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