St Louis Cardinals - Most Optimal 2015 Lineups

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I am using my simulator that plays actual baseball games to find what it believes are the most optimal lineups for the 2015 St Louis Cardinals.  I started out with over 10,000 permutations of lineups, a group that was filtered to remove such things as too many left handed hitters hitting back to back or the pitcher not hitting 8th or 9th etc... and I slowly widdled it down to the top 50 lineups.  I also compared the best lineup against the lineup that MLB Depth Charts shows as a likely lineup and also one of the worst lineups to see what kind of spread there is.  The top 50 lineups all came within a half of a win per 162 games so really anything in that range is pretty good.  When you start nearing a full win differential with the top lineup then you definitely have problems.  I typically simulated each lineup over 1 million times which eliminated a large portion of the random noise and I did so only against a right handed pitcher.  Below are a list of the top 50 lineups and a batting order spot frequence table, where you can see how many times each player appeared in each of the top 50 lineup.

                                       Top 50 Most Optimal Lineups

Rank	Lineup	Wins/162 Behind
1	Heyward-Carpenter-Holliday-Adams-Wong-Molina-Peralta-Pitcher-Jay	0
2	Carpenter-Heyward-Holliday-Adams-Wong-Molina-Peralta-Pitcher-Jay	0.014
3	Wong-Jay-Holliday-Carpenter-Heyward-Peralta-Adams-Molina-Pitcher	0.015
4	Carpenter-Heyward-Holliday-Adams-Wong-Peralta-Molina-Pitcher-Jay	0.032
5	Heyward-Jay-Holliday-Carpenter-Adams-Peralta-Molina-Pitcher-Wong	0.066
6	Wong-Heyward-Holliday-Carpenter-Adams-Peralta-Molina-Pitcher-Jay	0.086
7	Heyward-Jay-Holliday-Carpenter-Adams-Molina-Peralta-Pitcher-Wong	0.102
8	Heyward-Jay-Holliday-Carpenter-Adams-Peralta-Wong-Molina-Pitcher	0.120
9	Jay-Heyward-Holliday-Carpenter-Adams-Peralta-Molina-Pitcher-Wong	0.131
10	Wong-Jay-Holliday-Carpenter-Heyward-Molina-Adams-Peralta-Pitcher	0.151
11	Jay-Heyward-Holliday-Carpenter-Adams-Peralta-Wong-Molina-Pitcher	0.167
12	Jay-Heyward-Holliday-Carpenter-Wong-Peralta-Adams-Molina-Pitcher	0.171
13	Jay-Heyward-Holliday-Carpenter-Adams-Molina-Peralta-Pitcher-Wong	0.175
14	Heyward-Carpenter-Holliday-Adams-Wong-Peralta-Jay-Molina-Pitcher	0.184
15	Carpenter-Jay-Holliday-Adams-Heyward-Peralta-Wong-Molina-Pitcher	0.199
16	Jay-Heyward-Holliday-Adams-Carpenter-Peralta-Wong-Molina-Pitcher	0.200
17	Heyward-Jay-Holliday-Adams-Carpenter-Peralta-Wong-Molina-Pitcher	0.209
18	Wong-Jay-Peralta-Carpenter-Heyward-Holliday-Adams-Molina-Pitcher	0.243
19	Heyward-Adams-Holliday-Carpenter-Wong-Molina-Peralta-Pitcher-Jay	0.247
20	Carpenter-Heyward-Holliday-Adams-Jay-Peralta-Molina-Pitcher-Wong	0.253
