Super Bowl LVI Projection, Week 3, Final

Denver over Carolina

Dallas beat Philadelphia, but it would have taken a huge margin to raise them up to Carolina's level, and the NFC and Super Bowl projection overall remain the same.

TEAM	Record	Strength	Div	Plyff	WC	Qtr	Semi	Champ
DEN	3-0	0.582	49.6	85.6	61.8	35.1	19.7	10.7
CAR	3-0	0.575	53.6	82.6	56.9	31.4	17.2	9.3
BUF	2-1	0.572	69.5	79.5	50.3	27.9	15.2	8.2
LAR	3-0	0.550	39.7	79.4	52.2	27.3	14.1	7.3
ARI	3-0	0.553	38.5	76.6	50.1	26.3	13.7	7.1
LV	3-0	0.529	31.3	76.6	48.1	24.1	12.0	5.9
NO	2-1	0.560	24.5	65.2	39.9	21.1	11.2	5.9
CLE	2-1	0.544	34.8	61.1	36.5	18.9	9.7	4.9
DAL	2-1	0.534	56.4	64.2	35.3	17.8	8.8	4.4
CIN	2-1	0.530	34.9	61.3	35.7	18.0	8.9	4.4
TB	2-1	0.521	19.7	53.4	29.4	14.3	7.0	3.4
SF	2-1	0.520	16.2	52.8	29.5	14.3	6.9	3.4
LAC	2-1	0.515	14.5	51.9	29.0	14.0	6.8	3.2
TEN	2-1	0.478	50.4	59.0	29.4	13.0	5.7	2.5
BAL	2-1	0.495	23.3	48.1	25.1	11.7	5.4	2.5
MIN	1-2	0.514	34.0	42.7	21.8	10.4	5.0	2.4
GB	2-1	0.474	43.3	51.4	24.4	10.7	4.6	2.0
NE	1-2	0.508	18.7	36.9	19.0	9.1	4.3	2.0
HOU	1-2	0.483	31.4	39.6	19.1	8.6	3.8	1.7
PHI	1-2	0.500	20.8	30.7	15.0	7.0	3.2	1.5
KC	1-2	0.496	4.6	25.4	12.9	6.0	2.8	1.3
SEA	1-2	0.493	5.6	25.1	12.6	5.8	2.6	1.2
WAS	1-2	0.461	15.9	23.4	10.5	4.5	1.9	0.8
PIT	1-2	0.465	7.0	21.2	9.9	4.3	1.9	0.8
MIA	1-2	0.437	8.9	19.9	8.5	3.4	1.4	0.6
CHI	1-2	0.433	15.1	20.2	8.4	3.3	1.3	0.5
IND	0-3	0.457	9.5	15.1	6.7	2.8	1.2	0.5
NYG	0-3	0.465	6.8	10.4	4.6	2.0	0.9	0.4
DET	0-3	0.457	7.6	11.0	4.8	2.0	0.8	0.4
JAC	0-3	0.441	8.7	12.5	5.3	2.1	0.9	0.4
ATL	1-2	0.432	2.2	11.0	4.7	1.9	0.7	0.3
NYJ	0-3	0.416	2.9	6.4	2.6	1.0	0.4	0.1

[Week 1] Philadelphia over Houston
[Week 2, Thursday] Philadelphia over Houston
[Week 2, Sunday] Denver over Carolina
[Week 2, Final] Denver over Carolina
[Week 3, Thursday] Carolina over Denver
[Week 3, Sunday] Denver over Carolina

Super Bowl LVI Projection, Week 3, Sunday

Denver over Carolina

The teams stayed the same but the projection flipped, as Denver took back the top spot from Carolina. There are still 5 undefeated teams, and on the other end of the spectrum, 5 winless teams. New York got shut out to take over the title of weakest team, already down to a 6% chance of making the playoffs, and an 0.1% chance of winning the Super Bowl.

