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Old 06-29-2025, 12:53 PM   #1
weazardofinance
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Batting Order research

I read Tango's book on vacation and got a wild hair to test his notions about batting order (widely taken as gospel in the baseball community), which he presents as a set of heuristics i.e. top three hitters go in 1, 2, and 4, etc. But he makes little mention of OBP, baserunning / stealing, bb/k, or other stats that we know are important in the batting order. Can we quantify the importance of each metric for each spot in the batting order and see if Tango's wisdom is right?

I pulled MLB game and play-by-play data from 2022-2024 (after the DH change), and for each team in each game, calculated the following metrics for the starters in each batting order slot (1-9) in that game: wOBA, ubr (ultimate baserunning), wGDP (avoids GDPs), OBP, SLG, wSB (weighted stolen bases), BBrate, BBK, and BABIP, then ran a regression with all those as the independent variables, and the team's runs in the game as the dependent variable. Results are below. Note that some coefficients are zero - that's because I ran a lasso algorithm that adjusts for multi-collinearity and excludes variables with no predictive power.

================================================== ============================ ==========
R-squared: 0.835
Adj. R-squared: 0.835
No. Observations: 14833
================================================== ============================ ==========
coef (22-24)
---------- ----------
const -1.9413
woba_l1 2.3095
woba_l2 1.5956
woba_l3 1.8882
woba_l4 1.5724
woba_l5 2.4229
woba_l6 2.2028
woba_l7 2.7949
woba_l8 2.3715
woba_l9 2.6184
ubr1 0.2982
ubr2 0.3197
ubr3 0.3473
ubr4 0.3367
ubr5 0.3122
ubr6 0.3413
ubr7 0.3577
ubr8 0.3629
ubr9 0.3352
wGDP1 0.1421
wGDP2 0.1024
wGDP3 0.2283
wGDP4 0.1487
wGDP5 0.0837
wGDP6 0.1183
wGDP7 0.1538
wGDP8 0.1118
wGDP9 0.1297
OBP1 -1.1257
OBP2 -0.7473
OBP3 -0.9293
OBP4 -0.7294
OBP5 -1.2828
OBP6 -1.2923
OBP7 -1.7114
OBP8 -1.3609
OBP9 -1.5338
SLG1 0.4533
SLG2 0.7008
SLG3 0.7101
SLG4 0.8002
SLG5 0.3930
SLG6 0.4358
SLG7 0.2319
SLG8 0.3417
SLG9 0.1949
wSB1 -0.3763
wSB2 0.0000
wSB3 -0.3558
wSB4 0.0000
wSB5 0.0000
wSB6 0.0000
wSB7 0.0000
wSB8 -0.4314
wSB9 -0.3818
BBrate1 0.0000
BBrate2 0.0000
BBrate3 -0.3689
BBrate4 -0.5561
BBrate5 0.0000
BBrate6 0.0000
BBrate7 0.0000
BBrate8 0.0000
BBrate9 0.0000
BBK1 0.0690
BBK2 0.0000
BBK3 0.1177
BBK4 0.1725
BBK5 0.0000
BBK6 0.0000
BBK7 0.0516
BBK8 0.0000
BBK9 0.0000
BABIP_1 -0.3633
BABIP_2 -0.2989
BABIP_3 -0.3545
BABIP_4 -0.3829
BABIP_5 -0.3095
BABIP_6 -0.2576
BABIP_7 -0.2265
BABIP_8 -0.3095
BABIP_9 -0.1967

As you see we have an 83.5% R squared over 14,833 observations - not bad.

Some of the results are intuitive, like SLG4 having the highest coefficient in the SLG category.

Others make less sense at first glance. Take the first four slots for wOBA and OBP as an example:

woba_l1 2.3095
woba_l2 1.5956
woba_l3 1.8882
woba_l4 1.5724
OBP1 -1.1257
OBP2 -0.7473
OBP3 -0.9293
OBP4 -0.7294

The OBP coefficients are negative, but this does NOT mean that we want a bad OBP guy at #1. It means that wOBA and OBP are correlated i.e. wOBA already captures much of OBP, so it gets a negative coefficient whereby we don't double-count its effect. The way I interpret the negative coefficients is that the more negative they are, the more it hurts to have a batter suck at that stat in that spot in the order. So we really do want a good OBP guy at #1. But have a look at OBP for slots 5-9:

OBP5 -1.2828
OBP6 -1.2923
OBP7 -1.7114
OBP8 -1.3609
OBP9 -1.5338

Now it's not clear that our best OBP guy should be #1. OBP7 seems more important, and so does woba_l7, for that matter! I got this same pattern when using 2019-2024 data (i.e. three more years of data), so I don't think it's an anomaly - but I cannot explain it.

