the big question

Monday, commenter DM asked a number of questions related to whether or not more plunks leads to a better or worse offensive season in terms of hits and runs batted in. Essentially the question was "Do more plunks mean a better season or a worse season for Craig Biggio?" DM also asked "should we really be rooting for more plunks?" but the answer to that question is quite obviously yes, because there's a 103 year old record to be broken, and you just don't get to see that every day. Then again, I don't expect everyone to look at it the same way, since not everyone started a website about it. But getting back to the main question, here's the relevant data:

Year	Games	HBPs	Hits	RBI	H per HBP	RBI per HBP
1988	50	0	26	5	n/a	n/a
1989	134	6	114	60	19	10
1990	150	3	153	42	51	14
1991	149	2	161	46	80.5	23
1992	162	7	170	39	24.29	5.57
1993	155	10	175	64	17.5	6.4
1994	114	8	139	56	17.38	7
1995	141	22	167	77	7.59	3.5
1996	162	27	174	75	6.44	2.78
1997	162	34	191	81	5.62	2.38
1998	160	23	210	88	9.13	3.83
1999	160	11	188	73	17.10	6.64
2000	101	16	101	35	6.31	2.19
2001	155	28	180	70	6.43	2.5
2002	145	17	146	58	8.59	3.41
2003	153	27	166	62	6.15	2.30
2004	156	15	178	63	11.87	4.2
2005	155	17	156	69	9.18	4.06

As you can see, the lowest ratio of hits to plunks is in 1997 when he got hit 34 times and had 191 hits for a 5.62 hit to plunk ratio. That, by the way, is the 4th most hits ever by a player who was hit 30 or more times in a season, behind only those Hughie Jennings and Tommie Tucker guys and their 1896, 1895, and 1889 seasons. Of course that was a much different game - one in which it was possible for Jennings to get hit 51 times, get 209 hits, and bat .401.
The lowest hit to plunk ratio for Biggio was in 1991 when he was plunked just twice while he got 161 hits. His lowest RBI to plunk ratio was in his injury shortened 2000 season when his injured knee held him to 16 plunks and 35 RBI in just 101 games. Though RBIs are not a great measure for a guy who has been in the leadoff spot so much of his career, it does appear that his highest RBI years have coincided with high plunk year.

On the other hand, you could look at the numbers for the 1997 and 1998 seasons and say "hey, he dropped 11 plunks and added 19 hits and 7 RBI - career highs in both!", and you might use that as your argument that less plunks equals better production, but if you group the seasons as follows you see a different result:
In the 6 seasons Biggio has been under 10 HBPs he averaged 127 hits and 41 RBI, in the 6 seasons he's been hit between 10 and 19 times he averaged 157 hits and 60 RBI, and in the 6 seasons when he's been hit 20 or more times he averaged 181 hits and 76 RBI.
There is a clear upward trend. On the other hand, there might be more incentive for a pitcher to hit a batter, or at least try to pitch inside, when a batter is on pace for 200 hits compared to a batter who is on pace for 125. The data shows that high plunk totals have come with high hit totals, so clearly I can not choose the wine in front of me, but logic dictates that a player with a high hit total, playing on a high scoring team, would get more plate appearances and get thrown near more by virtue of being difficult to get out, so clearly I can not choose the wine in front of you.

Also, if you take those buckets used above and apply them to every season in which plunks were counted and a player played more than 100 games, it looks like this:

HBPs	Seasons	avg. RBI	avg. Hits
0 to 10	16392	60.06	129.77
10 to 19	844	70.46	144.11
20 or more	88	69.93	148.53

The RBI trend isn't quite so upward, but the average hits looks like it increases in seasons with more plunks, doesn't it? But, you'd also have to say that the "20 or more" bucket is an awfully small sample that could be easily skewed by a few high performers. So then we're done right? You'd like to think so wouldn't you! History shows that a great many of the seasons in which players got hit more than 20 times have also been seasons in which they got a high number of hits, so clearly I can not choose the goblet in front of me, but only a great fool would assume that the game has not changed dramatically over its long history, so only a great fool would choose the goblet in front of you.
So then take a look at the following table which shows average hit and RBI totals grouped by HBP total for every season in which a player played more than 100 games:

Seasons	HBPs	avg Hits	Avg RBI	Batting Avg
2318	0	116.50	51.68	0.272
3147	1	123.00	55.77	0.275
3045	2	128.81	58.47	0.276
2355	3	131.82	61.47	0.277
1793	4	137.35	65.39	0.280
1328	5	137.13	65.11	0.279
936	6	140.38	67.26	0.280
685	7	141.98	67.82	0.283
463	8	140.25	68.30	0.282
322	9	141.30	67.39	0.283
242	10	143.20	69.92	0.283
145	11	143.92	72.12	0.286
117	12	145.42	67.71	0.282
96	13	138.31	66.64	0.278
66	14	145.39	71.17	0.290
60	15	147.40	71.93	0.287
39	16	147.08	74.51	0.292
33	17	143.70	77.85	0.289
25	18	150.68	72.20	0.287
21	19	149.10	70.52	0.285
18	20	138.83	67.06	0.271
11	21	155.82	79.10	0.292
6	22	157.17	68.83	0.283
7	23	146.14	72.86	0.289
9	24	135.33	68.89	0.293
9	25	146.78	57	0.286
3	26	122.67	40.33	0.272
4	27	171.50	77.25	0.293
3	28	148.00	57.67	0.275
3	29	149.00	71.33	0.276
1	30	148.00	82	0.264
3	31	146.67	65.67	0.288
2	32	155.00	82.5	0.335
1	33	196.00	99	0.372
1	34	191.00	81	0.309
1	35	139.00	94	0.238
1	36	138.00	55	0.268
1	39	161.00	106	0.301
2	46	165.50	83	0.340
1	50	145.00	38	0.279
1	51	209.00	121	0.401

There are a lot of very good looking single seasons on the bottom end of this list and a few that aren't so great, but at the top end where most of the data points sit, there is an upward increase in hits as plunks go up. In seasons of more than 100 games, it does look like players who get hit more get an increased number of hits, but clearly every time a player gets hit by a pitch he risks suffering an injury that would prevent him from playing 100 game. But Ted, I do not believe we can have a triumphant plunk total until we have a most excellent batting average over a great many at-bats - yes Bill, but we can not have an excellent batting average over a great may at-bats if we suffer a heinous plunk related injury.
Oh right, wrong movie. How about... Life is pain - anyone who says differently is selling something. Often the plunks are the price of the hits. But there is one more thing you might be thinking of - maybe if Biggio hadn't gotten hit 34 times in 1997, he would have gotten even more than 191 hits. If you want to assume he wasn't going to walk or sacrifice in those 34 plate appearances, and figure he would have batted his season average of .309 in those 34 attempts, there's an extra 11 hits he could have had, and at least 6 of them would probably have been for extra bases. Or, maybe being hit so many times in the first several months of the season caused him to wear down and get plunked less in the rest of the season. Since we can, let's look at that idea.
Going into September of 1997, Biggio had been hit 25 times already, and had 165 hits. That September he batted .310, slightly better than his average for that season, and well up from the .265 August he had just had. Over all though, Biggio has batted .285 in months where he had less than 10 plunks on the season entering the month, .287 when he was between 10 and 20 plunks entering the month, and just .270 in months which he entered with 20 or more season plunks. But Biggio's career average in the month of September is just .255, easily his worst month, and it's not clear that his plunk total going into the month has a lot to do with it. For example, in 1996 he had 23 plunks going into September and batted .172, while in 1998 he had the same plunk total at the end of August, but tore through September batting .326. And in 1999 he entered September with just 9 HBPs, but still batted .250 for the month.
Here are his season by season September totals, including the number of HBPs he had on the season prior to September:

Year	Hits	at-bats	batting avg	games	HBP prior
1988	8	29	0.276	12	0
1989	17	89	0.191	25	5
1990	18	75	0.240	23	2
1991	26	94	0.277	24	2
1992	22	102	0.216	27	6
1993	32	103	0.311	26	8
1995	36	103	0.350	27	18
1996	16	93	0.172	25	23
1997	26	84	0.310	26	25
1998	31	95	0.326	23	23
1999	24	96	0.250	25	9
2001	15	78	0.192	20	25
2002	17	91	0.187	23	16
2003	29	98	0.296	26	21
2004	26	104	0.250	25	15
2005	24	104	0.231	26	15

The league-wide average for the month of September is .260 for the 1988-2005 seasons. It's the worst batting month among the full months of the baseball season. October and March are worse, but their haven't been enough regular season games in those months for it to be a fair comparison. June has been the best month in that span, with a .267 average.

The fact still remains though, that no player in the last 100 years has accumulated 278 plunks without also getting 2,878 hits while several players have gotten that many hits without being plunked nearly as many times. So while it's obviously possible to be a great hitter without being a great get-hitter, we haven't seen much of the opposite case - someone who has been a great get-hitter over a long career without being a very good hitter. Jason Kendall may end up being that guy, but even he had some very good hitting seasons. So, it may not be necessary to cheer for plunks to ensure Biggio of having a productive season, but his history appears to show that his plunks won't take away from his productivity, so long as he doesn't get hurt. And being able to get hit 278 times without landing on the DL is a pretty good track record on that front.

I probably should have thought of this one earlier:
"Let me 'plain... no, there is to much. Let me sum up."

Plunks good, injuries bad. Hits not necessarily related to plunks, but definitely related to injuries.