TEAM	Record	Strength	Div	Plyff	WC	Qtr	Semi	Champ
DEN	3-0	0.582	49.7	85.5	61.7	35.0	19.6	10.7
CAR	3-0	0.575	53.8	82.4	56.6	31.2	17.1	9.3
BUF	2-1	0.572	69.3	79.5	50.4	27.9	15.2	8.1
LAR	3-0	0.550	39.4	79.3	52.1	27.2	14.0	7.3
ARI	3-0	0.553	38.9	76.9	50.3	26.4	13.7	7.1
LV	3-0	0.529	31.4	76.5	48.0	24.1	12.0	5.9
NO	2-1	0.560	24.6	64.8	39.5	20.9	11.0	5.8
CLE	2-1	0.544	34.8	61.2	36.6	18.9	9.7	4.9
CIN	2-1	0.529	34.9	61.3	35.8	18.0	8.9	4.4
PHI	1-1	0.543	48.4	57.7	32.1	16.4	8.3	4.2
SF	2-1	0.520	16.1	52.8	29.5	14.3	6.9	3.4
TB	2-1	0.521	19.4	52.4	28.7	14.0	6.8	3.3
LAC	2-1	0.515	14.3	51.3	28.6	13.8	6.7	3.2
TEN	2-1	0.478	50.4	59.0	29.4	13.1	5.8	2.5
BAL	2-1	0.495	23.3	48.2	25.2	11.7	5.4	2.5
MIN	1-2	0.514	34.4	43.2	22.1	10.5	5.0	2.4
NE	1-2	0.508	18.9	37.4	19.3	9.2	4.4	2.1
GB	2-1	0.474	43.1	51.3	24.4	10.7	4.6	2.0
DAL	1-1	0.502	29.8	39.3	19.7	9.2	4.3	2.0
HOU	1-2	0.483	31.4	39.7	19.1	8.6	3.8	1.7
KC	1-2	0.496	4.6	25.3	12.9	6.0	2.8	1.3
SEA	1-2	0.493	5.6	25.0	12.6	5.7	2.6	1.2
PIT	1-2	0.465	7.0	21.3	10.0	4.3	1.9	0.8
WAS	1-2	0.461	15.3	22.7	10.2	4.3	1.8	0.8
MIA	1-2	0.437	8.9	19.9	8.5	3.4	1.4	0.6
CHI	1-2	0.433	15.0	20.1	8.4	3.3	1.3	0.5
IND	0-3	0.457	9.5	15.2	6.8	2.8	1.2	0.5
NYG	0-3	0.465	6.5	10.1	4.5	1.9	0.8	0.4
JAC	0-3	0.441	8.7	12.5	5.3	2.1	0.9	0.4
DET	0-3	0.457	7.4	10.6	4.6	1.9	0.8	0.3
ATL	1-2	0.432	2.3	11.3	4.8	1.9	0.8	0.3
NYJ	0-3	0.416	2.8	6.2	2.5	1.0	0.4	0.1

[Week 1] Philadelphia over Houston
[Week 2, Thursday] Philadelphia over Houston
[Week 2, Sunday] Denver over Carolina
[Week 2, Final] Denver over Carolina
[Week 3, Thursday] Carolina over Denver

Super Bowl LVI Projection, Week 3, Thursday

Carolina over Denver

Thursday's game featured 2 teams that have both been in my Superbowl projection twice already in this young season. Carolina beat Houston easily, and takes an even stronger lead in the NFC and the league as a whole. They're somewhat helped by being the only 3-0 team, and one of only two to have played 3 games. Still, 3-0 is a solid start. I often hear stories quoted about how unlikely an 0-2 team is to make the playoffs, and other such stats illustrating how much we can learn about teams in just the first few weeks.

