4. The “normal” values for variability among major leaguers, for comparison
with minor league DTs, is about 35 points of BA, 25 on walk rate, 45-50 on
power.

Making Contact

The real meat here is the chart of players who had at least 200 AB in AA/AAA in
one of the years during the period 1994-96, and who had at least 150 AB in the
majors the following year; the 200 figure was chosen to conform with STATS’
cutoffs for showing MLEs. In each case, the DT or MLE stats reflect play in AA
and AAA combined, while ignoring play in the majors or lower minor leagues for
the season shown. 1994 was chosen to minimize the effects of the strike (which
could really foul up the 1993 minor to 1994 major dataset), as well as to
minimize the impact of the Offensive Surge which, again, was mostly in the 1992
to 1993 and 1993 to 1994 seasons. This should not affect the DTs much, but the
MLEs could be floored by guessing the wrong overall level of league offense.

First off I need to remind everyone of a caveat that is true for both the DTs
and MLEs. They are not predictions; they are assessments of past performance.
However, since both aim to match a major league season, it is reasonable to
test their accuracy by seeing how different a DT/MLE is from the following
major league season, compared to how well one major league season is from
another.

#Rt is the number of times the Net score for a player was better using one set
or the other. For instance, Manny Alexander’s 1994-95 seasons was off in the
DTs by 7 BA points, 39 WR points, and 24 ISO points, for a net of
(2*7)+39+24=77 points.

His MLE errors were 16, 60, and 8, for a net error of 100. The DTs get credit
for “one right.”

```                  Averages       Standard deviations
Year     #Rt      BA WR ISO Net   BA WR ISO Net
1994-95  27 DT    -3  1   1 120   40 28  41  60
52 pl.   25 MLE   -5 19  -4 123   37 36  39  60

1995-96  30 DT    -4  1  -7 110   37 27  45  64
47 pl.   16 MLE   -1 13  -5 121   37 33  49  66

1996-97  31 DT    -7 -2  10 102   27 27  43  55
49 pl.   18 MLE   -9  3  -3 112   28 34  46  60

1994-96  88 DT    -5  0   1 111   35 27  43  60
148 pl.  59 MLE   -5 12  -4 119   34 35  45  62

1994-97 148 MjAge -2  2   4 112   35 25  46  57
```

The last line, MjAge, is an age-adjusted version of the major league norms,
using the averages and standard deviations for each age slot of the major
league table and the number of players in the minor-major survey in those same
slots. Relative to those, the DT minor/major adjustment is slightly too
generous with batting average, but shortchanges players a wee bit in walks and
power. It is just as good, even a little better, on the Net score, although it
is a little less reliable (having a higher standard deviation). Variability is
a little higher in walk rate, but actually a little better in slugging, with no
difference in BA.

There is nothing here to make anyone believe that this year’s minor league DT
is any worse of a predictor for next year’s major league DT than this year’s
major league DT.

The superiority of the DT method to the MLEs is pretty clear, especially over
the last two seasons. The DTs were more “right” than the MLEs by an 88-59
margin over the last three years (Jose Herrerra, in 1995-96, had a 45 point net
from each method for a tie); a split that large or greater over 147 entries
will occur by chance less than 1% of the time if the two have a genuinely equal
chance of being right. The DTs clearly do better in the net score totals,
having both a smaller average error and a smaller standard deviation. The
differences in BA between the two are insignificant; in isolated power the
differences are significant at the 95% (but not 99%) level; the differences in
walk rate are clearly significant.

Its those walk rates where the differences in the methods really arise. In the
past, David Grabiner has written that MLEs do not handle walks (and strikeouts,
which the DTs don’t attempt to cover) particularly well. The numbers above,
which show the standard deviation in walk rates to be much higher for MLEs than
for previous major league seasons, reinforce that conclusion. Yet the
difference in overall results is not entirely a function of walks. If you
ignore the walk rate term in the Net score, the DTs would still win the “right”
category by 78-69 (with one tie agin, this time Mike Lieberthal), thanks to a
slight edge in handling isolated power. That wouldn’t be a statistically
significant result; however, it’s still good enough to support a claim that DTs
are doing at least as well as the MLEs.