21	Heyward-Wong-Holliday-Adams-Carpenter-Peralta-Molina-Pitcher-Jay	0.257
22	Jay-Wong-Holliday-Carpenter-Heyward-Molina-Adams-Peralta-Pitcher	0.266
23	Heyward-Adams-Holliday-Carpenter-Wong-Peralta-Molina-Pitcher-Jay	0.269
24	Heyward-Jay-Holliday-Carpenter-Adams-Molina-Wong-Peralta-Pitcher	0.269
25	Wong-Jay-Molina-Carpenter-Heyward-Holliday-Adams-Peralta-Pitcher	0.284
26	Jay-Carpenter-Holliday-Heyward-Adams-Peralta-Molina-Pitcher-Wong	0.286
27	Heyward-Carpenter-Holliday-Adams-Molina-Wong-Peralta-Pitcher-Jay	0.286
28	Jay-Carpenter-Holliday-Adams-Heyward-Peralta-Molina-Pitcher-Wong	0.288
29	Heyward-Holliday-Carpenter-Adams-Peralta-Wong-Molina-Pitcher-Jay	0.289
30	Carpenter-Heyward-Holliday-Adams-Wong-Molina-Jay-Peralta-Pitcher	0.292
31	Jay-Adams-Holliday-Carpenter-Heyward-Peralta-Wong-Molina-Pitcher	0.299
32	Heyward-Wong-Holliday-Carpenter-Adams-Peralta-Jay-Molina-Pitcher	0.305
33	Wong-Carpenter-Holliday-Adams-Heyward-Peralta-Molina-Pitcher-Jay	0.310
34	Carpenter-Jay-Holliday-Adams-Heyward-Peralta-Molina-Pitcher-Wong	0.310
35	Peralta-Heyward-Carpenter-Holliday-Adams-Wong-Molina-Pitcher-Jay	0.317
36	Jay-Carpenter-Holliday-Heyward-Adams-Peralta-Wong-Molina-Pitcher	0.326
37	Jay-Wong-Molina-Carpenter-Heyward-Holliday-Adams-Peralta-Pitcher	0.327
38	Carpenter-Heyward-Holliday-Adams-Jay-Peralta-Wong-Molina-Pitcher	0.327
39	Wong-Carpenter-Holliday-Adams-Heyward-Peralta-Jay-Molina-Pitcher	0.343
40	Jay-Carpenter-Holliday-Adams-Heyward-Molina-Wong-Peralta-Pitcher	0.348
41	Jay-Heyward-Holliday-Adams-Carpenter-Molina-Peralta-Pitcher-Wong	0.353
42	Wong-Adams-Holliday-Carpenter-Heyward-Peralta-Molina-Pitcher-Jay	0.372
43	Heyward-Holliday-Adams-Carpenter-Peralta-Wong-Molina-Pitcher-Jay	0.382
44	Carpenter-Heyward-Holliday-Adams-Wong-Peralta-Jay-Molina-Pitcher	0.388
45	Carpenter-Wong-Holliday-Adams-Heyward-Molina-Peralta-Pitcher-Jay	0.403
46	Peralta-Heyward-Adams-Holliday-Carpenter-Wong-Molina-Pitcher-Jay	0.433
47	Heyward-Carpenter-Holliday-Adams-Wong-Molina-Jay-Pitcher-Peralta	0.439
48	Heyward-Peralta-Carpenter-Adams-Holliday-Wong-Molina-Pitcher-Jay	0.469
49	Heyward-Wong-Holliday-Adams-Carpenter-Molina-Peralta-Pitcher-Jay	0.477
50	Carpenter-Heyward-Holliday-Adams-Molina-Wong-Peralta-Pitcher-Jay	0.485
..	..	..
MLBDC	Carpenter-Heyward-Holliday-Adams-Molina-Peralta-Jay-Wong-Pitcher	1.090
BAD	Adams-Peralta-Jay-Wong-Molina-Carpenter-Holliday-Heyward-Pitcher	3.661

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              Batting Order Frequence Table

	1st	2nd	3rd	4th	5th	6th	7th	8th	9th
Heyward	17	16	0	2	15	0	0	0	0
Carpenter	10	10	3	21	6	0	0	0	0
Holliday	0	2	42	2	1	3	0	0	0
Adams	0	4	2	25	12	0	7	0	0
Wong	8	6	0	0	10	7	10	0	9
Peralta	2	1	1	0	2	26	10	7	1
Molina	0	0	2	0	2	14	17	15	0
Jay	13	11	0	0	2	0	6	0	18
Pitcher	0	0	0	0	0	0	0	28	22

Synergy:
10 most common back to back occurrences in lineup.