TEAM	Record	Strength	Div	Plyff	WC	Qtr	Semi	Champ
CAR	3-0	0.575	55.3	82.1	57.2	32.0	17.8	10.0
DEN	2-0	0.545	39.4	73.2	49.3	26.6	14.3	7.4
LV	2-0	0.525	33.6	70.0	45.1	23.3	12.0	5.9
BUF	1-1	0.549	44.6	62.7	38.7	21.1	11.4	5.9
LAR	2-0	0.536	30.7	66.0	40.9	21.0	10.7	5.6
ARI	2-0	0.535	29.2	64.3	39.5	20.2	10.2	5.3
NE	1-1	0.541	35.9	57.7	35.0	18.8	10.0	5.1
TB	2-0	0.531	28.9	63.9	38.5	19.4	9.8	5.1
SF	2-0	0.523	27.4	64.4	38.9	19.4	9.6	4.9
PHI	1-1	0.543	41.4	53.4	30.4	15.8	8.1	4.3
NO	1-1	0.534	13.9	45.9	26.1	13.2	6.7	3.5
CLE	1-1	0.509	26.3	46.2	26.3	13.1	6.5	3.1
CIN	1-1	0.500	25.5	45.0	25.2	12.3	6.0	2.8
KC	1-1	0.504	13.7	41.4	23.4	11.5	5.7	2.7
SEA	1-1	0.515	12.7	40.0	22.1	10.8	5.2	2.6
PIT	1-1	0.496	24.0	43.8	24.0	11.6	5.6	2.6
LAC	1-1	0.502	13.2	40.4	22.8	11.2	5.5	2.6
BAL	1-1	0.493	24.2	43.8	23.9	11.5	5.5	2.6
DAL	1-1	0.502	25.3	36.2	18.5	8.8	4.2	2.0
HOU	1-2	0.483	31.4	39.4	19.9	9.3	4.4	2.0
TEN	1-1	0.469	33.7	42.8	21.6	9.8	4.4	2.0
WAS	1-1	0.494	24.3	36.5	18.5	8.7	4.0	1.9
GB	1-1	0.470	32.9	39.0	18.4	8.1	3.5	1.6
CHI	1-1	0.468	30.6	36.9	17.3	7.6	3.3	1.5
MIN	0-2	0.494	22.4	28.1	13.7	6.3	2.9	1.4
IND	0-2	0.474	19.9	27.9	13.8	6.4	2.9	1.3
MIA	1-1	0.445	13.1	29.1	13.9	6.0	2.6	1.1
JAC	0-2	0.459	15.0	20.8	9.8	4.3	1.9	0.8
DET	0-2	0.467	14.1	18.5	8.4	3.7	1.6	0.7
NYG	0-2	0.475	9.0	15.9	7.5	3.4	1.5	0.7
NYJ	0-2	0.451	6.3	15.5	7.3	3.2	1.4	0.6
ATL	0-2	0.447	1.9	8.9	4.0	1.7	0.7	0.3

[Week 1] Philadelphia over Houston
[Week 2, Thursday] Philadelphia over Houston
[Week 2, Sunday] Denver over Carolina
[Week 2, Final] Denver over Carolina

Super Bowl LVI Projection, Week 2, Final

Denver over Carolina

Green Bay redeemed themselves a bit with a Monday night win over Detroit, but at 1-1 they had no significant effect on the NFC, and Denver over Carolina remains the Super Bowl projection.

TEAM	Record	Strength	Div	Plyff	WC	Qtr	Semi	Champ
DEN	2-0	0.545	39.5	72.8	48.7	26.2	14.0	7.3
CAR	2-0	0.548	43.0	70.3	45.0	24.0	12.7	6.8
BUF	1-1	0.549	44.7	62.4	38.3	20.8	11.2	5.9
LV	2-0	0.525	33.7	69.5	44.5	22.9	11.7	5.9
LAR	2-0	0.536	30.5	66.4	41.9	21.7	11.2	5.8
ARI	2-0	0.535	29.5	65.2	40.9	21.1	10.8	5.6
TB	2-0	0.531	36.1	66.0	40.5	20.7	10.6	5.5
SF	2-0	0.523	27.3	64.9	39.9	20.1	10.1	5.1
NE	1-1	0.541	36.0	57.3	34.6	18.4	9.8	5.1
PHI	1-1	0.544	41.4	54.3	31.4	16.5	8.6	4.6
NO	1-1	0.534	18.2	47.5	27.5	14.1	7.3	3.8
HOU	1-1	0.510	43.3	53.4	29.4	14.6	7.2	3.5
CLE	1-1	0.509	26.3	45.9	25.9	12.9	6.4	3.1
CIN	1-1	0.500	25.5	44.6	24.8	12.1	5.8	2.8
SEA	1-1	0.515	12.6	40.5	22.7	11.2	5.5	2.8
KC	1-1	0.504	13.8	40.9	22.9	11.2	5.5	2.6
PIT	1-1	0.496	24.0	43.4	23.7	11.4	5.5	2.6
BAL	1-1	0.493	24.2	43.4	23.5	11.3	5.4	2.5
LAC	1-1	0.502	13.0	39.5	22.0	10.8	5.3	2.5
DAL	1-1	0.502	25.3	37.1	19.3	9.3	4.4	2.2
WAS	1-1	0.494	24.2	37.4	19.3	9.2	4.3	2.1
TEN	1-1	0.469	28.2	39.3	19.8	9.0	4.0	1.8
GB	1-1	0.470	32.8	39.2	18.8	8.4	3.7	1.7
CHI	1-1	0.468	30.5	37.1	17.7	7.8	3.5	1.6
MIN	0-2	0.494	22.7	28.8	14.2	6.7	3.1	1.5
IND	0-2	0.474	16.4	25.3	12.5	5.7	2.6	1.2
MIA	1-1	0.445	13.1	28.6	13.6	5.9	2.5	1.1
DET	0-2	0.467	14.0	18.7	8.6	3.8	1.7	0.8
JAC	0-2	0.459	12.1	18.8	8.8	3.9	1.7	0.8
NYG	0-2	0.475	9.0	16.5	7.9	3.6	1.6	0.7
NYJ	0-2	0.451	6.2	15.0	7.0	3.1	1.3	0.6
ATL	0-2	0.447	2.7	9.8	4.4	1.9	0.8	0.3