The confounding part of this study is that DTs do have a built-in advantage.
DTs from any season always use the same baseline level of offense and the same
park factors. A 1995 MLE, by contrast, is set to the offensive level of 1995,
either AL or NL, depending on what league the player’s parent club was in, and
the park factor of the parent club. Lyle Mouton’s 1994 MLE was for Yankee
Stadium, for the 1994 American League, but his 1995 comparison season was
Comiskey for the 1995 AL season.

Proofing the Boxscore

Here’s a listing of all 148 minor-major players in the study.

“Age” and “Yr” represent the first year of the two-year samples. “Deltas” are
the difference between a statistic in Year2 minus Year1.

DTs are taken from formulations used in the 1998 Baseball Prospectus. For
example, Manny Alexander’s 1994 DT called for a .228 batting average, .254
on-base average, and .339 slugging; his 1995 DT was .234/.291/.321. That breaks
down to a .228 BA, .034 WR, and .111 ISO for 1994, .234/.073/.087 for 1995; so
the differences are +7, +39, and -24. (Note that, if OBA is based only on AB,
H, and BB, then walk rate is (OBA-BA)/(1-OBA)). Net is 2*7+39+24, or 77.

MLE deltas repesents the difference between actual major league performance in
year2 and the MLEs published in the Minor League Handbook for that year.

```                                   DT  MLE  DT MLE  DT Deltas       MLE Deltas
Last          First    Age   Yr      Net    Right   BA  WR  ISO    BA  WR  ISO
ALEXANDER     MANNY    23   1994   77  100  1  0     7  39  -24    16  60   -8
ALFONZO       EDGARDO  20   1994  112  120  1  0    15 -56  -26    16 -58  -30
ANDERSON      GARRETT  22   1994  137  131  0  1    37  -7   56    40   5   46
ANDREWS       SHANE    22   1994  144  126  0  1   -40 -55    9   -15 -64   32
ASHLEY        BILLY    23   1994  232  211  0  1   -53  -4 -122   -45  35  -86
BATES         JASON    23   1994   68  101  1  0    10  10   38     8  37   48
BECKER        RICH     22   1994  110  134  1  0   -23 -39  -25   -43 -10  -38
BROGNA        RICO     24   1994  145  160  1  0    54  28    9    63   2    5
BUFORD        DAMON    24   1994  163  221  1  0   -35  64  -29   -39 107  -36
CIRILLO       JEFF     24   1994  119   78  0  1   -32  24  -31    -5  48  -20
CORDOVA       MARTY    24   1994   99  160  1  0   -20   5   54   -41  45   33
CROMER        TRIPP    26   1994   97  103  1  0   -21 -23  -32   -25 -19  -34
DURHAM        RAY      22   1994   93   62  0  1   -16 -23  -38   -14   2  -32
EVERETT       CARL     24   1994  155  211  1  0    -7  73   68   -28  99   56
FABREGAS      JORGE    24   1994  168  180  1  0    64  16   24    55  33   37
GIAMBI        JASON    23   1994  103  134  1  0    25  24   29    23  60   28
GIL           BENJI    21   1994   85   54  0  1   -32 -10   11   -10   5   29
GONZALEZ      ALEX     21   1994   93   76  0  1   -27   4   35   -26   9   15
GOODWIN       CURTIS   21   1994   37   35  0  1     4 -11   18    -5   4   21
GOODWIN       TOM      25   1994   55   71  1  0    16  19    4     9  50   -3
GREEN         SHAWN    21   1994  185  173  0  1   -34 -31   86   -41 -26   65
GRUDZIELANEK  MARK     24   1994  100  156  1  0   -29  -7  -35   -42  21  -51
HIGGINSON     BOB      23   1994  135  198  1  0   -39  48   -9   -44  59  -51
HUNTER        BRIANL   23   1994   39   31  0  1     0 -16  -23   -13  -3   -2