Rank	Occurrences	Player 1	Player 2
1	32	Molina	Pitcher
2	28	Holliday	Adams
3	26	Pitcher	Jay
4	19	Heyward	Holliday
5	19	Holliday	Carpenter
6	19	Wong	Molina
7	17	Peralta	Pitcher
8	15	Carpenter	Heyward
9	15	Jay	Heyward
10	14	Pitcher	Wong

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10 most common back to back to back occurrences in lineup.

Rank	Occurrences	Player 1	Player 2	Player 3
1	16	Molina	Pitcher	Jay
2	13	Heyward	Holliday	Adams
3	13	Wong	Molina	Pitcher
4	12	Peralta	Molina	Pitcher
5	12	Pitcher	Jay	Heyward
6	10	Carpenter	Heyward	Holliday
7	10	Holliday	Carpenter	Adams
8	10	Peralta	Wong	Molina
9	10	Peralta	Pitcher	Jay
10t	9	Carpenter	Holliday	Adams
10t	9	Molina	Pitcher	Wong
10t	9	Pitcher	Wong	Jay

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                                         Analysis

Heyward:  Slots well at the top of the lineup as either the leadoff or second hitter.  With others better suited for the 3rd or 4th spot in the lineup, Heyward also slots in well as the 5th hitter but should not hit in the 6th thru 9th slots.

Carpenter: Surpsingly does well at cleanup along with Adams but also does well among the 1-2-5 spots like Heyward.  Carpenter shows a lot of lineup versatility if there is such a thing.

Holliday:  Should hit third.

Adams: The teams best cleanup hitter but can also move down to fifth in the lineup if need be.

Wong: No one great spot for Wong but he probably shows the most "lineup versatility" as anyone on the team  There are 6 lineup slots where Wong appeared at least 6 times.  When it comes to batting order spots, Wong is definitely the Nomad of the team.  Wong even makes 9 appearances hitting 9th, one spot behind the pitcher.

Peralta:  The simulator likes Peralta hitting 6th as he provides some pretty decent back of the lineup power.  He should definitely stay out of the top five spots in the lineup.

Molina:  6-7-8 are the best spots for Molina as only Heyward and Molina have a 14 or higher on their third most frequented lineup spot.

Jay:  Looks like the simulator likes Jay setting the table whether it be as the leadoff hitter or the quasi-leadoff hitter batting 9th.

Pitcher:  With Jay and Wong making appearances in the 9th spot the simulator pretty much calls it a crapshoot at hitting the pitcher 8th or 9th.  The pitcher should bat immediately after Molina does.

How Optimal Was The Cardinals 2014 Lineup

My simulator is a good tool for looking at optimal batting orders.  It can play tens of thousands and even millions (with a smaller set of games) of games while keeping the opponent static which can give you a good idea which lineups win more games.  Originally, taking an idea from the "straight arrows" over at The Book Blog, I decided to take the 2014 Dodgers most common lineup, that one can find over at the Baseball Reference website and compare how well that lineup does against tens of thousands of other possible lineup permutations.  Now I decided to move on to the St. Louis Cardinals mostly because I like doing this and the Cardinals have a very analytical friendly blog not one that spends endless hours discussing TV shows, taco trucks and their personal problems.  I did set some filters to cut down on the permutations, like I only looked at lineups where the pitcher hit 8th or 9th and where the best hitters didn't hit 8th or 9th and the worst hitters didn't hit 3rd or 4th etc...  I wanted to see how well one of the Cardinals most common lineups compared to what the simulator thought was the most optimal lineup.  Of course you can't expect any manager to be implementing the most optimal lineup but you also don't want him to be giving away fractions of wins each game that can add up over a 162 game season.  So down below, I list the Top 10 lineups along with the most common 2014 lineup in a table sorted by Wins/162 games.  I also list a table showing the frequency of where each player batted in each of the top 50 lineups.  I love the batting order frequency tables as they show you which players have a few dedicated positions in the order they should be hitting in and which players are more versatile in giving you an optimal lineup.  I used 2014 final season stats as the input projections for each hitter because that is for the most part similar to the data that the manager went by.  And I did all the simulations with the opposing team using a right handed starting pitcher.