[Week 1] Philadelphia over Houston
[Week 2, Thursday] Philadelphia over Houston
[Week 2, Sunday] Denver over Carolina

Super Bowl LVI Projection, Week 2, Sunday

Denver over Carolina

With 2-0 records, Denver and Carolina have taken over the AFC and NFC leads, respectively. Philadelphia and Houston both lost to fall to 1-1 and back into the middle of the pack. We had our first shutout of the year, with Miami failing to score. Combined with their 1 point win last week, the 35 point loss puts them at a -34 point differential and the weakest 1-1 team, down below several 0-2 teams. But, it's still early, so don't place all your bets on Denver to cover your Philadelphia losses just yet.

TEAM	Record	Strength	Div	Plyff	WC	Qtr	Semi	Champ
DEN	2-0	0.545	39.2	72.6	48.5	26.1	14.0	7.3
CAR	2-0	0.548	43.0	70.3	45.0	23.9	12.7	6.7
BUF	1-1	0.549	44.7	62.5	38.4	20.8	11.2	5.9
LV	2-0	0.525	33.9	69.7	44.6	23.0	11.8	5.9
LAR	2-0	0.536	30.4	66.0	41.5	21.5	11.1	5.8
ARI	2-0	0.535	29.4	64.8	40.4	20.8	10.7	5.6
TB	2-0	0.531	36.1	66.0	40.5	20.7	10.6	5.4
SF	2-0	0.523	27.6	65.0	39.9	20.0	10.0	5.1
NE	1-1	0.541	36.0	57.4	34.7	18.5	9.8	5.1
PHI	1-1	0.544	41.2	54.0	31.1	16.4	8.5	4.5
NO	1-1	0.534	18.2	47.4	27.4	14.1	7.2	3.7
HOU	1-1	0.510	43.3	53.5	29.5	14.6	7.2	3.5
CLE	1-1	0.509	26.3	45.7	25.8	12.8	6.3	3.1
CIN	1-1	0.500	25.5	44.4	24.7	12.0	5.8	2.8
SEA	1-1	0.515	12.6	40.0	22.4	11.0	5.4	2.7
KC	1-1	0.504	13.8	41.0	23.0	11.3	5.5	2.7
PIT	1-1	0.496	24.0	43.2	23.5	11.3	5.4	2.6
LAC	1-1	0.502	13.1	39.6	22.1	10.8	5.3	2.5
BAL	1-1	0.493	24.2	43.2	23.3	11.2	5.3	2.5
DAL	1-1	0.502	25.4	37.2	19.3	9.3	4.4	2.2
WAS	1-1	0.494	24.3	37.4	19.3	9.1	4.3	2.1
TEN	1-1	0.469	28.2	39.4	19.8	9.0	4.1	1.8
DET	0-1	0.491	27.7	34.4	17.1	8.0	3.7	1.8
CHI	1-1	0.468	28.6	35.5	16.9	7.5	3.3	1.5
MIN	0-2	0.494	21.2	27.4	13.5	6.3	3.0	1.4
GB	0-1	0.471	22.5	28.4	13.5	6.0	2.7	1.2
IND	0-2	0.474	16.4	25.4	12.6	5.7	2.6	1.2
MIA	1-1	0.445	13.1	28.7	13.7	5.9	2.5	1.1
JAC	0-2	0.459	12.1	18.8	8.8	3.9	1.7	0.8
NYG	0-2	0.475	9.1	16.6	7.9	3.6	1.6	0.7
NYJ	0-2	0.451	6.2	15.0	7.0	3.1	1.3	0.6
ATL	0-2	0.447	2.6	9.7	4.4	1.9	0.8	0.3

