Best Lineup - Tampa Bay Rays

Next up on my look at each teams most efficient lineup is the Tampa Bay Rays.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest. For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers
NL: Mets | Cubs

See the results after the jump...

Best Lineup - Chicago Cubs

Next up on my look at each teams most efficient lineup is the Chicago Cubs.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest. For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers
NL: Mets

See the results after the break.

Best Lineup - Texas Rangers

Next up on my look at most efficient lineups is the Texas Rangers.  I used my baseball simulator to run millions of games through various different possible lineup scenarios to see which lineup it spit out as the most likely to win a game vs a RH and LH pitcher.  Each lineup was simulated in 2.5 million games.

Please keep in mind that 2014 Steamer Projections were used as input, so if you don't like some of the results take it up with them.

Previous teams:
AL: Angels
NL: Mets

See the results after the break.

Best Lineup - New York Mets

Next up on my look at most efficient lineups is the New York Mets.  I used my baseball simulator to run millions of games through various different possible lineup scenarios to see which lineup it spit out as the most likely to win a game vs a RH and LH pitcher.  I tried my best to not stack left handed hitters and I always batted the pitcher 9th because no MLB manager will bat his pitcher 8th which is where most should hit.

Please keep in mind that 2014 Steamer Projections were used as input, so if you don't like some of the results take it up with them.

Previous teams:
AL: Angels
NL: None

See the results after the break.

Best Lineup - Los Angeles Angels

Not sure if this is going to be a series for all teams or just some teams, but I am going to kick things off with the best lineup for the Los Angeles Angels. The methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers. I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest. For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting LH back to back when reasonably possible.  Two million simulations make up the sample size.

See the results after the break.

Battle Of The Gold Gloves

One of the benefits of having a program that can accurately simulate a baseball game is that you can pretty much model anything and you can use the law of large numbers (or samples) to do the dirty work for you.  In my latest exercise, I decided to take the 2013 Gold Glove winners from both the National and American leagues and have them play against each other.  In order to make it fair, I ran sets of the simulation with each team being away/home and facing both a LH and RH starting pitcher.  I gave both teams the exact identical starting pitcher, bench and bullpen so that the only difference were the starting players.  I played by NL rules with no DH and gave both teams the same hitting skill for their pitcher.  And afterwards, I did the same thing but this time made all the players league average fielders to see which side was better solely on offense.

The simulator also allows me to determine the most efficient lineup for both teams (facing RHP and LHP).  The lineups that you see for both teams were the highest scoring lineups according to the simulator.  I put in a limitation of not batting any left handed hitters back to back as this seems to be something that most MLB managers follow and I always batted the pitcher ninth.

Here are the lineups

vs RHP	GGNL	GGAL		vs LHP	GGNL	GGAL
1	G.Parra	D.Pedroia		1	G.Parra	D.Pedroia
2	Y.Molina	A.Gordon		2	Y.Molina	S.Victorino
3	P.Goldschmidt	S.Victorino		3	P.Goldschmidt	E.Hosmer
4	C.Gonzalez	E.Hosmer		4	C.Gonzalez	A.Jones
5	N.Arenado	A.Jones		5	N.Arenado	A.Gordon
6	C.Gomez	S.Perez		6	A.Simmons	S.Perez
7	A.Simmons	M.Machado		7	B.Phillips	M.Machado
8	B.Phillips	J.Hardy		8	C.Gomez	J.Hardy
9	Pitcher	Pitcher		9	Pitcher	Pitcher

(GGNL - Gold Glove NL, GGAL - Gold Glove AL)

And here are the results

This table has all the players set to their defensive values.

Description	Away	Home	Winner	Away RS	Home RS	Win %	Total Runs
vs RHP	GGNL	GGAL	GGAL	3.43	3.32	50.42	6.75
vs RHP	GGAL	GGNL	GGNL	3.14	3.61	57.72	6.75
vs LHP	GGNL	GGAL	GGAL	3.48	3.36	50.37	6.84
vs LHP	GGAL	GGNL	GGNL	3.16	3.67	58.13	6.83

... and this table has all the players set to league average defensive values.

Description	Away	Home	Winner	Away RS	Home RS	Win %	Total Runs
vs RHP	GGNL	GGAL	GGAL	3.77	3.80	52.19	7.57
vs RHP	GGAL	GGNL	GGNL	3.60	3.97	56.33	7.57
vs LHP	GGNL	GGAL	GGAL	3.82	3.84	52.10	7.66
vs LHP	GGAL	GGNL	GGNL	3.63	4.04	56.69	7.67

Back Napkin Analysis:
It looks like the National League team is better both defensively and offensively.  Now keep in mind that the results will reflect the input data or player projections both offensively and defensively.  Not wanting to be biased, I used 2014 Steamer projections for the offense and I eye-balled the defensive values for each player from a mixture of UZR, FSR and Zips (if available).  I tended not to go above 15 runs saved per 150 games for any player.  Below are the defensive numbers I used for each player.

	NL	AL
C	Y.Molina (15)	S.Perez (13)
1B	P.Goldschmidt (4)	E.Hosmer (3)
2B	B.Phillips (8)	D.Pedroia (10)
3B	N.Arenado (12)	M.Machado (15)
SS	A.Simmons (15)	J.Hardy (10)
LF	C.Gonzalez (10)	A.Gordon (7)
CF	C.Gomez (13)	A.Jones (-3)
RF	G.Parra (12)	S.Victorino (15)

How Does BABIP Effect Run Scoring

It is pretty obvious, the higher a teams batting average on balls in play (BABIP) is the more runs they will score.  But the million dollar question is what is the relationship between BABIP and runs scored.  How many more or less runs can a team expect to score based on an increase or decrease in their BABIP.

When I posed this question to subject matter expert Tom Tango, he gave me the following answer.

You get +.75 runs for turning a sure out into a sure hit.

If you change BABIP from .300 to .301, you will get an extra .001 x .75 runs per ball in play.

