Here is scenario in which KT wins 78 additional games (96 total) but does not reach the postseason.

Here are the final standings in the scenario:
            Team	W	L	D	PCT	GB
          Doosan	96	45	3	0.6809	0.0
             KIA	95	45	4	0.6786	0.5
              LG	95	45	4	0.6786	0.5
              NC	94	46	4	0.6714	1.5
         Samsung	94	46	4	0.6714	1.5
              KT	96	47	1	0.6713	1.0
          Kiwoom	51	93	0	0.3542	46.5
             SSG	45	98	1	0.3147	52.0
          Hanwha	28	115	1	0.1958	69.0
           Lotte	14	128	2	0.0986	82.5

To construct the scenario, we start with the current standings:
            Team	W	L	D	GL	PCT	GB
             KIA	26	16	1	101	0.619	0.0
              NC	25	17	1	101	0.595	1.0
         Samsung	24	18	1	101	0.571	2.0
          Doosan	25	20	1	98	0.556	2.5
              LG	23	20	2	99	0.535	3.5
             SSG	23	20	1	100	0.535	3.5
          Kiwoom	18	24	0	102	0.429	8.0
              KT	18	25	1	100	0.419	8.5
          Hanwha	16	26	1	101	0.381	10.0
           Lotte	14	26	1	103	0.350	11.0

The next two tables show, respectively, how many of their remaining games each team wins and ties against each of the other teams in the scenario:

					Scenario Additional Wins Against
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Wins
Doosan	-	10	7	10	8	1	13	2	7	13	71
Hanwha	0	-	0	0	0	0	12	0	0	0	12
KIA	3	11	-	12	0	0	14	10	9	10	69
Kiwoom	0	10	0	-	0	0	10	0	0	13	33
KT	2	10	10	11	-	12	11	11	1	10	78
LG	9	14	10	11	1	-	10	3	4	10	72
Lotte	0	0	0	0	0	0	-	0	0	0	0
NC	9	11	1	14	0	6	10	-	7	11	69
Samsung	2	13	1	11	13	6	10	3	-	11	70
SSG	0	10	0	0	0	0	12	0	0	-	22
-----------------------------------------------------------------------------------
Losses	25	89	29	69	22	25	102	29	28	78

					Scenario Additional Draws (Ties) With
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Total
Doosan	-	0	1	0	0	1	0	0	1	0	2
Hanwha	0	-	0	0	0	0	0	1	0	0	0
KIA	0	0	-	0	0	0	0	2	1	0	3
Kiwoom	0	0	0	-	0	0	0	0	0	0	0
KT	0	0	0	0	-	0	1	0	0	0	0
LG	1	0	0	0	0	-	0	1	1	1	2
Lotte	0	0	0	0	0	0	-	0	1	0	1
NC	0	0	2	0	0	1	0	-	0	0	3
Samsung	1	0	1	0	0	0	1	0	-	0	3
SSG	0	0	0	0	0	0	0	0	0	-	0
-----------------------------------------------------------------------------------
Total	2	0	3	0	0	2	1	3	3	0

The next two tables show, respectively, how many total games each team wins and ties against each of the other teams in the scenario:

					Scenario Total Wins Against
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Wins
Doosan	-	14	9	15	13	5	14	5	8	13	96
Hanwha	2	-	1	2	3	1	13	1	1	4	28
KIA	6	15	-	16	3	4	16	12	11	12	95
Kiwoom	1	14	0	-	1	4	15	0	2	14	51
KT	3	13	13	15	-	13	12	14	1	12	96
LG	10	15	12	12	3	-	15	7	7	14	95
Lotte	2	3	0	1	3	1	-	1	2	1	14
NC	11	14	2	16	2	8	15	-	10	16	94
Samsung	7	15	4	14	15	8	13	6	-	12	94
SSG	3	12	4	2	4	1	15	0	4	-	45
-----------------------------------------------------------------------------------
Losses	45	115	45	93	47	45	128	46	46	98

					Scenario Total Draws (Ties) With
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Total
Doosan	-	0	1	0	0	1	0	0	1	0	3
Hanwha	0	-	0	0	0	0	0	1	0	0	1
KIA	0	0	-	0	0	0	0	2	1	0	4
Kiwoom	0	0	0	-	0	0	0	0	0	0	0
KT	0	0	0	0	-	0	1	0	0	0	1
LG	1	0	0	0	0	-	0	1	1	1	4
Lotte	0	0	0	0	0	0	-	0	1	0	2
NC	0	0	2	0	0	1	0	-	0	0	4
Samsung	1	0	1	0	0	0	1	0	-	0	4
SSG	0	0	0	0	0	0	0	0	0	-	1
-----------------------------------------------------------------------------------
Total	3	1	4	0	1	4	2	4	4	1