Defensive Positioning of the Team

In an earlier post, I discussed how to find the best bating order.  However, this method neglected the defensive positioning of the players.

In this post, I will describe how to find the best lineup considering both offensive and defensive aspects of the team's performance.

First, I found the positions of each of the players on the team can play.  I wanted to find the best lineup and batting order for each of the three pitchers on the team.

For each of the three pitchers, I developed 100 random lineups that filled the 9 defensive positions along with the DH.  I did not consider the batting order at this point.  However, I ran the Monte Carlo simulation for each of the random lineups with a random batting order.  Then I screened out the lineups that did not provide sufficient average runs per game.   In this way, I had all of the defensive positions filled and still had a reasonably good average runs per game.

On examination of the lineups that were not screend out, I found that seven players were in each of the lineups.  They were the strongest offensive players.  I reordered the lineups so that these seven players would be in a specific place in the first seven positions in the batting order to maximize the average number of runs per game.  One of these players could possibly play DH.

The last three players in the lineup filled out the defensive positions.  So at this point, I had a number of lineups with batting orders that provided good offensive statistics.

I ran the Monte Carlo simulation to do a runoff of the batting orders to find the best offensive lineup for each pitcher while also having all of the defensive positions filled out.

Likelihood of Making the Final Four Tournament with an Eight Team League

In an earlier post, I predicted the chances of team G making the four team final weekend tournament based on the 7 team playoff format. The probability that I estimated for team G was 45%.

This probability would change in the 8 team league. The first round playoff format could have 1st play 8th, 2nd play 7th, 3rd play 6th and 4th play 5th.  The opposition for team G plays in the first round will depend on how the new team performs.

Teams A, B, C and D will be in the North Division.  Teams E, F, G and H will be in South Division.

I will assume the new team is team A.  I used the Pythagorean Formula to determine the runs for and against for team A based on various values of their winning percentage.  Then I adjusted the runs for and against for from the 2012 season for the other teams based on the results for team A.  I then calculated the winning percentage for the other teams in the league.

Then I found the final standings based on the winning percentage of each team.

The final standings would be as shown below based on the performance of team A.

Team A Percent	0.400	0.450	0.500	0.550	0.600	0.650	0.700	0.750
Standings
1	E	E	E	E	E	E	E	A
2	B	B	B	B	A	A	A	E
3	C	C	C	A	B	B	B	B
4	G	G	A	C	C	C	C	C
5	F	F	G	G	G	G	G	G
6	H	A	F	F	F	F	F	F
7	A	H	H	H	H	H	H	H
8	D	D	D	D	D	D	D	D

So if team A has a winning percentage between a 0.400 or 0.450, team G plays team F in the first round.  Based on team G's head-to-head winning percentage versus team F, the probability of winning the first round of the playoffs would be 0.500.

If team A has a 0.500 winning percentage, then team G would play team A in the first round.  Team G's head-to-head winning percentage versus team A is in this case expected to be 0.452.  Thus, the probability of team G winning the first round would be 0.411.

For all of the other cases, team G would play team C in the first round.  Team G's head-to-head winning percentage versus team C is expected to be 0.435.  Thus the probability of winning the first round of the playoffs would be 0.380.

The Effect on Regular Season Performance of Adding an Eighth Team to the League

In an earlier post, I discussed how I used the runs for and against to predict the win percentage of a team.

Then I described how the win percentages for two teams could be used to predict results of head-to-head competiton.

Finally, I used the head-to-head win percentage to predict the regular season results for a 7 team league.

This season an eighth team has joined the league. It is difficult to predict their win percentage.

The league will be divided into two divisions. The teams will play three games against the other teams in their division and two games against the teams in the other division for a 17 game schedule.

My prediction for runs for and against are the same for team G, namely 104 runs for and 120 runs against. Thus, the predicted win percentage for team G is 0.429.

I assumed that teams A, B, C and D were in Division I and teams E, F, G and H were in Division II. I also assumed the two divisions were identical. I calculated the percentile for the standings in each division, that is, 0.8, 0.6, 0.4 and 0.2.

Then I used the inverse normal distribution to calculate the win percentage for the teams in the divisions by finding the standard deviation that would make team G and team C have a win percentage of 0.429.

The table below shows my predictions for the win percentage of the 8 teams.

Division I	Rank	Normal	Win Percent
A	1	0.80	0.736
B	2	0.60	0.571
C	3	0.40	0.429
D	4	0.20	0.264
Division II	Rank	Normal	Win Percent
E	1	0.80	0.736
F	2	0.60	0.571
G	3	0.40	0.429
H	4	0.20	0.264

I can now calculate the head-to-head performance of the 8 teams as shown in the table below.

		0.736	0.571	0.429	0.264	0.736	0.571	0.429	0.264
		A	B	C	D	E	F	G	H
0.736	A	0.500	0.677	0.788	0.886	0.500	0.677	0.788	0.886
0.571	B	0.323	0.500	0.639	0.788	0.323	0.500	0.639	0.788
0.429	C	0.212	0.361	0.500	0.677	0.212	0.361	0.500	0.677
0.264	D	0.114	0.212	0.323	0.500	0.114	0.212	0.323	0.500
0.736	E	0.500	0.677	0.788	0.886	0.500	0.677	0.788	0.886
0.571	F	0.323	0.500	0.639	0.788	0.323	0.500	0.639	0.788
0.429	G	0.212	0.361	0.500	0.677	0.212	0.361	0.500	0.677
0.264	H	0.114	0.212	0.323	0.500	0.114	0.212	0.323	0.500

Then I can predict the regular season performance of the 8 teams as shown in this table.

	A	B	C	D	E	F	G	H	Wins
A	0	2	2	3	1	1	2	2	13
B	1	0	2	2	1	1	1	2	10
C	1	1	0	2	0	1	1	1	7
D	0	1	1	0	0	0	1	1	4
E	1	1	2	2	0	2	2	3	13
F	1	1	1	2	1	0	2	2	10
G	0	1	1	1	1	1	0	2	7
H	0	0	1	1	0	1	1	0	4
Losses	4	7	10	13	4	7	10	13

Thus my prediction of the regular season results is

Div I	Wins	Losses	Win Percent
A	13	4	0.750
B	10	7	0.574
C	7	10	0.426
D	4	13	0.250
Div II	Wins	Losses	Win Percent
E	13	4	0.750
F	10	7	0.574
G	7	10	0.426
H	4	13	0.250