If you assume that 70% of PA are balls in play, then changing BABIP from .300 to .301, you will get an extra .70 x .001 x .75 runs per PA.

If you have say 38 PA per game, then changing BABIP from .300 to .301 will get you an extra 38 x .70 x .001 x .75 runs per game.

So, 1 point in BABIP is .02 runs per game.

Naturally, this only works at very modest changes. If you go from .300 to .400, well, that 38 PA won’t hold. On top of which, you have compounding effects, so runs are not linear any more.

          *****     *****     *****     *****     *****
My intention all along was to use my simulator to figure this out but now I had a baseline to compare my results against.  Would the simulator come up with something close to the "1 point in BABIP is .02 runs per game"?

Where the power of the simulator comes in, it allows you to pick and choose your run environment and to change the BABIP of all pitcher/hitter matchups to any value all the while leaving all other variables the same.  Maybe the 0.02 runs per game only holds for a certain BABIP value?  By using BABIP numbers all the way from 0.000 to 1.000 the simulator should be able to show what kind of relationship BABIP and runs scores has on a basic x/y-line graph.  It can also zero in on specific ranges of BABIP that are more common in the major leagues.

Methodology
I don't want to overload this post with all the boring details (tldr) so I will give you the basics.  I created two teams Team A(way) and Team (H)ome making the teams fairly even and making their run environment at right around 8.2 combined runs (Away team = 4.4 rpg, 0.300 BABIP).  Since the away team bats in the 9th inning every game, I used them as the guinea pigs.  I hard-coded every single pitcher/hitter matchup for their team to have the same BABIP no matter what.  All other variables were held the same.  I would simulate 2.5 million games with the away team having a BABIP of 0.300 in one trial and then turn around and simulate 2.5 million games with the away team having a BABIP of 0.301 etc... then look at the results and see how the change in BABIP effected the total runs scored of the away team.  Now, I didn't simulate every single BABIP from 0.000 to 1.000 but I did simulate every BABIP from 0.300 to 0.340 and many of the points in between there and 0.000 and 1.000 in order to get a good graph of the relationship.

The graph above shows the runs scored for the Away team on the y-axis and their BABIP on the x-axis. This graph gives you a good look at how the run totals change for all values of team BABIP from 0.000 to 1.000. When looking at the entire BABIP spectrum the plot looks non-linear.

Next up (below) is a graph showing the same thing but zooming in on the more common BABIP range (from 0.290 to 0.350) and as you can tell the plot now becomes linear for all practical purposes.

Now let's take a look at which BABIP total Tom Tango's 0.02 run/game for a 0.001 of BABIP comes in at. The plot below gives you a pretty good idea.

You can tell from the plot that the 0.02 (run per game, for 1 point of BABIP) is somewhere in between 0.326 and 0.336. Anything below this range and you are looking at a number less than 0.02 for what 1 point of BABIP is worth and anything greater than 0.336 you are looking at a number greater than 0.02 for what 1 point of BABIP is worth.  This graph does have some noise in it, but you can still get a good idea of the trend.

So there is no one right answer without knowing the run environment you are in and what original BABIP you are using as a baseline.  If you use a run environment of around 4.4 runs per game (for the Away team) and a BABIP of 0.300 then one point (0.001) of BABIP is worth 0.0175 runs per game.  You don't see the 0.02 value until you raise the BABIP to over 0.326.

For the extremes you will see a runs/game value of around 0.01 when the BABIP is pegged at 0.150.  A BABIP of 0.400 will make one extra point of BABIP worth 0.025 runs per game.  A BABIP of 0.900 will make one extra point of BABIP worth 0.07 runs per game.

When you get to the extremes the type of hitters and pitchers you have plays a bigger role in what a point of BABIP is worth.  When you use a very small BABIP number, hitters who hit a lot of HRs become more important to offense as almost any ball put into play will become an out.  The defense will want a pitcher who does not have a tendancy to give up HRs.  When you use a very large BABIP number, hitters who do not strike-out often become very valuable as not many outs are made on balls in play and of course the defense will want a pitcher who strikes out a lot of hitters.

And finally, here is a table showing how often the Away team won the game based on what their BABIP was pegged to.

BABIP	Away Runs	Win %
0.000	1.3881	16.29%
0.100	1.9519	24.59%
0.200	2.9111	37.45%
0.300	4.3959	54.38%
0.400	6.5478	72.20%
0.500	9.5178	86.66%
0.600	13.4578	95.28%
0.700	18.5295	98.8766%
0.800	24.6065	99.8373%
0.900	31.3568	99.9871%
1.000	38.8769	99.9997%

2013 Vegas Park Factors

There are more than a few ways of calculating park factors.  The simplest system of all and the one that tells the best story of which park played as a hitter or pitchers park based on the empirical data (actual results) is the one where you simply divide runs per game at home scored by both teams by runs per game on the road scored by both teams.  ESPN does a great job of providing this data for previous seasons.

One problem with these year to year park factors (for runs scored) is that there is a ton of noise (variance) from year to year.  It is just very difficult to pin down what the true park factor should be for each park.  Some people like to take the previous two or three seasons and weight the more recent seasons heavier to come up with a number.  This is actually a safe way of doing it and one I usually prefer.

When it comes to betting on baseball run totals (over/unders) one needs a really good idea on what a stadiums' true park factor is.  From this base park factor number you can adjust up or down based off of weather or wind conditions if you like, but you need a good park factor number for each stadium first.  The Vegas sportsbooks obviously have their own numbers and if they don't you can easily reverse engineer the numbers that they used over the course of the season for each park.  All you need to do is take all of their run total numbers and adjust for juice to come up with an over/under number for each game.  Let's say you calculate that number as 7.25 runs scored.  You do this for all games and use this 7.25 (calculated number) as a substitute for the actual number of runs that were scored in that game and calculate each teams' park factor based off of this calculated number instead of the actual total number of runs scored.  In doing so, you can get a glimpse into what Vegas used as park factors for each team and then compare their park factors with the actual empirical number.  I calculate these Vegas park factors as the season progresses as kind of a sanity check against the park factors that I use in my day to day baseball game simulations.