Before we begin, here is the common Cardinals lineup that I compared against

Carpenter-Wong-Holliday-Craig-Molina-Adams-Peralta-Bourjos-Pitcher.


                                                      Top 10 Lineups

Rank	Lineup	Wins/162 Behind
1	Peralta-Carpenter-Holliday-Adams-Wong-Bourjos-Molina-Craig-Pitcher	0.000
2	Peralta-Carpenter-Adams-Holliday-Wong-Molina-Craig-Pitcher-Bourjos	0.081
3	Bourjos-Carpenter-Holliday-Adams-Peralta-Wong-Molina-Craig-Pitcher	0.092
4	Peralta-Carpenter-Adams-Holliday-Wong-Bourjos-Molina-Craig-Pitcher	0.118
5	Holliday-Carpenter-Peralta-Adams-Wong-Molina-Craig-Pitcher-Bourjos	0.119
6	Holliday-Carpenter-Adams-Peralta-Wong-Molina-Craig-Pitcher-Bourjos	0.158
7	Bourjos-Carpenter-Peralta-Holliday-Adams-Wong-Molina-Craig-Pitcher	0.161
8	Carpenter-Holliday-Adams-Peralta-Wong-Molina-Craig-Pitcher-Bourjos	0.162
9	Carpenter-Wong-Peralta-Holliday-Adams-Bourjos-Molina-Craig-Pitcher	0.206
10	Wong-Carpenter-Holliday-Peralta-Adams-Bourjos-Molina-Craig-Pitcher	0.216

And how did the Cardinals common lineup fair? Wel, it finished 2.07 wins/162 games worse than the top ranking lineup according to the simulator. Good thing that lineup wasn't actually used 162 times but it kind of gives you a general idea of how many wins the Cardinals manager may have been leaving off the table during the entire season if you trust the output of the simulator. When I did this for the Dodgers, Mattingly's most common lineup was only 0.84 wins/162 games off from the most optimal.

           Batting Order Frequency Table

	1st	2nd	3rd	4th	5th	6th	7th	8th	9th
Carpenter	15	19	7	6	3	0	0	0	0
Peralta	5	5	11	9	7	10	3	0	0
Holliday	3	6	17	17	6	1	0	0	0
Adams	0	5	12	18	10	3	2	0	0
Wong	9	5	0	0	22	12	2	0	0
Molina	0	3	3	0	0	12	31	0	1
Bourjos	18	7	0	0	2	12	4	0	7
Craig	0	0	0	0	0	0	8	42	0
Pitcher	0	0	0	0	0	0	0	8	42

Player by Player Analysis

Leadoff:  Matt Carpenter.  Matheny bats Carpenter leadoff and the simulator agrees that that is a good spot for him but he would be a little better off hitting second not first.  Good

Second:  Kolten Wong.  Matheny bats Wong second and the simulator doesn't think that is one of the top three places for him to hit.  It is not a totally glaring mistake as the simulator does have Wong hitting second in the 9th most optimal lineup but a better selection can be made here.  Below Average

Third:  Matt Holliday.  Matheny bats Holliday third and pretty much nails this one.  The simulator thinks that Holliday is a good third or fourth hitter in this lineup.  While Holliday does have some batting order versatility and could even slot into the second and fifth slots without deserving to be taken out behind the shed.  Great

Cleanup:  Allen Craig.  Matheny bats Craig cleanup and as you know Craig had an awful season.  To Matheny's credit he probably didn't know Craig was going to be this bad and stay this bad as long as he did but nonetheless batting Craig cleanup was not a good choice and if done enough times would be extremely costly.  The simulator liked Craig batting 8th, in front of the pitcher.  Bad

