Projecting BABIP Part One: Applying Bayes' Theorem

I am intrigued by the idea of stabilizing BABIP and its awful amount of variance year to year. The first step in my process begins here, by finding the rate in which a ballplayer reaches base via LD, FB, and GB.

One reason why you should care is because a large amount of the variability in BABIP year to year, lies within the volatility of the actual batted ball info that it measures. For one, BABIP for LD, FB, and GB individually possess an incredible amount of noise year to year (which we will get to later).

Thus, it came to my attention that possibly there is a way to measure nearly the same thing as BABIP, but with much less noise year to year.

To do so, I will apply Bayes' Rule to BABIP to find this hidden batted-ball rate. (Note: for those who are not sure of what Bayes' Theorem is the formula is below:

BAYES' RULE

P(A | B) = P(B | A) P(A)

P(B)

The symbol "|" signifies a conditional probability.

For a simple example, imagine you want to find the probability that Dominic Brown walks given that its a Tuesday. That probability would look like this P(Walk | Tuesday). And of course the answer would be never or zero.

APPLYING BAYES' RULE

Lets get started!

To do this all we will need is LD%, FB%, GB%, OBP, and LD_BABIP, GB_BABIP, and FB_BABIP. All totals were found in Retrosheet.

We know the probability for each player to get on base is their OBP, this will be our P(A) or our "prior".

The posterior we want to find is P(A|B), where "A" is the batted ball we want (LD, FB, GB) and "B" is the probability of getting on base. In other words, our posterior is the probability of the selected batted ball (LD,FB,GB) given that the player made it on base.

Now hopefully you can see why this is different than just BABIP for LD's, and that once we isolate this number, there will be much less statistical noise.

Let's piece it all together using Bayes Rule above, using Line-Drives as an example:

P(LD | OB) = P(OB | LD) P(LD)

P(OB)

Here, OB is just the probability a player reaches base. We will call the product of this formula bLD,

We wil do the same when selecting for FB and GB, when we find bFB and bGB.

RESULTS

Now for the moment of truth. Using data from 2008 to 2012, with all players having 250 PA and above we will see just how well bLD, bFB, and bGB correlates year to year, and how it compares to BABIP for LD, GB, and FB individually.

Here are the raw results from the above study:

BABIP	R^2	bMetrics	R^2	DIFF
LD_BABIP	0.031	bLD	0.206	0.175
FB_BABIP	0.331	bGB	0.516	0.185
GB_BABIP	0.181	bFB	0.396	0.215

As you can see, the bMetrics are huge improvements in decreasing the noise year to year in BABIP as it is. For one, the year to year correlations are not perfect but are vastly improved. In a sense, the bMetrics are calculating nearly the same thing as BABIP, but instead we are looking at the probability of each outcome when a player makes it on base rather than the probability of geting on base when hitting a certain batted-ball type.

These bMetrics will come in handy later on when we try to predict BABIP as a whole. Since there is less noise in these metrics in comparison to LD_BABIP and etcetera, they will be useful for when we convert projected batted ball info into BABIP.

If you still don't understand the why this new method is useful let me explain it to you in a simple way:

In 2012, Mark Trumbo led the league in LD_BABIP at .857. At the same time he had the 9th lowest bLD at 29%.

Hope you get the picture, that bMetrics combine the rate in which a player reaches base via a LD, FB, or GB, not the batting average in which they hit a LD, FB or GB. So we can isolate a player's actual propensity to both hit a certain batted-ball type and reach base safely.

In closing here is a sortable table you can play with while you wait for the next installment of the series where we will implement these metrics with our previous pLD, pFB, and pGB models to predict BABIP.

CLOSING RESULTS

(sortable table)

