Updating the Milwaukee Brewers' Win Projections

About a month ago, when I first started writing here, I made a series of posts projecting how the Brewers players stack up according to Wins Above Replacement. I strongly recommend that you take a look at these posts again to get a handle on my methods, although I will glaze over them again so I can fit this all in one post.

Here’s the original series: Hitters, Pitchers.

First, let’s look at hitters. The run values are all based on wOBA. For more on how that works, read the link.

PLAYER	POS	mPA	wOBA	Outs	RAA	WAA	WAR	DefRAA/150	PosAdj/700	DefRAA	PosAdj	DefWAA	TotalWAR	Value (M$)	Salary
Rivera ,Mike	C	150	0.33	101	0	0	0.43	0	12.5	0	2.68	0.27	0.7	3.13	0.45
Kendall, Jason	C	550	0.3	388	-16.26	-1.63	-0.05	10	12.5	8.46	9.82	1.83	1.77	7.98	4.6
Nelson ,Brad	1B	50	0.34	33	0.39	0.04	0.18	-8	-12.5	-0.62	-0.89	-0.15	0.03	0.14	0.4
Fielder, Prince	1B	650	0.38	402	29.96	3	4.85	-8	-12.5	-8	-11.61	-1.96	2.89	13.01	9
Weeks, Rickie	2B	600	0.34	394	7.3	0.73	2.44	-9	2.5	-8.31	2.14	-0.62	1.83	8.23	2.3
Hall, Bill	3B	500	0.33	338	-1.74	-0.17	1.25	-1	2.5	-0.77	1.79	0.1	1.36	6.1	4.93
Lamb, Mike	3B	200	0.32	136	-1.74	-0.17	0.4	-12	2.5	-3.69	0.71	-0.3	0.1	0.45	0.4
Hardy, J.J.	SS	625	0.34	410	8.15	0.82	2.6	1	7.5	0.96	6.7	0.77	3.37	15.15	4.5
Braun, Ryan	LF	625	0.38	385	29.89	2.99	4.77	2	-7.5	1.92	-6.7	-0.48	4.3	19.34	3.05
Cameron, Mike	CF	575	0.33	384	2	0.2	1.84	3	2.5	2.65	2.05	0.47	2.31	10.41	10
Hart, Corey	RF	600	0.35	393	8.35	0.83	2.55	2	-7.5	1.85	-6.43	-0.46	2.09	9.41	2.4
Gwynn, Tony	OF	150	0.31	104	-3	-0.3	0.13	-6	-2.5	-1.38	-0.54	-0.19	-0.06	-0.29	0.4
Duffy, Chris	OF	150	0.31	104	-3	-0.3	0.13	9	-2.5	2.08	-0.54	0.15	0.28	1.27	0.4
Replacement	C	7	0.3	5	-0.2	-0.02	0	-11.61	12.5	-0.13	0.13	0	0	0	0
Replacement	1B	8	0.3	6	-0.23	-0.02	0	11.61	-12.5	0.14	-0.14	0	0	0	0
Replacement	2B	100	0.3	70	-2.87	-0.29	0	-2.32	2.5	-0.36	0.36	0	0	0	0
Replacement	3B	7	0.3	5	-0.2	-0.02	0	-2.32	2.5	-0.03	0.03	0	0	0	0
Replacement	SS	75	0.3	53	-2.15	-0.22	0	-6.96	7.5	-0.8	0.8	0	0	0	0
Replacement	LF	7	0.3	5	-0.2	-0.02	0	6.96	-7.5	0.08	-0.08	0	0	0	0
Replacement	CF	7	0.3	5	-0.2	-0.02	0	-2.32	2.5	-0.03	0.03	0	0	0	0
Replacement	RF	8	0.3	6	-0.23	-0.02	0	6.96	-7.5	0.09	-0.09	0	0	0	0
Totals	-	5849	-	3725	60.3	6.03	21.53			-5.88	0.23	-0.56	20.97	94.34	42.83

The additions here from last time are Duffy and Lamb, but you’ll notice that a few things have changed a bit. 