Fifth:  Yadier Molina:  Matheny bats Molina fifth and the simulator does not like him there at all.  The simulator likes the slow legged and power hitting catcher batting seventh or sixth at best where he can knock in runs and not get knocked in himself.  Bad

Sixth:  Matt Adams.  Matheny bats Adams sixth and the simulator thinks that is too low.  Mostly because the simulator already knows how bad Craig is.  The simulator likes Craig batting cleanup or in one of the other traditional power hitting slots (third or fifth).  Bad

Seventh:  Jhonny Peralta.  Matheny bats Peralta seventh and maybe he didn't know at the time he was building these lineups that Peralta would be one of his better hitters in 2014.  A look up above at the 'Batting Order Frequency' table and you really see how versatile Peralta is in this lineup.  Peralta hits leadoff in three of the four top optimal lineups and the simulator think the third, fourth and fifth slots are his best.  Good

Eighth:  Peter Bourjos.  Matheny puts the all glove not stick Bourjos eighth.  From above the simulator thinks that spot should be reserved for Allen Craig.  The simulator touts leadoff or ninth, which in and of itself is a second leadoff spot, as the most optimal placement for Bourjos.  Bourjos is leadoff in 2 of the top ten lineups and bats ninth in 4 of the top ten lineups.  There is often efficiency in batting the pitcher 8th if you have the right personnel to do it.  Bad

Ninth:  Pitcher.  The simulator has the pitcher batting 9th in 84% of the Top 50 lineups.  Good

Overall:
So overall Matheny did not do a very good job with this lineup but to his credit the simulator is using end of season (or after the fact) input projections.  If Matheny was hitting Craig cleanup when it was obvious he wasn't very good then he is greatly to blame, otherwise he gets some slack.  How much slack is up for debate.
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Giants vs Cardinals - NLCS Game 1 Simulation Results

Away	Home	Away Pitcher	Home Pitcher	Favorite	Away RS	Home RS	Win %	Total Runs
Giants	Cardinals	Madison Bumgarner	Adam Wainwright	Cardinals	3.23	3.31	53.97	6.54

                                        Top 100 Most Likely Final Scores

Rank	Giants	Cardinals	Occurences		Rank	Giants	Cardinals	Occurences
1	1	2	51984		51	0	7	5049
2	2	3	50320		52	7	5	4734
3	3	4	37246		53	4	7	4615
4	2	1	35587		54	7	0	4435
5	3	2	34541		55	8	2	4376
6	0	1	32271		56	1	8	4193
7	1	3	29215		57	7	6	4147
8	3	1	25493		58	2	8	4038
9	4	3	25184		59	8	1	4010
10	0	2	23776		60	8	3	3931
11	1	0	23609		61	5	7	3809
12	2	4	23466		62	3	8	3513
13	4	5	22704		63	8	4	3331
14	4	2	21990		64	0	8	3204
15	1	4	21599		65	8	0	2960
16	2	0	21129		66	9	2	2800
17	0	3	20184		67	4	8	2727
18	4	1	17931		68	8	5	2682
19	3	0	16465		69	7	8	2668
20	0	4	15865		70	9	3	2550
21	5	3	15630		71	1	9	2523
22	2	5	15629		72	9	1	2518
23	5	4	15317		73	2	9	2498
24	1	5	15007		74	8	6	2225
25	5	2	14922		75	5	8	2223
26	3	5	14872		76	3	9	2169
27	5	1	13014		77	9	4	2044
28	4	0	12785		78	0	9	2016
29	5	6	12400		79	9	0	1902
30	0	5	11196		80	8	7	1814
31	6	2	10140		81	10	2	1755
32	2	6	10126		82	6	8	1728
33	1	6	9963		83	4	9	1639
34	6	3	9545		84	10	1	1635
35	5	0	9207		85	9	5	1633
36	3	6	9180		86	2	10	1542
37	6	4	9084		87	1	10	1521
38	6	1	8977		88	10	3	1498
39	6	5	8413		89	10	4	1292
40	4	6	7885		90	3	10	1269
41	0	6	7762		91	5	9	1249
42	1	7	6557		92	9	6	1221
43	6	0	6550		93	10	0	1151
44	7	2	6505		94	0	10	1148
45	2	7	6297		95	8	9	1096
46	7	3	6227		96	11	2	1046
47	7	1	6142		97	4	10	1022
48	6	7	5924		98	11	3	988
49	3	7	5468		99	6	9	985
50	7	4	5384		100	10	5	961