Name	yearID	bLD	bGB	bFB	LD_BABIP	GB_BABIP	FB_BABIP
Ryan Braun	2012	0.240	0.252	0.257	0.736	0.327	0.381
Matt Holliday	2012	0.244	0.321	0.227	0.629	0.338	0.316
Edwin Encarnacion	2012	0.247	0.207	0.286	0.684	0.305	0.281
Hunter Pence	2012	0.251	0.363	0.251	0.594	0.286	0.316
Miguel Cabrera	2012	0.268	0.262	0.247	0.636	0.319	0.353
Rickie Weeks	2012	0.273	0.324	0.271	0.636	0.283	0.281
Andrew McCutchen	2012	0.282	0.260	0.212	0.75	0.346	0.36
Mark Trumbo	2012	0.290	0.277	0.282	0.857	0.295	0.339
Miguel Montero	2012	0.291	0.224	0.233	0.764	0.286	0.355
Josh Willingham	2012	0.293	0.211	0.274	0.793	0.285	0.328
Ian Desmond	2012	0.293	0.323	0.231	0.753	0.312	0.308
Aramis Ramirez	2012	0.303	0.208	0.270	0.745	0.251	0.295
Danny Espinosa	2012	0.306	0.337	0.288	0.662	0.293	0.346
Drew Stubbs	2012	0.308	0.353	0.288	0.745	0.247	0.308
Corey Hart	2012	0.311	0.223	0.336	0.714	0.246	0.367
Aaron Hill	2012	0.311	0.227	0.286	0.676	0.304	0.294
Derek Jeter	2012	0.313	0.331	0.125	0.71	0.261	0.388
Albert Pujols	2012	0.314	0.200	0.303	0.716	0.207	0.325
B.J. Upton	2012	0.320	0.300	0.364	0.677	0.293	0.348
Torii Hunter	2012	0.321	0.328	0.174	0.767	0.34	0.369
Carlos Pena	2012	0.324	0.248	0.323	0.625	0.26	0.295
Adam Jones	2012	0.326	0.302	0.267	0.67	0.29	0.361
Carlos Gonzalez	2012	0.328	0.214	0.220	0.811	0.235	0.4
Paul Konerko	2012	0.328	0.210	0.260	0.687	0.238	0.333
Cameron Maybin	2012	0.330	0.359	0.162	0.769	0.243	0.214
Robinson Cano	2012	0.330	0.259	0.211	0.634	0.261	0.403
Shane Victorino	2012	0.330	0.334	0.183	0.691	0.269	0.19
Carlos Santana	2012	0.332	0.225	0.183	0.784	0.235	0.218
Carlos Beltran	2012	0.333	0.226	0.271	0.722	0.239	0.317
Dustin Pedroia	2012	0.333	0.269	0.210	0.716	0.251	0.258
Nick Swisher	2012	0.335	0.210	0.274	0.724	0.261	0.339
Adrian Beltre	2012	0.336	0.238	0.232	0.769	0.294	0.28
Nelson Cruz	2012	0.339	0.202	0.328	0.759	0.205	0.333
Josh Hamilton	2012	0.340	0.175	0.315	0.787	0.229	0.378
Erick Aybar	2012	0.341	0.319	0.184	0.791	0.263	0.27
Mark Reynolds	2012	0.342	0.174	0.358	0.731	0.205	0.368
Prince Fielder	2012	0.342	0.207	0.194	0.699	0.26	0.302
Mark Teixeira	2012	0.343	0.221	0.282	0.667	0.204	0.271
Justin Upton	2012	0.344	0.260	0.197	0.788	0.28	0.262
Ben Zobrist	2012	0.347	0.207	0.204	0.734	0.221	0.27
Billy Butler	2012	0.350	0.227	0.212	0.741	0.243	0.373
J.J. Hardy	2012	0.352	0.347	0.264	0.671	0.258	0.214
Austin Jackson	2012	0.361	0.302	0.142	0.775	0.366	0.214
Martin Prado	2012	0.362	0.329	0.150	0.664	0.287	0.215
Jay Bruce	2012	0.367	0.188	0.317	0.753	0.22	0.296
Michael Bourn	2012	0.367	0.333	0.141	0.735	0.272	0.252
Jose Reyes	2012	0.370	0.274	0.186	0.661	0.23	0.224
Dan Uggla	2012	0.370	0.189	0.218	0.829	0.254	0.211
Brandon Phillips	2012	0.371	0.314	0.210	0.687	0.255	0.248
Howie Kendrick	2012	0.371	0.349	0.142	0.771	0.255	0.292
Yunel Escobar	2012	0.374	0.425	0.147	0.624	0.236	0.183
Starlin Castro	2012	0.374	0.280	0.220	0.709	0.229	0.267
Jimmy Rollins	2012	0.375	0.204	0.281	0.738	0.194	0.253
Elvis Andrus	2012	0.377	0.357	0.110	0.702	0.255	0.214
Ian Kinsler	2012	0.380	0.206	0.267	0.729	0.211	0.244
Dexter Fowler	2012	0.381	0.229	0.195	0.75	0.313	0.312
Alfonso Soriano	2012	0.382	0.194	0.303	0.81	0.235	0.299
Matt Wieters	2012	0.382	0.176	0.273	0.789	0.168	0.324
Andre Ethier	2012	0.387	0.242	0.223	0.724	0.253	0.308
Kelly Johnson	2012	0.387	0.276	0.249	0.696	0.23	0.279
Gordon Beckham	2012	0.389	0.268	0.287	0.654	0.23	0.222
Coco Crisp	2012	0.392	0.244	0.206	0.75	0.212	0.223
Jamey Carroll	2012	0.392	0.345	0.129	0.657	0.243	0.256
Omar Infante	2012	0.394	0.271	0.227	0.714	0.242	0.212
Alex Gordon	2012	0.394	0.208	0.213	0.784	0.245	0.324
Yadier Molina	2012	0.399	0.236	0.169	0.721	0.265	0.216
Neil Walker	2012	0.404	0.270	0.203	0.722	0.274	0.259
Adrian Gonzalez	2012	0.406	0.208	0.254	0.752	0.23	0.318
Colby Rasmus	2012	0.408	0.271	0.301	0.693	0.246	0.244
Angel Pagan	2012	0.410	0.273	0.173	0.771	0.274	0.206
Alexei Ramirez	2012	0.412	0.360	0.212	0.68	0.254	0.206
Alberto Callaspo	2012	0.413	0.232	0.177	0.747	0.199	0.185
David DeJesus	2012	0.418	0.232	0.183	0.717	0.228	0.208
Curtis Granderson	2012	0.419	0.153	0.374	0.75	0.19	0.35
Alcides Escobar	2012	0.420	0.341	0.131	0.75	0.263	0.228
Jhonny Peralta	2012	0.422	0.240	0.287	0.667	0.202	0.272
Carlos Lee	2012	0.422	0.229	0.188	0.697	0.205	0.185
Asdrubal Cabrera	2012	0.423	0.204	0.231	0.747	0.205	0.269
Jeff Francoeur	2012	0.430	0.265	0.296	0.684	0.2	0.298
Freddie Freeman	2012	0.441	0.203	0.257	0.677	0.218	0.278
Delmon Young	2012	0.458	0.311	0.212	0.739	0.261	0.222
Michael Young	2012	0.473	0.371	0.106	0.717	0.242	0.154
Darwin Barney	2012	0.498	0.276	0.157	0.723	0.186	0.169
Ichiro Suzuki	2012	0.504	0.400	0.157	0.642	0.247	0.202

All statistics are from Fangraphs, or the Lahman and Retrosheet database

Follow @MaxWeinstein21