HUSON         JEFF     29   1994   85   77  0  1   -37  -7   -4   -34   8    1
JOHNSON       CHARLES  22   1994   59  122  1  0     6   9  -38    18  45  -41
JOHNSON       MARK     26   1994  163  149  0  1   -46  21   50   -43  47   16
JONES         CHRIS    28   1994  109   39  0  1    32   2   43   -16   3   -4
LEWIS         MARK     24   1994  283  242  0  1   108  30   37    96  21   29
LOCKHART      KEITH    29   1994  264  178  0  1    77 -26   84    54   1   69
MABRY         JOHN     23   1994  168  178  1  0    61   0  -46    67   6  -38
MANTO         JEFF     29   1994  127   67  0  1   -27 -36   37   -15 -35   -2
MASTELLER     DAN      26   1994   49  131  1  0    -9  28    3   -28  50  -25
MERULLO       MATT     28   1994   48   73  1  0     8  13  -19     1  28  -43
MILLER        ORLANDO  25   1994  158  166  1  0    65  28    0    51  52   12
MOUTON        LYLE     25   1994  137   73  0  1    32  26   47    13  43   -4
NEVIN         PHIL     23   1994  124  134  1  0   -46   7  -25   -36  57   -5
NIEVES        MELVIN   22   1994  149  136  0  1   -41 -35   32   -56   2   22
O'LEARY       TROY     24   1994   78   69  0  1   -10 -54   -4     7 -53   -2
OFFERMAN      JOSE     25   1994  125  160  1  0    39  19   28    19  64   58
OLIVA         JOSE     23   1994  300  253  0  1  -111  11  -67   -86  25  -56
PAQUETTE      CRAIG    25   1994   43   53  1  0   -11 -11   10   -20  -2  -11
PEGUES        STEVE    26   1994  109   72  0  1   -33   0  -43   -20   3  -29
PERRY         HERB     24   1994   81   22  0  1    20 -18   23     8   1   -5
PHILLIPS      J.R.     24   1994  211  210  0  1   -63 -15  -70   -59  -8  -84
STAHOVIAK     SCOTT    24   1994   64   90  1  0     6 -21  -31   -16  -1  -57
TAVAREZ       JESUS    23   1994  107  115  1  0    42   9   14    37  22   19
TIMMONS       OZZIE    23   1994   20   57  1  0     8   0   -4    22   8    5
TUCKER        MIKE     23   1994   84   42  0  1     3 -34  -44    15   0  -12
VERAS         QUILVIO  23   1994  134  201  1  0    15  53   51    30  85   56
WILLIAMS      EDDIE    29   1994  103  201  1  0   -22 -11  -48   -44  14  -99
YOUNG         KEVIN    25   1994   90   56  0  1   -36 -14   -4   -21  -6    8
TOTAL                                      27 25

DT  MLE  DT MLE  DT Deltas       MLE Deltas
Last          First    Age   Yr      Net    Right   BA  WR  ISO    BA  WR  ISO
ALLENSWORTH   JERMAINE 23   1995   42   89  1  0     7  17   11     9  35   36
ARIAS         GEORGE   23   1995   97  129  1  0     7 -33  -50   -10 -19  -90
AURILIA       RICH     23   1995  150  117  0  1   -38 -25  -49   -29 -23  -36
BARTEE        KIMERA   22   1995   43   66  1  0     8   1  -26    22  19   -3
BATISTA       TONY     21   1995  111  159  1  0    42  12  -15    59  25  -16
BENARD        MARVIN   24   1995   31   44  1  0    -8   4  -11   -15  14    0
BRAGG         DARREN   25   1995  142  156  1  0   -36  50   20   -29  70   28
BURNITZ       JEROMY   26   1995  107   88  0  1   -24  39   20   -15  57    1
CEDENO        ROGER    20   1995   29   53  1  0    -5 -15   -4    -6  13   28
CIANFROCCO    ARCHI    28   1995   64   42  0  1    27  -2    8    16   6    4
CLARK         TONY     23   1995  156  164  1  0     4 -40  108    12 -56   84
COOMER        RON      28   1995   62   37  0  1     6   9   41    -2  26    7
DAMON         JOHNNY   21   1995  192  171  0  1   -35 -67  -55   -39 -48  -45