[Week 1] Philadelphia over Houston
[Week 2, Thursday] Philadelphia over Houston

Super Bowl LVI Projection, Week 2, Thursday

Philadelphia over Houston

For the second year in a row (see 2020 here) my least favorite projection day doesn't include a 2-0 team that artificially appears in much better position than they are. Both Washington and New York were 0-1 going into last night, so this was inevitable. We do have New York artificially low as the only 0-2 team, but no one's really paying attention to the bottom of the table, right?

TEAM	Record	Strength	Div	Plyff	WC	Qtr	Semi	Champ
PHI	1-0	0.529	46.6	63.0	38.5	20.1	10.5	5.5
NO	1-0	0.529	35.0	61.3	38.0	19.9	10.3	5.4
HOU	1-0	0.521	49.9	64.3	38.9	20.2	10.4	5.3
LAR	1-0	0.526	26.9	58.1	35.7	18.5	9.5	5.0
DEN	1-0	0.524	28.3	57.0	35.1	18.3	9.6	4.9
ARI	1-0	0.527	26.7	56.6	34.6	18.0	9.3	4.9
PIT	1-0	0.515	35.9	58.4	35.2	18.1	9.2	4.7
SEA	1-0	0.520	24.4	54.0	32.5	16.6	8.5	4.4
MIA	1-0	0.503	42.6	58.6	34.0	17.0	8.5	4.2
LV	1-0	0.509	24.2	53.5	31.8	16.1	8.1	4.0
CAR	1-0	0.513	28.6	53.2	31.3	15.8	7.9	4.0
CIN	1-0	0.505	33.0	53.8	31.5	15.8	7.9	3.9
LAC	1-0	0.510	23.7	51.4	30.5	15.4	7.8	3.9
KC	1-0	0.506	23.8	52.9	31.2	15.7	7.9	3.9
SF	1-0	0.509	22.0	51.9	30.5	15.2	7.6	3.8
TB	1-0	0.503	26.7	52.4	30.3	14.9	7.3	3.7
WAS	1-1	0.494	25.7	42.4	22.9	11.1	5.4	2.6
MIN	0-1	0.495	28.3	37.8	20.0	9.6	4.6	2.3
NE	0-1	0.497	19.1	34.4	18.6	9.1	4.5	2.2
DET	0-1	0.491	26.9	35.3	18.2	8.7	4.2	2.0
DAL	0-1	0.497	18.8	31.8	16.8	8.2	4.0	2.0
CLE	0-1	0.494	15.7	31.0	16.7	8.2	4.0	1.9
NYJ	0-1	0.487	19.0	32.9	17.5	8.4	4.1	1.9
BAL	0-1	0.491	15.4	30.9	16.5	8.0	3.9	1.9
BUF	0-1	0.485	19.3	31.6	16.5	7.9	3.8	1.8
IND	0-1	0.480	18.2	31.4	16.3	7.8	3.7	1.7
JAC	0-1	0.479	15.5	29.0	15.0	7.1	3.4	1.6
CHI	0-1	0.474	22.9	30.7	15.2	7.0	3.2	1.5
TEN	0-1	0.473	16.3	28.8	14.7	6.9	3.2	1.5
GB	0-1	0.471	21.9	29.2	14.3	6.5	3.0	1.4
ATL	0-1	0.471	9.7	23.9	12.0	5.5	2.5	1.2
NYG	0-2	0.474	8.9	18.4	9.1	4.2	2.0	0.9

[Week 1] Philadelphia over Houston

Super Bowl LVI Projection, Week 1

Philadelphia over Houston

As is tradition, rather than re-explaining, allow me to copy and past from 2014's introductory post.