Below is a look at each teams' Vegas park factor and Actual 2013 park factor and the difference between the two sorted by parks that Vegas had the run environment too low on.  Just because Vegas was off on a park factor may or may not mean they were dumb on selecting their park factor for that team as like I said above there is quite a bit of noise involved here.  But it would've obviously made for some good betting opportunities.

Team	Vegas PF	Actual 2013 PF	2013 Delta
Tigers	1.022	1.139	0.1167
Cubs	1.083	1.192	0.1091
Phillies	1.023	1.107	0.0838
Blue Jays	1.044	1.118	0.0743
Mariners	0.918	0.991	0.0733
Marlins	0.959	1.030	0.0715
Royals	1.016	1.082	0.0661
Astros	1.009	1.074	0.0652
Brewers	1.046	1.110	0.0642
Yankees	1.028	1.087	0.0590
Twins	0.975	1.020	0.0446
Nationals	0.969	1.013	0.0444
Rockies	1.239	1.273	0.0343
Orioles	1.038	1.057	0.0187
Angels	0.964	0.968	0.0036
Braves	0.955	0.956	0.0008
White Sox	1.003	0.998	-0.0050
Rays	0.941	0.931	-0.0103
Giants	0.889	0.869	-0.0204
Dodgers	0.896	0.868	-0.0279
Athletics	0.919	0.889	-0.0295
Reds	1.032	0.989	-0.0425
Indians	0.977	0.933	-0.0442
Padres	0.877	0.831	-0.0461
Pirates	0.961	0.907	-0.0535
Mets	0.941	0.867	-0.0736
Cardinals	0.979	0.892	-0.0868
Red Sox	1.083	0.960	-0.1227
Diamondbacks	1.098	0.974	-0.1237
Rangers	1.121	0.985	-0.1357

As a further exercise I computed the RMSE for the Vegas 2013 park factors against the actual park factors for the 2013, 2012 and 2011 seasons for the fun of it.

The RMSE (sum of the squares of the 32 park factor errors)... were.....
2013 = 0.1429
2012 = 0.4396
2011 = 0.2423
(these numbers are pre-square root)

You would expect to see the 2013 number be the lowest as that is what Vegas was predicting against.  The 2012 park factors had a lot of noise as there were a few crazy outliers bringing the error total up.  The 2011 park factors did pretty well, but about where you would expect it.

How Important Is Roster Flexibility

Let me make a simplified hypothetical situation to make this as easy as possible.  Let's say you have the choice between being the GM of one of these two teams.  Everything about these two teams is equal, except you know that Team A has a 6 WAR player and a 0 WAR player and Team B has a pair of 3 WAR players.  This is all we know about these two teams, assume everything else is equal (contracts, payroll etc...).  Which of these two teams would you rather have and why?

Team A:  6+0
Team B: 3+3

Would you value the flexibility that Team A has given that they have a 0 WAR player that should be pretty easy to replace via free agency or trade?  Assume each team was allowed to increase their payroll a little bit by the same amount.  Which team would be able to improve quicker?

So what would it be.

Team A because of roster flexibility and the ease to improve.
Team B because of ???
Niether because there is no difference.

Cardinals vs Red Sox - World Series Game 6 Simulation Results

                                 Top 100 Most Likely Final Scores

Rank	Cardinals	Red Sox	Occurrences		Rank	Cardinals	Red Sox	Occurrences
1	2	3	46999		51	0	6	5999
2	1	2	42946		52	7	5	5618
3	3	4	38604		53	5	7	5295
4	3	2	31632		54	8	2	5002
5	2	1	29386		55	8	3	4855
6	1	3	26044		56	7	0	4782
7	4	5	25588		57	7	6	4773
8	4	3	25509		58	8	1	4687
9	3	1	24553		59	2	8	4549
10	0	1	24505		60	3	8	4438
11	2	4	24284		61	8	4	4241
12	4	2	23464		62	1	8	4058
13	4	1	19553		63	0	7	4032
14	0	2	18971		64	4	8	3684
15	1	4	18844		65	8	5	3471
16	2	0	17124		66	7	8	3422
17	5	2	16992		67	9	2	3249
18	2	5	16953		68	5	8	3121
19	5	3	16898		69	8	0	3114
20	5	4	16834		70	9	3	2932
21	3	5	16698		71	2	9	2878
22	1	0	16525		72	9	1	2862
23	0	3	15380		73	3	9	2745
24	3	0	15106		74	8	6	2736
25	5	1	14806		75	0	8	2612
26	5	6	14668		76	6	8	2582
27	1	5	13277		77	1	9	2539
28	4	0	13106		78	9	4	2513
29	6	2	11928		79	4	9	2273
30	0	4	11608		80	8	7	2170
31	6	3	11600		81	9	5	2157
32	3	6	11574		82	9	0	1906
33	2	6	10701		83	10	2	1880
34	6	1	10696		84	10	3	1799
35	6	4	10389		85	2	10	1736
36	4	6	10098		86	10	1	1706
37	5	0	9960		87	5	9	1703
38	6	5	9508		88	0	9	1692
39	1	6	9212		89	9	6	1669
40	0	5	8388		90	3	10	1632
41	7	2	8029		91	1	10	1556
42	7	3	7639		92	8	9	1538
43	6	7	7575		93	10	4	1538
44	6	0	7299		94	6	9	1491
45	7	1	7074		95	4	10	1390
46	2	7	6994		96	10	5	1237
47	3	7	6785		97	9	7	1228
48	7	4	6619		98	7	9	1145
49	4	7	6430		99	10	0	1117
50	1	7	6244		100	5	10	1078

World Series Remaining Game Odds

With a maximum of two games remaining in the 2013 World Series this is the last installment of the reverse engineered game odds.  The only unknown left is the odds for Game #7.  The Game #6 odds and the final series winner odds are both out and from those two knowns we can reverse engineer what the Game #7 odds are (or should be).

