Best Lineup - San Francisco Giants

Next up on my look at each teams most efficient lineup is the San Francisco Giants.  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 | Rays | Twins | Blue Jays | Indians
NL: Mets | Cubs | Padres | Marlins | Reds

See the results after the jump

Best Lineup - Cleveland Indians

Next up on my look at each teams most efficient lineup is the Cleveland Indians.  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 | Rays | Twins | Blue Jays
NL: Mets | Cubs | Padres | Marlins | Reds

See the results after the jump

Best Lineup - Cincinnati Reds

Next up on my look at each teams most efficient lineup is the Cincinnati Reds.  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, therefore I didn't attempt to let Joey Votto and Jay Bruce hit back to back.  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 | Rays | Twins | Blue Jays
NL: Mets | Cubs | Padres | Marlins

See the results after the jump

Best Lineup - Toronto Blue Jays

Next up on my look at each teams most efficient lineup is the Toronto Blue Jays.  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 | Rays | Twins
NL: Mets | Cubs | Padres | Marlins

See the results after the jump...

Best Lineup - Miami Marlins

Next up on my look at each teams most efficient lineup is the Miami Marlins.  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 | Rays | Twins
NL: Mets | Cubs | Padres

See the results after the jump...

Best Lineup - Minnesota Twins

Next up on my look at each teams most efficient lineup is the Minnesota Twins.  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 | Rays
NL: Mets | Cubs | Padres

See the results after the jump...

Best Lineup - San Diego Padres

Next up on my look at each teams most efficient lineup is the San Diego Padres.  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 | Rays
NL: Mets | Cubs

See the results after the jump...

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