Of course, wOBA and OBP are not the only variables here, and a significant chunk of a player's run value is explained by other stats. But even regressing just OBP and wOBA, there is something important about the 7-hole that defies intuition:

OLS Regression Results with Lasso-selected and significant predictors (p <= 0.05):
OLS Regression Results
================================================== ============================
Dep. Variable: b_r R-squared: 0.659
Model: OLS Adj. R-squared: 0.659
Method: Least Squares F-statistic: 2385.
Date: Sun, 29 Jun 2025 Prob (F-statistic): 0.00
Time: 12:40:41 Log-Likelihood: -30028.
No. Observations: 14833 AIC: 6.008e+04
Df Residuals: 14820 BIC: 6.018e+04
Df Model: 12
Covariance Type: nonrobust
================================================== ============================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const -3.9382 0.054 -73.297 0.000 -4.044 -3.833
OBP2 0.3557 0.151 2.359 0.018 0.060 0.651
OBP4 -0.3838 0.150 -2.560 0.010 -0.678 -0.090
OBP7 -0.4039 0.152 -2.650 0.008 -0.703 -0.105
woba_l1 3.2970 0.061 54.158 0.000 3.178 3.416
woba_l2 2.8710 0.133 21.583 0.000 2.610 3.132
woba_l3 3.2193 0.057 56.710 0.000 3.108 3.331
woba_l4 3.6385 0.132 27.504 0.000 3.379 3.898
woba_l5 3.0625 0.057 53.512 0.000 2.950 3.175
woba_l6 2.8208 0.058 48.538 0.000 2.707 2.935
woba_l7 3.1684 0.142 22.355 0.000 2.891 3.446
woba_l8 2.8598 0.058 49.614 0.000 2.747 2.973
woba_l9 2.6762 0.057 46.603 0.000 2.564 2.789
================================================== ============================
Omnibus: 1225.014 Durbin-Watson: 1.958
Prob(Omnibus): 0.000 Jarque-Bera (JB): 2278.586
Skew: 0.581 Prob(JB): 0.00
Kurtosis: 4.529 Cond. No. 20.1
================================================== ============================

Any idea what is going on here?

Next steps are to extend this analysis back into further periods by excluding pitchers batting, and also looking at LHP/RHP splits and batter handedness. Like: is there data support for alternating L and R handed batters?

In the meantime I am trialing these lineup findings with the Braves in OOTP. Will post an update here if I run more data or figure out what's up with the 7-spot.
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Old 06-29-2025, 01:26 PM   #2
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This is too smart for me. However, I will be absolutely fascinated if you post a dummy version
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Old 06-29-2025, 01:41 PM   #3
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I'm not near the regression expert I wish I was, but there's enough odd stuff there that my guess is you did something wrong. What that is, I don't know, but maybe it was a simple data formatting error.

Like that r-squared really does seem pretty high, which would be great, but it's almost too good to be true. Then you've got wOBA 2-4 are lower than the rest when wouldn't you expect higher? OBA is negative which you've seemingly explained, but are you sure about that especially considering the wOBA numbers? Maybe try 1 set, but not the other? SLG5 even looks suspiciously low to me. I'm also surprised by how many 0.00s you have.

I don't know. Others here like RonCo would know better, but yeah, I think you made a mistake somewhere.
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Old 06-29-2025, 02:22 PM   #4
weazardofinance
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I just re-ran the regression using only OBP and SLG, and here the results look a lot different. OBP is clearly preferred in slots 1-2, and SLG at #4 (like wisdom says). R^2 is lower, but the anomaly at #7 disappears!