For one, I’ve changed the runs/win from 10.5 to 10. I was reading some things by some people that are more educated for me and it turns out that 10 is the correct number here (based on pythagorean records).

I’ve also adjusted plate appearances to what I feel are more realistic ideas. Either way, here we have 21 wins above replacement. Setting a replacement N.L. team at 51 wins (this is based on empirical observation of actual replacement players), we have 72 wins with just the position players.

Now, the pitchers. I’ve made more of a change with the pitchers, changing to finding Wins Above Replacement using something called a “Dynamic Runs Estimator.”

The basic principle behind this is that saving runs becomes less important as the runs pile on. This makes intuitive sense—the difference between saving the first run is much more important than saving the 8th run in a game.  

Another way of looking at this is that the difference between a 2.00 ERA pitcher and a 3.00 ERA pitcher is much larger than the difference between a 5.00 ERA pitcher and a 6.00 ERA pitcher. If anybody is interested, I can post the formula in the comments later. Here are the pitchers:

Name	IP	ERA	HR	K	BB	FIP	Win%	Leverage	WAR	Value	Actual Salary
Gallardo, Yovani	160	3.65	14.18	141.77	56.71	3.67	0.58	1	3.67	16.5	0.45
Capuano, Chris	160	4.5	18.23	121.52	48.61	4.19	0.52	1	2.6	11.71	0.4
Parra, Manny	160	4.44	16.12	139.28	67.91	4.07	0.53	1	3	13.5	0.5
Bush, Dave	169	4.31	23	118	45	4.4	0.49	1	2.32	10.44	4
Suppan, Jeff	169	4.85	21	98	63	4.8	0.45	1	0.42	1.88	12.5
Replacement Starter	45.67	5.7	-	-	-	5.7	0.37	1	0
STARTERS TOTAL	863.67							1	12.01	54.03	17.85
Hoffman, Trevor	53	3.74	6	43	17	4.04	0.53	1.8	0.78	3.49	6
Villanueva, Carlos	96	4.03	13	82	34	4.34	0.5	1.1	0.47	2.11	0.5
McClung, Seth	89	4.35	9	70	44	4.45	0.49	1.1	0.31	1.38	1.2
Swindle, RJ	49	2.79	4	45	8	2.94	0.67	1.1	1.24	5.58	0.4
Stetter, Mitch	38	4.03	4	33	18	4.28	0.51	0.85	0.17	0.75	0.4
Julio, Jorge	46	4.4	5	44	22	4.16	0.52	0.85	0.26	1.17	0.95
DiFelice, Mike	35	4.37	5	28	12	4.52	0.48	0.75	0.06	0.27	0.4
Dillard, Tim	32	4.22	4	23	12	4.54	0.48	0.75	0.05	0.23	0.4
Coffey, Todd	43	4.81	6	33	16	4.63	0.47	0.7	0.03	0.14	0.4
Riske, David	53	4.25	7	39	23	4.78	0.45	0.6	-0.02	-0.09	4.25
Replacement Reliever	347.33	4.72	-	-	-	4.72	0.46		0	0
RELIEVERS TOTAL	594.33							1	3.34	15.03	14.9
PITCHERS TOTAL	1458								15.35	69.07	32.75

The “win%” that you see here is exactly what it sounds like—it’s what the team’s winning percentage would be with a league average offense and that pitcher pitching every inning of every game.

A replacement level SP has a .370 win% and a replacement level RP has a .460 win%. Here we see that our pitchers are worth 15.35 wins. So this means with a replacement level offense, the Brewers would win about 66 games. Just think, in 2004, our whole team was only worth 16 wins above replacement.

Now we can get to the interesting stuff. Our total wins above replacement comes out to 35.32.  So with our baseline set at 51 wins, we are expected to win 86.32 games, for a winning percentage of .538.  

I don’t expect that these projections are spot on - they can’t be, we’re not going to some how win .32 of a game along the line - so we can use a tool called a binomial distribution to see the probabilities of winning certain amounts of games.  Here I have graphed the probabilities of winning at least a certain amount of games (the red lines represent 75% and 25% chances).

Brewer Win Probabilities

I’ll keep updating this as the offseason goes, so keep your eyes open!