Each year I project the Super Bowl match-up after each day of games. The method is not of my own design, but the implementation is. Each team's strength is determined based on points scored and points allowed, and scaled to make the average of all teams .500. Then, the remainder of the season and playoffs are simulated millions of times, and I report to you the chances of each team reaching each round of the playoffs. It's had mixed results in the past, but that's the nature of taking 1 weighted random sample out of millions of potential outcomes.

For the second year in a row, I needed to modify my software to accommodate some changes in the NFL. Last year they added 2 playoff teams, for a total of 14. This year each team plays 17 games. I had a lot of hard-coded 16s, as well as some other hard-coded numbers from 14 up to 23 to index into certain data structures. Avoid hard-coded constants for things that might ever change, kids. Hopefully that fix will bring me closer to my eventual goal of being able to project baseball, basketball, and hockey if I can figure out how to project overtime and shootouts.

The first week of the season is not terrible indicative of the outcome of the season, because of so much uncertainty remaining. For example, last year Tampa sat at 1.7% after a week 1 loss. But, by virtue of a 32-6 win, and a weaker division that New Orleans, who won 38-3, Philadelphia takes the NFC lead. Philadelphia is the only 1-0 team in the NFC East, while there are 3 1-0 teams in the NFC South. In the AFC, Houston is the only 1-0 team in the AFC South, which gives them a huge boost in playoff odds currently. Miami is in the same position, but only won by a point, putting their strength very near .500

All in all, don't place any wagers based on week 1. In fact, don't ever do that based on this amateur stuff.

TEAM	Record	Strength	Div	Plyff	WC	Qtr	Semi	Champ
PHI	1-0	0.529	47.3	63.3	38.7	20.2	10.5	5.5
NO	1-0	0.529	35.0	61.4	38.1	19.9	10.4	5.5
HOU	1-0	0.520	49.9	64.2	38.9	20.2	10.4	5.3
LAR	1-0	0.526	26.9	58.2	35.8	18.5	9.6	5.0
DEN	1-0	0.524	28.4	57.1	35.1	18.3	9.6	4.9
ARI	1-0	0.527	26.7	56.6	34.7	18.0	9.4	4.9
PIT	1-0	0.515	35.9	58.3	35.2	18.0	9.2	4.7
SEA	1-0	0.520	24.4	54.1	32.6	16.7	8.5	4.4
MIA	1-0	0.503	42.6	58.6	34.0	17.0	8.4	4.2
LV	1-0	0.509	24.2	53.5	31.8	16.1	8.1	4.1
CAR	1-0	0.513	28.6	53.3	31.4	15.8	8.0	4.0
CIN	1-0	0.505	33.0	53.8	31.5	15.8	7.9	3.9
LAC	1-0	0.510	23.6	51.4	30.4	15.4	7.8	3.9
KC	1-0	0.506	23.8	52.9	31.2	15.7	7.9	3.9
SF	1-0	0.509	22.0	52.0	30.6	15.3	7.6	3.9
TB	1-0	0.503	26.7	52.5	30.4	15.0	7.4	3.7
MIN	0-1	0.495	28.3	37.8	20.0	9.7	4.7	2.3
NE	0-1	0.497	19.1	34.4	18.6	9.1	4.5	2.2
DET	0-1	0.491	26.9	35.3	18.3	8.7	4.2	2.0
DAL	0-1	0.497	19.1	32.0	16.9	8.3	4.0	2.0
CLE	0-1	0.494	15.7	31.0	16.7	8.2	4.0	1.9
NYJ	0-1	0.487	19.0	32.9	17.5	8.4	4.1	1.9
WAS	0-1	0.490	18.3	32.1	16.9	8.1	3.9	1.9
BAL	0-1	0.491	15.4	30.9	16.5	8.0	3.9	1.9
BUF	0-1	0.485	19.3	31.7	16.5	7.9	3.8	1.8
IND	0-1	0.480	18.2	31.4	16.3	7.8	3.7	1.7
JAC	0-1	0.480	15.5	29.1	15.0	7.1	3.4	1.6
CHI	0-1	0.474	22.9	30.8	15.3	7.1	3.3	1.5
TEN	0-1	0.473	16.3	28.8	14.7	6.9	3.2	1.5
NYG	0-1	0.476	15.3	27.6	14.1	6.6	3.1	1.4
GB	0-1	0.471	21.9	29.2	14.3	6.6	3.0	1.4
ATL	0-1	0.471	9.7	24.0	12.1	5.6	2.6	1.2