How many bases does it take to score a run?

Its a simple question, and four is of course the answer. It has been the subject of the research I am doing lately. I presented on the subject today at the Pacific Northwest SABR chapter meeting today. In a basic way, I presented my Total Bases Acquired formula. This is a formula I've devised based on combining offensive elements that have, when simply added together and then divided by games played, at least as high a correlation to team runs scored as OPS.

TBAq/G= [Total Bases + Walks + Hit By Pitcher + Reach on Error + Stolen Bases]/Games Played

Its a relatively simple formula, and quite similar to one Henry Chadwick used called TBA, which was total bases divided by games.

Now, this does not necessarily predict individual runs, but what it does do is predict team runs. Also, you can see with it that any team, by hook or by crook, pretty much that you have to simply produce bases to score runs. Interestingly enough, the more bases you produce, the efficiency with which you produce runs increases. Thus as your bases increase, the number of bases needed to score a run decreases, magnifying the impact of added bases.

Here are the teams in the MLB as of today. First is their runs scored per game, in the third column you'll see their TBAq. In between the two is something I call the Base Efficiency, which is how many bases it takes that team to score a single run. And these are only bases acquired without also creating an out, so a hit, walk, hit by pitch, reaching on error, or stolen base. The BEFF is reached by dividing TBAq and Runs Per Game. Next you see what would have been the expected bases based on their actual runs scored. If there is a negative, that means that team is inefficient in converting their acquired bases to runs. Thus, we could say Washington should have only needed 17.19 bases to produce 3.9 runs per game. However, it took them 18.27 bases, thus as a team, they have to produce more bases than say Toronto in order to score an equal number of runs. It doesn't mean their a good ball club, just that they make do better with what they've got. One thing that is interesting in this year of pitching dominance, is that 66% of teams are under-performing right now in terms of their ability to convert bases to runs (the model I use goes back to 1998). Some of those teams will see their run scoring increase. More than likely, it will be the teams with the high percentage differential as well as being near the top in runs produced. Basically, they have the crude oil needed to produce the gas in the first place, so that will show through.

		RUNS	BEFF	TBAqG	exp base	diff	% diff
2012	WSN	3.90	4.686	18.27	17.19	-1.08	-5.91%
2012	TOR	4.73	4.007	18.95	19.16	0.20	1.07%
2012	TEX	5.25	3.965	20.82	20.38	-0.43	-2.07%
2012	TBR	4.38	4.152	18.19	18.33	0.14	0.78%
2012	STL	4.86	4.118	20.02	19.46	-0.55	-2.76%
2012	SFG	4.03	4.379	17.65	17.50	-0.14	-0.82%
2012	SEA	4.02	4.233	17.02	17.48	0.46	2.72%
2012	SDP	3.37	5.063	17.06	15.94	-1.12	-6.56%
2012	PIT	3.24	4.806	15.57	15.64	0.06	0.41%
2012	PHI	4.29	4.274	18.33	18.12	-0.22	-1.18%
2012	OAK	3.80	4.607	17.51	16.96	-0.55	-3.14%
2012	NYY	4.76	4.325	20.59	19.23	-1.36	-6.61%
2012	NYM	4.52	4.040	18.26	18.66	0.40	2.18%
2012	MIN	4.25	4.314	18.33	18.02	-0.31	-1.70%
2012	MIL	4.31	4.408	19.00	18.16	-0.84	-4.40%
2012	MIA	3.67	4.854	17.81	16.65	-1.16	-6.52%
2012	LAD	4.35	4.195	18.25	18.26	0.01	0.07%
2012	LAA	4.03	4.428	17.85	17.50	-0.34	-1.93%
2012	KCR	3.82	4.678	17.87	17.01	-0.87	-4.84%
2012	HOU	4.25	4.165	17.70	18.02	0.32	1.80%
2012	DET	4.42	4.249	18.78	18.42	-0.36	-1.91%
2012	COL	5.21	3.936	20.51	20.29	-0.22	-1.06%
2012	CLE	4.32	4.262	18.41	18.19	-0.23	-1.22%
2012	CIN	4.41	4.283	18.89	18.40	-0.49	-2.59%
2012	CHW	4.78	3.991	19.08	19.27	0.20	1.03%
2012	CHC	3.69	4.637	17.11	16.70	-0.41	-2.40%
2012	BOS	4.98	3.969	19.77	19.75	-0.02	-0.10%
2012	BAL	4.56	4.225	19.27	18.75	-0.51	-2.65%
2012	ATL	4.66	4.030	18.78	18.99	0.21	1.11%
2012	ARI	4.27	4.409	18.83	18.07	-0.76	-4.03%

Another thing I'm interesting in is strikeouts. Did you know that players will have a higher OPS in games in which they strikeout vs games in which don't. Also, K's are way up the last few years. That K phenomenon shows up in the OPS of players even when you add in hits, like even 1 or 2 hits a game. In fact, its still about even for players in games in which they go 2 for 4 and have a K vs a game in which they go 2 for 4 and have a different kind of out. Some, at the top end have a higher OPS (all are high in that circumstance, since they start with a .500 BA and probably have a walk). What I think this has to do with is a strikeout is evidence of a pitcher advantage. There is no way to measure that advantage until you see it stretched out over 1,500 at bats. In the short term, strikouts don't make a difference, an outs an out. But just as a hit is not a hit, an out is not an out.