DELGADO       CARLOS   23   1995  157   95  0  1   -56  -8  -37   -25   4  -41
DYE           JERMAINE 21   1995   50   87  1  0     8 -22   12    27 -16   17
EVERETT       CARL     25   1995  155  196  1  0   -28  34  -65   -41  43  -71
FOX           ANDY     24   1995  249  238  0  1   -81  -9  -78   -81  -3  -73
GREENE        WILLIE   23   1995   73  114  1  0    12   9   40    20  25   49
GUTIERREZ     RICKY    25   1995  124   68  0  1    55   2  -12    24  17   -3
HERRERA       JOSE     22   1995   45   45  0  0    -9 -10   17     8   1   28
HUSKEY        BUTCH    23   1995   97  117  1  0     3 -20   71    12 -21  -72
JETER         DEREK    21   1995   92   96  1  0    16 -33   27    19 -27   31
KENDALL       JASON    21   1995   32   13  0  1    -1 -22   -8     0 -12   -1
LAWTON        MATT     23   1995   48   69  1  0   -11   0  -26    -4  -8  -53
LIEBERTHAL    MIKE     23   1995  120  121  1  0    -8 -66   38    -1 -67   52
LORETTA       MARK     23   1995   78   86  1  0    -2   9  -65     2  26  -56
MCCARTY       DAVE     25   1995  271  254  0  1   -91   6  -83   -86  12  -70
MCCRACKEN     QUINTON  25   1995  150  192  1  0   -54  31   11   -72  40   -8
MOUTON        LYLE     26   1995   77   49  0  1    23  11   20     9  23    8
MUELLER       BILL     24   1995  125  135  1  0    59   6    1    57   9   12
NEWFIELD      MARC     22   1995   30  108  1  0     0  -9   21    22  10   54
OBANDO        SHERMAN  25   1995  104  109  1  0   -22  33   27   -20  50   19
OCHOA         ALEX     23   1995  113  127  1  0    42 -16   13    40 -10   37
ORDONEZ       REY      23   1995  160  139  0  1    61 -10  -28    57  -9  -16
OTERO         RICKY    23   1995   48   71  1  0    19  -3    7    23   2   23
OWENS         JAYHAWK  26   1995  202  335  1  0   -37  52  -76   -55  86 -139
OWENS         ERIC     24   1995  299  289  0  1   -89   0 -121   -85   4 -115
PEREZ         ROBERT   26   1995   60   88  1  0     3   5  -49     6  17  -59
PEREZ         EDDIE    27   1995   88  103  1  0    -6  16   60    12  24   55
RANDA         JOE      25   1995  143  130  0  1    58 -17   10    57   2   14
RENTERIA      EDGAR    19   1995  120  135  1  0    45  28    2    44  34   13
RODRIGUEZ     ALEX     19   1995   23   90  1  0    -3  11    6    20  19   31
SANTANGELO    F.P.     27   1995  125  159  1  0    36  13   40    45  24   45
SWEENEY       MARK     25   1995  205  181  0  1   -72  15  -46   -54  43  -30
TUCKER        MIKE     24   1995  121  163  1  0   -13  21   74   -19  49   76
VITIELLO      JOE      25   1995  109  121  1  0   -11  71  -16    -6 108    1
YOUNG         ERNIE    25   1995   53   32  0  1    -7 -16   23     5   1   21
TOTAL                                      30 16

DT  MLE  DT MLE  DT Deltas       MLE Deltas
Last          First    Age   Yr      Net    Right   BA  WR  ISO    BA  WR  ISO
ABREU         BOB      22   1996   66   29  0  1     8 -31  -19     1 -23    4
ALLENSWORTH   JERMAINE 24   1996  128  152  1  0   -32  19  -45   -41  32  -38
AMARO         RUBEN    31   1996   36   72  1  0    -3  19   11    -6  43   17
BARRON        TONY     29   1996   17   37  1  0    -1  10   -5     3  16  -15
BELLHORN      MARK     21   1996   59   47  0  1    -8  14   29    -2  28   15
BENITEZ       YAMIL    23   1996   35   51  1  0   -11 -10    3    20   0   11
BREDE         BRENT    24   1996  101  169  1  0   -26 -35  -14   -44 -42  -39