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Note: Based off of 1 millions games simulated.
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Dodgers vs Cardinals - NLDS Game 4 Simulation Results

Away	Home	Away Pitcher	Home Pitcher	Favorite	Away RS	Home RS	Win %	Total Runs
Dodgers	Cardinals	Clayton Kershaw	Shelby Miller	Dodgers	3.92	2.76	60.78	6.67

                                      Top 100 Most Likely Final Scores

Rank	Dodgers	Cardinals	Occurrences		Rank	Dodgers	Cardinals	Occurrences
1	1	2	44148		51	0	5	5338
2	2	3	41490		52	9	1	5095
3	2	1	38620		53	7	5	4955
4	3	2	35107		54	9	0	4731
5	3	1	31492		55	9	2	4540
6	3	4	30381		56	8	4	4019
7	2	0	30194		57	2	7	4011
8	1	0	29112		58	7	6	3885
9	0	1	28103		59	3	7	3815
10	3	0	26348		60	4	7	3596
11	4	2	25349		61	9	3	3529
12	4	1	25304		62	1	7	3481
13	4	3	24420		63	0	6	3451
14	4	0	21859		64	10	1	3286
15	1	3	19450		65	8	5	3126
16	5	1	19022		66	10	0	3098
17	5	2	18849		67	5	7	3041
18	4	5	18836		68	10	2	3019
19	5	0	17394		69	9	4	2646
20	2	4	16857		70	2	8	2496
21	0	2	16665		71	7	8	2481
22	5	3	16534		72	8	6	2383
23	5	4	14567		73	10	3	2359
24	6	1	14365		74	3	8	2322
25	1	4	13525		75	1	8	2280
26	6	2	13437		76	0	7	2261
27	6	0	13409		77	11	1	2134
28	6	3	11542		78	4	8	2015
29	0	3	11246		79	11	0	2008
30	3	5	11034		80	9	5	1972
31	2	5	10801		81	11	2	1914
32	5	6	10720		82	5	8	1872
33	7	1	10543		83	8	7	1855
34	7	0	9854		84	10	4	1703
35	7	2	9672		85	2	9	1646
36	6	4	9468		86	11	3	1553
37	1	5	8825		87	3	9	1546
38	6	5	8055		88	6	8	1449
39	0	4	7869		89	9	6	1435
40	7	3	7729		90	0	8	1426
41	8	1	7302		91	12	1	1408
42	8	0	6853		92	1	9	1396
43	3	6	6844		93	4	9	1293
44	8	2	6740		94	12	2	1289
45	2	6	6625		95	12	0	1274
46	7	4	6286		96	11	4	1210
47	4	6	6189		97	10	5	1194
48	1	6	5698		98	8	9	1134
49	8	3	5397		99	5	9	1027
50	6	7	5359		100	9	7	1018

Note 1 Million games simulated.
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Dodgers vs Cardinals - NLDS Game 3 Simulation Results

Away	Home	Away Pitcher	Home Pitcher	Favorite	Away RS	Home RS	Win %	Total runs
Dodgers	Cardinals	Hyun-Jin Ryu	John Lackey	Dodgers	4.19	3.49	55.46	7.68