     Individual Game Odds

Game #	Red Sox	Cardinals
Game 1	100%	0%
Game 2	0%	100%
Game 3	0%	100%
Game 4	100%	0%
Game 5	100%	0%
Game 6	53.16%	46.84%
Game 7	55.75%	44.25%
Series	79.27%	20.73%

And using the nifty spreadsheet calculator that one of my readers made for me, we can also see the chances that each team wins the series in X number of games.  There are only three possible outcomes left obviously and they are the Red Sox winning in six or seven games or the Cardinals winning in seven games.  Here is another table showing those odds.

Result	Chance %	Odds
	79.27%
Red Sox in 4	0.0%	NA
Red Sox in 5	0.0%	NA
Red Sox in 6	53.16%	0.88
Red Sox in 7	26.11%	2.83
	20.73%
Cardinals in 4	0.0%	NA
Cardinals in 5	0.0%	NA
Cardinals in 6	0.0%	NA
Cardinals in 7	20.73%	3.82

Red Sox vs Cardinals - World Series Game 5 Simulation Results

                                       Top 100 Most Likely Final Scores

Rank	Red Sox	Cardinals	Occurrences		Rank	Red Sox	Cardinals	Occurrences
1	1	2	4605		51	7	3	565
2	2	3	4516		52	7	1	558
3	3	4	3443		53	6	0	552
4	2	1	3214		54	1	8	502
5	3	2	3180		55	5	7	495
6	0	1	2873		56	7	5	485
7	1	3	2820		57	3	8	453
8	4	3	2422		58	7	6	424
9	3	1	2362		59	0	8	418
10	2	4	2359		60	2	9	396
11	1	4	2255		61	7	0	377
12	0	2	2239		62	8	3	375
13	4	5	2233		63	8	2	374
14	1	0	2142		64	1	9	367
15	4	2	2117		65	4	8	351
16	0	3	1986		66	8	1	348
17	2	0	1793		67	3	9	343
18	4	1	1771		68	5	8	316
19	2	5	1748		69	8	4	308
20	0	4	1672		70	0	9	304
21	1	5	1659		71	8	5	277
22	3	5	1558		72	7	8	276
23	5	4	1533		73	4	9	256
24	3	0	1512		74	9	2	254
25	5	2	1481		75	8	0	249
26	5	3	1471		76	1	10	231
27	5	1	1253		77	8	6	228
28	2	6	1249		78	2	10	225
29	5	6	1216		79	6	8	225
30	0	5	1188		80	9	3	216
31	4	0	1167		81	9	1	211
32	1	6	1150		82	0	10	204
33	3	6	1132		83	3	10	198
34	6	3	1003		84	8	7	198
35	6	2	958		85	9	4	193
36	4	6	918		86	5	9	165
37	1	7	912		87	9	5	164
38	6	4	857		88	4	10	162
39	0	6	854		89	9	0	159
40	6	5	844		90	10	3	149
41	5	0	828		91	6	9	144
42	2	7	814		92	2	11	143
43	6	1	792		93	10	1	141
44	3	7	704		94	1	11	137
45	4	7	636		95	9	6	135
46	0	7	606		96	8	9	128
47	7	4	597		97	10	2	127
48	6	7	595		98	9	7	123
49	7	2	578		99	0	11	118
50	2	8	571		100	3	11	113

Red Sox vs Cardinals - World Series Game 4 Simulation Results

                                       Top 100 Most Likely Final Scores

Rank	Red Sox	Cardinals	Occurrences		Rank	Red Sox	Cardinals	Occurrences
1	2	3	4134		51	7	1	665
2	1	2	3603		52	7	6	629
3	3	4	3391		53	5	7	598
4	3	2	2866		54	6	0	569
5	2	1	2674		55	0	7	561
6	4	3	2535		56	2	8	542
7	1	3	2373		57	8	3	530
8	4	5	2328		58	8	2	528
9	2	4	2280		59	3	8	514
10	3	1	2163		60	1	8	493
11	4	2	2153		61	8	4	465
12	1	4	1964		62	8	5	447
13	0	1	1903		63	4	8	444
14	5	4	1774		64	8	1	441
15	4	1	1701		65	7	0	433
16	2	5	1685		66	1	9	420
17	0	2	1672		67	0	8	376
18	3	5	1652		68	7	8	376
19	5	3	1643		69	5	8	370
20	5	2	1619		70	3	9	366
21	1	0	1593		71	2	9	360
22	2	0	1562		72	8	6	351
23	0	3	1544		73	9	3	340
24	1	5	1534		74	8	0	315
25	5	6	1496		75	9	2	308
26	5	1	1372		76	9	4	301
27	3	0	1342		77	6	8	300
28	0	4	1250		78	9	1	292
29	6	3	1209		79	4	9	290
30	2	6	1175		80	8	7	272
31	3	6	1150		81	2	10	251
32	6	2	1118		82	1	10	240
33	6	4	1108		83	0	9	233
34	1	6	1085		84	9	5	221
35	6	5	1083		85	4	10	214
36	4	0	1059		86	3	10	207
37	0	5	1044		87	10	2	206
38	4	6	1023		88	5	9	205
39	6	1	909		89	10	3	200
40	6	7	817		90	8	9	196
41	5	0	807		91	9	6	196
42	1	7	803		92	6	9	182
43	2	7	793		93	10	4	179
44	3	7	779		94	10	1	172
45	7	4	761		95	2	11	158
46	0	6	759		96	3	11	157
47	7	3	759		97	9	0	157
48	4	7	713		98	9	7	149
49	7	2	698		99	0	10	148
50	7	5	667		100	10	5	141