BRITO         TILSON   24   1996  106  125  1  0   -16 -27  -47   -17 -20  -71
CAMERON       MIKE     23   1996  113  177  1  0   -26  27  -34   -28  28  -93
CASTILLO      LUIS     20   1996  103  131  1  0   -26 -21  -30   -48  -6  -29
CRUZ          JOSE     22   1996  158  165  1  0    -9 -34  106   -15 -52   83
CUMMINGS      MIDRE    24   1996   88  114  1  0     4  47   33    -9  57   39
DIFELICE      MIKE     27   1996   82   91  1  0   -21  -3  -37   -19   6  -47
ERSTAD        DARIN    22   1996   65   95  1  0    -6 -13   40    12 -21   50
FRANCO        MATT     26   1996   69   86  1  0   -16  10   27   -29  16   12
GIL           BENJI    23   1996   43   41  0  1    11 -16    5    12 -17    0
GILES         BRIAN    25   1996  107  168  1  0   -30  36  -11   -31  46  -60
GLANVILLE     DOUG     25   1996   48   47  0  1     9  16   14     9  22    7
GOODWIN       CURTIS   23   1996   89   96  1  0    -4 -48  -33    12 -49  -23
GRAFFANINO    TONY     24   1996  111  115  1  0     0  43   68    -2  58   53
GUERRERO      VLADIMIR 20   1996  121  102  0  1   -34 -36  -17   -27 -30  -18
GUERRERO      WILTON   21   1996   98   84  0  1    20 -27   31     8 -20   48
HATTEBERG     SCOTT    26   1996  163   98  0  1    38 -46   41    16 -60    6
LAWTON        MATT     24   1996  100  131  1  0    -7  43   43   -22  62   25
MCDONALD      JASON    24   1996  211  203  0  1    54  32   71    48  41   66
MCGUIRE       RYAN     24   1996   79   90  1  0    12 -19   36    23 -13   31
MUELLER       BILL     25   1996  196  155  0  1    44  30   78    21  39   74
NEVIN         PHIL     25   1996   99  219  1  0   -31 -18   19   -48 -42  -81
NUNNALLY      JON      24   1996  128  160  1  0    39  11   39    56  23   25
OCHOA         ALEX     24   1996  211  243  1  0   -62 -37  -50   -75 -48  -45
ORIE          KEVIN    23   1996   65   39  0  1   -14 -12   25    -3 -15   18
PEREZ         EDDIE    26   1996  102   63  0  1   -29  -3   41   -15  -4   29
PEREZ         NEIFI    21   1996   77  108  1  0    -1  32   43   -33  38    4
POLCOVICH     KEVIN    26   1996  175  161  0  1    41  37   56    28  47   58
POSADA        JORGE    24   1996   92   29  0  1    18 -26   30     0 -29    0
REESE         POKEY    23   1996   21   43  1  0    -5   3    8     9  12   13
ROLEN         SCOTT    21   1996   52   74  1  0    -7   1   37    -9  25   31
SPIEZIO       SCOTT    23   1996   16   23  1  0     1 -10   -4     6  -6   -5
STEVENS       LEE      29   1996   98  204  1  0   -11 -60  -16   -17 -74  -96
STEWART       SHANNON  22   1996   61   71  1  0     1  -8   51    13   4   41
STYNES        CHRIS    23   1996   58   69  1  0     8  -6  -36    23   5  -18
SVEUM         DALE     32   1996   43   80  1  0    -5   7  -26    -7  15  -51
SWEENEY       MIKE     22   1996  160  102  0  1   -38 -25  -59   -21  -5  -55
VIDRO         JOSE     21   1996   62   82  1  0     7  16  -32    14  17  -37
VOIGT         JACK     30   1996  192  186  0  1   -32 -23  105   -39 -41   67
WALKER        TODD     23   1996  245  271  1  0   -67 -21  -90   -74 -16 -107
WIDGER        CHRIS    25   1996  139  129  0  1   -50  12   27   -60   7    2
WOMACK        TONY     26   1996  100   73  0  1    26  13   35    11  19   32
YOUNG         DMITRI   22   1996  221  207  0  1   -61  30  -69   -48  53  -58
TOTAL                                      31 18
```

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