                                           Top 100 Most Likely Final Scores

Rank	Dodgers	Cardinals	Occurrences		Rank	Dodgers	Cardinals	Occurrences
1	2	3	38820		51	8	3	6124
2	1	2	33765		52	2	7	6086
3	3	4	33268		53	0	5	6039
4	3	2	31617		54	3	7	6034
5	2	1	28810		55	4	7	5888
6	4	3	25660		56	8	4	5319
7	3	1	25175		57	5	7	5116
8	4	2	24109		58	1	7	5106
9	4	5	23843		59	8	0	4806
10	4	1	20331		60	9	2	4778
11	1	3	19012		61	8	5	4552
12	2	4	18768		62	9	1	4522
13	5	2	18291		63	7	8	4397
14	5	3	18225		64	9	3	4183
15	2	0	18029		65	0	6	4139
16	5	4	17716		66	3	8	4125
17	0	1	17041		67	2	8	4077
18	3	0	16492		68	8	6	3729
19	1	0	16369		69	4	8	3644
20	5	1	15884		70	9	4	3557
21	5	6	15075		71	1	8	3431
22	1	4	14840		72	9	0	3281
23	3	5	14150		73	8	7	3256
24	4	0	13818		74	5	8	3254
25	2	5	13560		75	10	2	3213
26	6	3	13178		76	0	7	2988
27	6	2	13141		77	10	1	2982
28	0	2	12817		78	10	3	2861
29	6	1	12129		79	6	8	2841
30	6	4	11978		80	9	5	2827
31	5	0	11394		81	2	9	2720
32	6	5	11017		82	3	9	2704
33	0	3	10364		83	10	4	2451
34	1	5	10148		84	9	6	2374
35	7	2	9872		85	4	9	2336
36	3	6	9756		86	10	0	2267
37	2	6	9130		87	1	9	2175
38	7	3	9129		88	11	2	2070
39	7	1	9116		89	8	9	2067
40	6	0	9003		90	11	1	2027
41	4	6	8921		91	0	8	1987
42	6	7	8511		92	11	3	1876
43	7	4	8319		93	10	5	1872
44	0	4	8032		94	5	9	1863
45	1	6	7350		95	9	7	1842
46	7	5	7211		96	2	10	1802
47	8	2	6870		97	3	10	1752
48	7	0	6788		98	6	9	1752
49	8	1	6642		99	4	10	1545
50	7	6	6213		100	11	4	1544

Note: Based off of 1 million games simulated.
.

Cardinals vs Dodgers - NLDS Game 2 Simulation Results

Away	Home	Away Pitcher	Home Pitcher	Favorite	Away RS	Home RS	Win %	Total Runs
Cardinals	Dodgers	Lance Lynn	Zach Greinke	Dodgers	3.10	4.03	63.2572	7.13

                                       Top 100 Most Likely Final Scores

Rank	Cardinals	Dodgers	Occurrences		Rank	Cardinals	Dodgers	Occurrences
1	2	3	48798		51	7	2	5686
2	1	2	46130		52	7	4	5527
3	3	4	38320		53	3	8	5360
4	1	3	29091		54	0	8	5169
5	0	1	28194		55	5	7	4980
6	3	2	26629		56	7	5	4946
7	2	1	26013		57	7	1	4623
8	4	5	25848		58	7	6	4591
9	2	4	25111		59	2	9	4503
10	0	2	23969		60	1	9	4497
11	1	4	23862		61	4	8	4250
12	0	3	22085		62	6	0	4102
13	4	3	21297		63	7	8	3833
14	2	5	19514		64	8	3	3749
15	3	1	19220		65	3	9	3733
16	4	2	18548		66	0	9	3656
17	0	4	17950		67	8	2	3631
18	1	5	17554		68	5	8	3470
19	3	5	16821		69	8	4	3444
20	5	6	15098		70	1	10	3040
21	1	0	14606		71	8	1	3005
22	5	4	14223		72	2	10	2977
23	4	1	14066		73	8	5	2967
24	0	5	14036		74	4	9	2894
25	5	3	13721		75	7	0	2691
26	1	6	12928		76	8	6	2547
27	2	0	12866		77	0	10	2459
28	2	6	12832		78	3	10	2456
29	5	2	12745		79	6	8	2456
30	3	6	12114		80	9	3	2340
31	0	6	10412		81	9	2	2240
32	3	0	10248		82	9	4	2132
33	5	1	10000		83	8	7	2127
34	4	6	9600		84	5	9	2070
35	2	7	9234		85	1	11	1945
36	1	7	9133		86	2	11	1934
37	6	3	8959		87	9	1	1862
38	6	4	8693		88	4	10	1833
39	6	2	8502		89	8	0	1802
40	6	5	8337		90	9	5	1783
41	3	7	8000		91	8	9	1694
42	4	0	7863		92	3	11	1646
43	6	7	7794		93	0	11	1591
44	0	7	7603		94	6	9	1572
45	6	1	6976		95	9	6	1471
46	4	7	6924		96	10	3	1402
47	1	8	6602		97	10	2	1352
48	2	8	6319		98	1	12	1337
49	5	0	5856		99	5	10	1305
50	7	3	5749		100	2	12	1255