Red Sox vs Cardinals - World Series Game Three Simulation Results

                                       Top 100 Most Likely Final Scores

Rank	Red Sox	Cardinals	Occurrences		Rank	Red Sox	Cardinals	Occurrences
1	2	3	42948		51	7	5	5988
2	1	2	39386		52	4	7	5746
3	3	4	34579		53	8	2	5340
4	3	2	34437		54	8	3	5065
5	2	1	31669		55	7	0	4965
6	4	3	27558		56	7	6	4930
7	3	1	25972		57	5	7	4921
8	1	3	25255		58	8	1	4567
9	4	2	24954		59	8	4	4314
10	4	5	23285		60	2	8	4309
11	2	4	23199		61	0	7	4220
12	0	1	21848		62	3	8	3973
13	4	1	20504		63	1	8	3933
14	1	4	19894		64	8	5	3770
15	1	0	18953		65	9	2	3396
16	2	0	18407		66	4	8	3313
17	5	2	18295		67	9	3	3118
18	5	3	18030		68	8	0	3091
19	0	2	17869		69	7	8	3048
20	5	4	17791		70	8	6	2962
21	2	5	16750		71	9	1	2951
22	3	5	16213		72	5	8	2838
23	3	0	16131		73	9	4	2740
24	0	3	15911		74	0	8	2668
25	5	1	14740		75	2	9	2637
26	1	5	14168		76	3	9	2536
27	5	6	13207		77	1	9	2466
28	4	0	12717		78	8	7	2355
29	0	4	12516		79	6	8	2297
30	6	3	12475		80	9	5	2069
31	6	2	12189		81	9	0	2041
32	6	4	11058		82	4	9	2002
33	2	6	10874		83	10	2	1900
34	3	6	10684		84	10	3	1839
35	6	1	10537		85	10	1	1815
36	6	5	10108		86	9	6	1761
37	5	0	9662		87	2	10	1657
38	4	6	9613		88	10	4	1615
39	1	6	9589		89	0	9	1598
40	0	5	9303		90	5	9	1591
41	7	2	8209		91	3	10	1532
42	7	3	7940		92	1	10	1475
43	7	4	7458		93	6	9	1314
44	7	1	7135		94	10	5	1314
45	6	0	7028		95	10	0	1238
46	6	7	6862		96	9	7	1230
47	2	7	6788		97	8	9	1202
48	3	7	6475		98	4	10	1178
49	1	7	6343		99	11	2	1149
50	0	6	6312		100	11	3	1092

World Series Individual Game Odds Reverse Engineered

Here are the odds of each remaining World Series game based on the knowledge of the Vegas odds that each team wins the World Series and the Vegas odds for games 1,2 and 3.  The odds for games 1,2 and 3 give us a good approximation for the odds in games 5,6 and 7 and we can move the game four odds around in such a way that the chances for each team winning the series match the Vegas odds.

Here is a look at the table with the individual game odds.

Game #	Red Sox	Cardinals
Game 1	100.0%	0.0%
Game 2	0.0%	100.0%
Game 3	50.6%	49.4%
Game 4	49.3%	50.7%
Game 5	45.9%	54.1%
Game 6	52.0%	48.0%
Game 7	58.6%	41.4%
Series	52.4%	47.6%

And here is a table with the chances of the series ending with one team winning in X number of games.

Result	Chance %	Odds
	52.4%
Red Sox in 4	0.0%	NA
Red Sox in 5	11.5%	7.73
Red Sox in 6	19.0%	4.28
Red Sox in 7	22.0%	3.55
	47.6%
Cardinals in 4	0.0%	NA
Cardinals in 5	13.5%	6.38
Cardinals in 6	18.5%	4.40
Cardinals in 7	15.5%	5.43

Notes
- HFA of 4% is assumed
- Data was computed with spreadsheet provided by one of my readers.

World Series Individual Game Odds

Vegas has come out and given the Red Sox a 68.75% chance of winning the World Series.  So I am going to try to reverse engineer the odds of the remaining games as if we didn't know who the pitchers were, just where the games were being played (no advanced handicapping).  What we know is that the Red Sox were a 53.9% favorite in Game #1 and are a 53.4% favorite in Game #2.  Knowing the odds in Game #1 gives me a hint at the odds in Game #5 (assuming 4 man rotations and HFA of 4%), so I am going to subtract 8% from the Game #1 odds and give the Red Sox a 45.9% chance of winning Game #5.  I can do a similar thing with the Game #6 odds, as I can copy the Game #2 odds as that game will be played in the same park.  Now I just need to massage the numbers in games 3,4,5 and 7 in an attempt to make the Red Sox chances of winning come as close to 68.75% as possible.  The game 7 odds will be an 8% difference of the game 3 odds.

Using the nifty spreadsheet that my reader gave me in one of the previous similar exercises I did in the NLCS we come up with the following table of individual game odds needed to have the Red Sox be 68.75% favorites to win the World Series following the Game #1 results.  To take this to the next level you would break down the odds of games three and four by looking at the probably starting pitchers.  Where one of the two games would move up in odds, the other would need to move down.

Game #	Red Sox	Cardinals
Game 1	100.0%	0.0%
Game 2	53.4%	46.6%
Game 3	49.7%	51.2%
Game 4	49.7%	51.2%
Game 5	45.9%	51.2%
Game 6	53.4%	46.6%
Game 7	57.7%	43.2%
Series	68.7%	31.3%

And below is the table that shows the percent chances and odds of each possible result in the World Series.

Result	Chance %	Odds
	68.7%
Red Sox in 4	13.2%	6.58
Red Sox in 5	17.5%	4.70
Red Sox in 6	20.1%	3.98
Red Sox in 7	17.9%	4.59
	31.3%
Cardinals in 4	0.0%	NA
Cardinals in 5	6.4%	14.58
Cardinals in 6	11.8%	7.47
Cardinals in 7	13.1%	6.62