Dep. Variable: b_r R-squared: 0.659
Model: OLS Adj. R-squared: 0.658

================================================== ============================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const -3.5564 0.057 -62.546 0.000 -3.668 -3.445
OBP1 1.9057 0.091 20.843 0.000 1.727 2.085
OBP2 1.9076 0.091 21.000 0.000 1.730 2.086
OBP3 1.6125 0.089 18.118 0.000 1.438 1.787
OBP4 1.6011 0.090 17.796 0.000 1.425 1.777
OBP5 1.5441 0.089 17.259 0.000 1.369 1.719
OBP6 1.3970 0.089 15.736 0.000 1.223 1.571
OBP7 1.3939 0.086 16.120 0.000 1.224 1.563
OBP8 1.4632 0.086 16.956 0.000 1.294 1.632
OBP9 1.4442 0.085 16.898 0.000 1.277 1.612
SLG1 0.9998 0.046 21.573 0.000 0.909 1.091
SLG2 0.9455 0.043 21.870 0.000 0.861 1.030
SLG3 1.1245 0.042 26.851 0.000 1.042 1.207
SLG4 1.1699 0.043 27.445 0.000 1.086 1.253
SLG5 1.0590 0.044 24.249 0.000 0.973 1.145
SLG6 0.9914 0.046 21.742 0.000 0.902 1.081
SLG7 0.9791 0.045 21.657 0.000 0.890 1.068
SLG8 0.9758 0.046 21.056 0.000 0.885 1.067
SLG9 0.8737 0.046 18.874 0.000 0.783 0.964
================================================== ============================
Omnibus: 1151.939 Durbin-Watson: 1.966
Prob(Omnibus): 0.000 Jarque-Bera (JB): 2141.570
Skew: 0.552 Prob(JB): 0.00
Kurtosis: 4.498 Cond. No. 12.5
================================================== ============================

But throw in wOBA and you get:

coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const -3.7229 0.058 -63.888 0.000 -3.837 -3.609
OBP1 0.8611 0.284 3.035 0.002 0.305 1.417
OBP2 1.2661 0.250 5.061 0.000 0.776 1.756
OBP3 0.8055 0.233 3.462 0.001 0.349 1.262
OBP4 0.7066 0.240 2.947 0.003 0.237 1.177
OBP5 0.4469 0.267 1.673 0.094 -0.077 0.971
OBP6 0.5972 0.281 2.126 0.034 0.047 1.148
OBP7 -0.1157 0.272 -0.426 0.670 -0.648 0.417
OBP8 0.1656 0.279 0.593 0.553 -0.382 0.713
OBP9 0.5081 0.277 1.831 0.067 -0.036 1.052
SLG1 0.4663 0.147 3.176 0.001 0.179 0.754
SLG2 0.5999 0.132 4.531 0.000 0.340 0.859
SLG3 0.7007 0.119 5.867 0.000 0.467 0.935
SLG4 0.7054 0.124 5.684 0.000 0.462 0.949
SLG5 0.4691 0.139 3.372 0.001 0.196 0.742
SLG6 0.5526 0.149 3.715 0.000 0.261 0.844
SLG7 0.1781 0.142 1.257 0.209 -0.100 0.456
SLG8 0.2835 0.146 1.937 0.053 -0.003 0.570
SLG9 0.3922 0.141 2.773 0.006 0.115 0.669
woba_l1 1.7975 0.466 3.859 0.000 0.884 2.711
woba_l2 1.1207 0.408 2.750 0.006 0.322 1.920
woba_l3 1.3879 0.370 3.747 0.000 0.662 2.114
woba_l4 1.5492 0.385 4.020 0.000 0.794 2.305
woba_l5 1.9122 0.434 4.402 0.000 1.061 2.764
woba_l6 1.4129 0.462 3.061 0.002 0.508 2.318
woba_l7 2.6334 0.444 5.928 0.000 1.763 3.504
woba_l8 2.2601 0.457 4.946 0.000 1.364 3.156
woba_l9 1.6051 0.448 3.582 0.000 0.727 2.484

Now the oddness has returned. I think the main issue is that wOBA is kind of a synthesis of OBP and SLG, so having all three stats makes it hard to interpret any one of their set of coefficients in isolation.
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Old 06-29-2025, 02:32 PM   #5
kq76
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Quote:
Originally Posted by weazardofinance View Post
Now the oddness has returned. I think the main issue is that wOBA is kind of a synthesis of OBP and SLG, so having all three stats makes it hard to interpret any one of their set of coefficients in isolation.
Yeah, the top one looks a lot more like what I'd expect. Sometimes less is just better.
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Old 06-29-2025, 03:08 PM   #6
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You can crunch all the numbers you like. The human element will override any “gospel” on batting orders.
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Old 06-29-2025, 11:57 PM   #7
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Originally Posted by mytreds View Post
You can crunch all the numbers you like. The human element will override any “gospel” on batting orders.

Facts.
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