Chances of each team scoring X number of runs

Runs Scored	Cardinals	Dodgers
0	13.99%	6.28%
1	17.27%	11.66%
2	17.33%	15.12%
3	14.72%	15.90%
4	11.62%	14.22%
5	8.57%	11.43%
6	5.98%	8.36%
7	4.04%	5.85%
8	2.61%	3.95%
9	1.62%	2.65%
10	0.96%	1.72%

Note: Based on 1 million games simulated

Cardinals vs Dodgers - NLDS Game 1 Simulation Results

Away	Home	Away Pitcher	Home Pitcher	Favorite	Away RS	Home RS	Win %	Total Runs
Cardinals	Dodgers	Adam Wainwright	Clayton Kershaw	Dodgers	1.97	3.27	69.713	5.24

                                   Top 100 Most Likely Final Scores

Rank	Cardinals	Dodgers	Occurences		Rank	Cardinals	Dodgers	Occurences
1	0	1	36711		51	6	0	1531
2	1	2	36555		52	4	7	1526
3	0	2	27147		53	0	10	1353
4	2	3	26247		54	7	2	1344
5	0	3	22578		55	7	1	1331
6	1	3	19914		56	3	8	1306
7	2	1	19333		57	6	7	1306
8	0	4	16891		58	7	3	1275
9	1	0	16225		59	2	9	1201
10	3	4	14714		60	1	10	1091
11	1	4	14711		61	7	4	1071
12	3	2	13676		62	5	7	957
13	0	5	12308		63	7	5	903
14	2	4	11691		64	0	11	900
15	2	0	10994		65	7	0	897
16	3	1	10788		66	4	8	863
17	1	5	9691		67	3	9	828
18	0	6	8502		68	2	10	769
19	4	3	7979		69	7	6	744
20	2	5	7900		70	8	2	740
21	4	2	7791		71	8	1	722
22	4	5	7234		72	8	3	709
23	3	0	6664		73	1	11	650
24	1	6	6612		74	8	4	576
25	4	1	6519		75	5	8	542
26	3	5	5515		76	4	9	541
27	0	7	5381		77	3	10	517
28	2	6	4976		78	8	5	507
29	5	3	4237		79	2	11	491
30	4	0	4185		80	0	12	457
31	5	2	4153		81	7	8	454
32	1	7	4074		82	8	0	430
33	5	4	3825		83	9	2	409
34	5	1	3813		84	1	12	396
35	3	6	3724		85	9	1	366
36	0	8	3494		86	8	6	360
37	2	7	3197		87	9	3	352
38	5	6	3194		88	3	11	349
39	1	8	2686		89	6	8	336
40	5	0	2489		90	4	10	322
41	6	2	2423		91	5	9	302
42	4	6	2419		92	8	7	301
43	6	3	2344		93	2	12	293
44	6	1	2267		94	9	4	293
45	0	9	2156		95	0	13	285
46	3	7	2131		96	9	0	264
47	2	8	2021		97	9	5	241
48	6	4	2016		98	10	2	224
49	6	5	1819		99	6	9	218
50	1	9	1718		100	4	11	212

Note: Based off of 500,000 games simulated.

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