Cardinals vs Red Sox - World Series Game #2 Simulation

                                     Top 100 Most Likely Final Scores

Rank	Cardinals	Red Sox	Occurrences		Rank	Cardinals	Red Sox	Occurrences
1	2	3	4554		51	0	6	629
2	1	2	4157		52	7	5	570
3	3	4	3803		53	5	7	565
4	3	2	3029		54	8	3	558
5	2	1	2810		55	7	6	522
6	1	3	2629		56	8	1	490
7	4	5	2596		57	8	2	483
8	4	3	2491		58	7	0	470
9	3	1	2392		59	3	8	466
10	2	4	2380		60	1	8	463
11	0	1	2326		61	8	4	442
12	4	2	2278		62	2	8	431
13	1	4	1864		63	0	7	403
14	0	2	1855		64	4	8	379
15	4	1	1805		65	7	8	351
16	2	5	1736		66	8	5	351
17	5	4	1714		67	9	3	334
18	5	3	1690		68	5	8	331
19	3	5	1684		69	8	0	322
20	5	2	1657		70	9	2	322
21	2	0	1541		71	3	9	299
22	0	3	1523		72	9	1	298
23	1	0	1516		73	8	6	297
24	5	6	1497		74	2	9	286
25	5	1	1447		75	6	8	274
26	3	0	1417		76	0	8	263
27	1	5	1361		77	1	9	259
28	0	4	1186		78	9	5	256
29	4	0	1153		79	4	9	252
30	6	2	1152		80	8	7	248
31	3	6	1149		81	9	4	248
32	6	3	1136		82	10	2	213
33	2	6	1122		83	10	3	203
34	6	4	1029		84	2	10	202
35	6	1	1023		85	10	1	198
36	4	6	1019		86	9	0	193
37	6	5	982		87	3	10	179
38	1	6	926		88	0	9	177
39	5	0	925		89	10	4	175
40	7	2	858		90	5	9	171
41	0	5	854		91	1	10	170
42	7	3	805		92	6	9	169
43	6	7	782		93	8	9	155
44	7	1	750		94	4	10	150
45	2	7	708		95	9	6	150
46	7	4	685		96	10	5	146
47	3	7	683		97	10	0	135
48	4	7	671		98	9	7	126
49	1	7	651		99	2	11	123
50	6	0	639		100	5	10	120

Dodgers vs Cardinals - NLCS Game 6 Simulation Results

                                        Top 100 Most Likely Final Scores

Rank	Dodgers	Cardinals	Occurrences		Rank	Dodgers	Cardinals	Occurrences
1	1	2	55644		51	2	7	3958
2	2	3	47399		52	1	7	3864
3	2	1	46487		53	8	3	3677
4	0	1	40899		54	6	7	3640
5	3	2	39392		55	3	7	3525
6	1	0	37008		56	7	5	3487
7	3	1	35558		57	4	7	3011
8	2	0	34242		58	9	1	2871
9	3	4	31401		59	0	7	2784
10	3	0	29748		60	8	4	2772
11	4	1	26597		61	7	6	2716
12	4	2	26194		62	9	2	2708
13	4	3	24893		63	9	0	2676
14	1	3	24725		64	2	8	2414
15	0	2	24467		65	5	7	2296
16	4	0	22782		66	1	8	2281
17	2	4	18654		67	9	3	2213
18	5	1	18438		68	8	5	2054
19	5	2	17797		69	3	8	1993
20	4	5	17141		70	10	1	1771
21	0	3	16860		71	0	8	1766
22	1	4	16560		72	4	8	1679
23	5	0	16291		73	10	0	1617
24	5	3	15305		74	9	4	1580
25	5	4	13258		75	1	9	1513
26	6	1	12394		76	7	8	1504
27	2	5	11494		77	10	2	1499
28	0	4	11377		78	2	9	1447
29	6	2	11352		79	8	6	1425
30	6	0	11028		80	5	8	1321
31	3	5	10829		81	3	9	1283
32	1	5	10001		82	10	3	1239
33	6	3	9689		83	8	7	1181
34	5	6	8201		84	9	5	1105
35	7	1	7817		85	0	9	1085
36	6	4	7616		86	6	8	1013
37	0	5	7334		87	11	1	1009
38	7	0	7134		88	4	9	925
39	7	2	7117		89	11	0	916
40	2	6	6745		90	10	4	906
41	6	5	6394		91	11	2	875
42	3	6	6350		92	2	10	870
43	1	6	6199		93	1	10	847
44	7	3	5984		94	9	6	808
45	4	6	5486		95	11	3	770
46	8	1	5063		96	5	9	711
47	7	4	4682		97	3	10	698
48	0	6	4511		98	0	10	648
49	8	2	4507		99	10	5	603
50	8	0	4448		100	4	10	568

The Odds Couple of Games

Vegas now lists the Dodgers chances of winning the NLCS as 23.2% and gives them a 55.7% chance of winning Game #6 in which Clayton Kershaw pitches. From those two pieces of information we can reverse engineer the Dodgers odds in Game #7. Below is a table showing this information. The math is getting a lot easier with only two possible games remaining.

Game	LAD Pitcher	STL Pitcher	LAD Win%
6	C.Kershaw	M.Wacha	55.70%
7	H.Ryu	A.Wainwright	41.70%
NLCS Winner			23.20%

Oddly Enough for The Dodgers

Not hope remains for the Dodgers in the NLCS. Vegas odds give the Dodgers a 13.6% chance of winning the NLCS, a feat that would involve winning the last three games of the series, with the last two games being played in St.Louis. The Dodgers are a generous 61.8% Vegas favorite in Game #5 and knowing that and the 13.6% number we can reverse engineer the probable odds of Game #6 and Game #7. Also we can easily calculate the odds that the series ends in a 5, 6 or 7 game victory for the Cardinals or a seven game victory for the Dodgers.

Reverse Engineered Game Odds

Game	LAD Starter	LAD Win%
5	Z.Greinke	61.8
6	C.Kershaw	56.0
7	H.Ryu	39.2

Series Result Odds

Result	% Chance
Cardinals in 5	38.2%
Cardinals in 6	27.2%
Cardinals in 7	21.0%
Dodgers in 7	13.6%

Cardinals vs Dodgers - NLCS Game 5 Simulation Results

                                      Top 100 Most Likely Final Scores

Rank	Cardinals	Dodgers	Occurrences		Rank	Cardinals	Dodgers	Occurrences
1	2	3	47717		51	6	0	5803
2	1	2	46491		52	7	4	5517
3	3	4	36734		53	2	8	5216
4	2	1	31634		54	1	8	5031
5	3	2	31556		55	7	5	4969
6	0	1	28974		56	5	7	4517
7	1	3	28481		57	3	8	4446
8	2	4	24433		58	7	6	4316
9	3	1	24073		59	8	2	4254
10	4	3	24073		60	7	0	4063
11	4	5	23300		61	8	3	3917
12	0	2	23094		62	8	1	3825
13	1	4	22658		63	0	8	3790
14	4	2	21292		64	4	8	3514
15	0	3	20818		65	8	4	3485
16	1	0	19501		66	2	9	3222
17	2	0	17878		67	1	9	3154
18	2	5	17871		68	7	8	2988
19	4	1	17347		69	8	5	2869
20	1	5	16348		70	9	2	2760
21	0	4	16344		71	3	9	2751
22	3	5	16179		72	5	8	2712
23	5	4	15200		73	8	0	2675
24	5	3	15119		74	9	3	2551
25	3	0	14883		75	9	1	2425
26	5	2	14625		76	0	9	2381
27	5	6	12964		77	8	6	2377
28	5	1	12424		78	4	9	2100
29	0	5	12041		79	9	4	2087
30	2	6	11533		80	6	8	2072
31	4	0	11337		81	2	10	1981
32	1	6	11299		82	8	7	1977
33	3	6	10786		83	1	10	1916
34	6	2	9871		84	9	5	1814
35	6	3	9760		85	9	0	1720
36	4	6	9252		86	3	10	1691
37	6	4	9013		87	10	2	1659
38	6	1	8731		88	10	3	1611
39	0	6	8642		89	5	9	1537
40	6	5	8585		90	10	1	1487
41	5	0	8043		91	9	6	1419
42	2	7	7781		92	0	10	1393
43	1	7	7553		93	6	9	1278
44	3	7	6874		94	10	4	1272
45	7	3	6445		95	4	10	1264
46	7	2	6319		96	8	9	1244
47	6	7	6308		97	2	11	1167
48	4	7	5914		98	1	11	1150
49	7	1	5876		99	9	7	1067
50	0	7	5811		100	3	11	1039

A Case For Ricky Nolasco Game Four NLCS

In case you've been on the moon or busy watching soccer there has been some discussion in Dodgers-Land about whether or not to skip Ricky Nolasco in Game #4 of the NLCS or bring back Zack Greinke to pitch on short rest. I decided to take a back of the envelope look at which decision is the correct way to go. My exercise won't go into the nitty-gritty details which would add a little more precision to the numbers but it will provide a good framework and maybe some guidance into what the best decision is.

In general there is a 0.5 RA/9ip penalty for pitching on three days rest and there is probably a little penalty for pitching on too many days rest but let's leave that number unknown for now. What I did is made a table with the RA/9 expectancies for each of the Dodgers four starting pitchers. Then output tables showing which starting pitching arrangement looks best. The RA/9ip estimates can be changed if you don't agree with them, this is just the framework and with the framework you can tell how bad of a pitcher Nolasco must be to make skipping him and starting Greinke (and even perhaps Kershaw and Ryu) on short rest.

Input Table

Pitcher	RA/9IP
Kershaw	2.25
Greinke	3
Ryu	3.5
Nolasco	4

Now let's come up with some rotation arrangements. Let's first start off with the one where Nolasco pitches Game #4 and Greinke, Kershaw and Ryu all pitch on regular rest.

Game	Rest	LAD Starter	RA/9
4	Normal	Nolasco	4
5	Normal	Greinke	3
6	Normal	Kershaw	2.25
7	Normal	Ryu	3.5
		Total	12.75

Now let's see what happens if Nolasco is skipped and Greinke (G4, G7), Kershaw (G5) and Ryu (G6) all pitch on short rest. Notice the 0.5 RA/9ip penalty applied.

Game	Rest	LAD Starter	RA/9
4	Short	Greinke	3.5
5	Short	Kershaw	2.75
6	Short	Ryu	4
7	Short	Greinke	3.5
		Total	13.75

This particular arrangement does not fair too well as you are applying four 0.5 RA/9ip penalties, adding up to 2.0 RA/9ip over four games. Nolasco's projection MUST be very very bad for this option to win out. How bad? I will visit that later.

Now onto the arrangement where Zack Greinke pitches Game #4 on short rest then Nolasco pitches Game #5 and Kershaw and Ryu pitch the last two games on full rest. I call this the "Rearranging The Deck Chairs" option.

Game	Rest	LAD Starter	RA/9
4	Short	Greinke	3.5
5	Normal	Nolasco	4
6	Normal	Kershaw	2.25
7	Normal	Ryu	3.5
		Total	13.25

This option always loses out to the first option as you are just swapping Game #4 and Game #5 starters and adding a penalty to Greinke's start. This option is stupid.

So it comes down to the first two options and the first option will win out unless you think that Nolasco is a terrible pitcher. Just how terrible in terms of RA/9ip? And you can feel free to combine Nolasco's RA/9ip with that of Volquez if you think they will tag team their start. Only good thing about that is that you can get an early pinch hitter at-bat in the game. But let's get back to the question of how bad would Nolasco's RA/9ip projection have to be to make the second option a better one than the third. The break even point for Nolasco's RA/9ip projection is 5.0. If you think his RA/9ip projection is worse than 5.0 then the second option would be better and you would go with a three man rotation. Of course there are some other minor things to take into consideration, so you could add or subtract those in to the RA/9ip projections but this exercise gives you an idea for which rotation arrangement is best.

I think the Dodgers should start Nolasco and if he isn't terribly sharp or being hit hard to pinch hit for him in either his first or second at-bat and then to use Volquez until he bats and then to let the bullpen finish out the game. Hopefully, you won't go extra innings as you will be using a lot of your bullets early on in the game.

Cardinals vs Dodgers - Simulation Results NLCS Game #4

                                           Top 100 Most Likely Final Scores

Rank	Cardinals	Dodgers	Occurrences		Rank	Cardinals	Dodgers	Occurrences
1	2	3	47593		51	4	7	5743
2	1	2	45843		52	7	0	5119
3	3	4	37546		53	7	5	5073
4	3	2	32889		54	8	2	4861
5	2	1	32175		55	5	7	4685
6	0	1	26993		56	8	1	4659
7	1	3	26242		57	8	3	4645
8	3	1	25777		58	2	8	4494
9	4	3	24897		59	7	6	4422
10	4	5	23715		60	0	7	4222
11	2	4	23270		61	1	8	4010
12	4	2	23148		62	8	4	3910
13	0	2	20166		63	3	8	3894
14	1	4	20038		64	4	8	3309
15	1	0	19628		65	8	0	3294
16	4	1	19421		66	8	5	3151
17	2	0	18995		67	9	2	3124
18	0	3	16564		68	7	8	3084
19	3	0	16546		69	9	1	3048
20	5	2	16208		70	9	3	2906
21	2	5	16185		71	5	8	2835
22	3	5	16180		72	0	8	2710
23	5	3	16170		73	2	9	2671
24	5	4	16055		74	8	6	2535
25	5	1	14543		75	1	9	2514
26	1	5	14020		76	3	9	2456
27	5	6	13413		77	9	4	2441
28	4	0	13388		78	6	8	2209
29	0	4	12681		79	9	0	2171
30	6	2	11328		80	8	7	2043
31	6	3	10590		81	10	2	2034
32	2	6	10570		82	4	9	2001
33	3	6	10537		83	9	5	1925
34	6	1	10135		84	10	1	1837
35	5	0	9768		85	10	3	1737
36	6	4	9653		86	2	10	1716
37	1	6	9428		87	0	9	1704
38	0	5	9345		88	3	10	1559
39	4	6	9132		89	1	10	1506
40	6	5	8882		90	5	9	1484
41	7	2	7527		91	10	4	1482
42	6	0	7235		92	9	6	1427
43	7	1	7133		93	8	9	1369
44	7	3	7039		94	10	0	1353
45	2	7	6749		95	6	9	1222
46	6	7	6682		96	4	10	1202
47	0	6	6512		97	9	7	1172
48	3	7	6264		98	11	2	1167
49	1	7	6150		99	11	1	1128
50	7	4	6137		100	10	5	1119

Updates NLCS Individual Game Odds

Here is an updated list of the individual game odds for the remaining games of the NLCS. As a reminder, the way the game odds are calculated is take the Vegas odds of the Cardinals winning the NLCS, which the last time I looked was (-350, +290) 76.19% chance of winning. We can give the Dodgers a 0% chance of winning for the games they already lost and we can input a win probability of 47.4% for Game #3 as those odds have already been published. Now to figure out the odds of the remaining games (Games 4-7) we need to adjust them until the string of games gives us a 23.81% chance of the Dodgers winning the series. To do this, I used the nifty excel spreadsheet that one of my readers gave me in the comments of the previous post on this topic. While these won't be the likely odds for Games four thru seven they are good "ballpark" estimates. And if you don't agree with any of these game odds, that is fine... but you will need to adjust the odds of some of the other games to even out any changes you made one way or the other.

Game	Away Starter	Home Starter	Dodgers Odds
1	Zack Greinke	Joe Kelly	0.0%
2	Clayton Kershaw	Michael Wacha	0.0%
3	Adam Wainwright	Hyun-Jin Ryu	47.4%
4	Shelby Miller	Ricky Nolasco	59.0%
5	Joe Kelly	Zack Greinke	65.0%
6	Clayton Kershaw	Michael Wacha	57.0%
7	Hyun-Jin Ryu	Adam Wainwright	42.0%
	Total		23.8%

Cardinals vs Dodgers - NLCS Game #3 Simulation Results

                                     Top 100 Most Likely Final Scores

Rank	Cardinals	Dodgers	Occurrences		Rank	Cardinals	Dodgers	Occurrences
1	1	2	5588		51	1	7	409
2	2	3	4837		52	2	7	402
3	2	1	4349		53	8	3	386
4	0	1	4108		54	3	7	375
5	3	2	3616		55	6	7	366
6	3	1	3297		56	7	5	365
7	1	0	3264		57	4	7	356
8	3	4	3223		58	9	2	321
9	2	0	3041		59	9	0	320
10	1	3	2654		60	9	1	319
11	4	2	2591		61	8	4	304
12	3	0	2521		62	5	7	286
13	0	2	2511		63	0	7	285
14	4	3	2464		64	7	6	261
15	4	1	2379		65	2	8	253
16	4	0	2025		66	9	3	251
17	2	4	2015		67	8	5	248
18	0	3	1830		68	1	8	227
19	4	5	1823		69	3	8	220
20	5	1	1790		70	10	1	217
21	1	4	1746		71	10	0	192
22	5	2	1684		72	10	2	184
23	5	3	1571		73	9	4	174
24	5	0	1423		74	0	8	169
25	5	4	1419		75	4	8	162
26	2	5	1273		76	8	6	160
27	6	1	1213		77	7	8	158
28	0	4	1209		78	2	9	156
29	3	5	1180		79	1	9	151
30	1	5	1149		80	10	3	137
31	6	2	1142		81	11	1	132
32	6	0	998		82	8	7	131
33	6	3	978		83	5	8	126
34	5	6	957		84	9	5	119
35	6	4	813		85	3	9	117
36	0	5	794		86	10	4	117
37	7	1	788		87	11	2	115
38	7	2	769		88	11	0	110
39	3	6	731		89	11	3	107
40	1	6	725		90	4	9	102
41	2	6	672		91	6	8	101
42	7	0	670		92	0	9	94
43	6	5	633		93	10	5	91
44	7	3	606		94	9	6	90
45	4	6	605		95	3	10	80
46	8	1	557		96	2	10	78
47	0	6	536		97	12	0	73
48	7	4	497		98	9	7	68
49	8	2	462		99	10	6	68
50	8	0	451		100	12	2	68