The Sophomore Slump in the NFL

Whenever an NFL rookie has a remarkable first year, their sophomore campaign often seems to not measure up, and the player is labeled as going through the dreaded "sophomore slump". Sometimes this decline appears to foreshadow future problems (see: Robert Griffin III) and other times it isn't anything but a blip in a long-term successful career (see: Matt Ryan). 

There have been two notable cases of it this year: Jameis Winston and Marcus Mariota. Winston was selected to the Pro Bowl last year, and Mariota had a solid rookie year as well. However, both players have regressed in Year 2. Why do some players take a step back in their second year? Shouldn't they improve as they gain more pro experience?

I pulled the numbers on the notable "sophomore slumps" in the past 10 seasons, sticking to QBs only. Limiting myself to QBs allows me to use "QB Rating" to quantify their performance in each year (and more imporantly, compare each player to the average for that year).

Player	Team	Year	QB Rating Year 1	QB Rating Year 2	Difference
Jameis Winston	TB	2016	84.2	75.9	-8.3
Marcus Mariota	TEN	2016	91.5	88.3	-3.2
Robert Griffin III	WAS	2013	102.4	82.2	-20.2
Sam Bradford	STL	2011	76.5	70.5	-6
Matt Ryan	ATL	2009	87.7	80.9	-6.8
				Average	-8.9

On average, these QBs' rating fell almost 9 points from Year 1 to Year 2. What if we compare each player's performance to the average QB rating in each year?

Player	Team	Year	QB Rating Year 1	QB Rating Year 2	Difference	vs Avg Year 1	vs Avg Year 2
Jameis Winston	TB	2016	84.2	75.9	-8.3	-6.8	-10.9
Marcus Mariota	TEN	2016	91.5	88.3	-3.2	0.5	1.5
Robert Griffin III	WAS	2013	102.4	82.2	-20.2	16.5	-5.2
Sam Bradford	STL	2011	76.5	70.5	-6	-9.7	-13.6
Matt Ryan	ATL	2009	87.7	80.9	-6.8	3.8	-2.5
				Average	-8.9	0.9	-6.1

These rookies were slightly above average in their first year, but do indeed check in well below average in their second year. This would seem to imply there is indeed regression and the "sophmore slump" is real! BUT...

Player	Team	Year	QB Rating Year 1	QB Rating Year 2	Difference	vs Rookie Avg Year 1	vs 2nd Year Avg Year 2
Jameis Winston	TB	2016	84.2	75.9	-8.3	7.5	-4.5
Marcus Mariota	TEN	2016	91.5	88.3	-3.2	14.8	7.9
Robert Griffin III	WAS	2013	102.4	82.2	-20.2	25.7	1.8
Sam Bradford	STL	2011	76.5	70.5	-6	-0.2	-9.9
Matt Ryan	ATL	2009	87.7	80.9	-6.8	11.0	0.5
				Average	-8.9	11.7	-0.8

The key word here is regression. Regression to the mean. In Year 1, this set of QBs was almost 12 points above the rookie average, but in Year 2, they simply regressed to the mean (almost literally, to less than 1 point below the 2nd Year average). This "sophmore slump" is real in the sense of declining year-over-year, but is simply another way of describing regression to the mean.

"What are the odds?" That I Get a Parking Ticket at FIU

"I've been parking in a construction lot at FIU since June with no problem. I got ticketed today for the first time, but need to continue parking there through December. Should I purchase a parking permit, pay for hourly/daily parking, or keep risking it?"

This question is a straight-forward cost/benefit analysis if we can gauge the expected cost of each of these options. So here are our parameters:

Timeline: June to December (28 weeks)
Frequency: 3 times a week
Cost of Parking Permit: $140
Cost of Daily Parking: $8/day
Cost of Parking Ticket: $20

Option A: Purchase a parking permit
The only factor to consider here is the cost of the permit, which is $140. Upon obtaining that, there is a 0% chance of getting fined further.

Option B: Pay for daily parking
19 weeks have elapsed already, with 9 weeks to go. At 3 times a week * 9 weeks * $8, that's a cost of $216. As with Option A, there is a 0% chance of getting fined further.

Option C: Risk it
This is the option that takes a bit more math. First we have to gauge the probability of getting caught. Through 19 weeks, they've gotten fined once. If parking patrol is actively looking for this same car now, then the probability of getting caught again is higher. However, for simplicity we'll assume it's evenly distributed: 1/(19*3) = 1/57 = 1.75%. Assuming the fine doesn't escalate for repeat offenders, we take 1.75% * 9 weeks remaining * 3 days a week * $20 = $9.47.

Clearly risking it is the superior strategy, given our assumptions and your level of risk aversion.

"What are the odds?" That My Softball Team Makes the Co-Ed Novice League Playoff for 1st Place

The following is a shameless plug for my Clark County Co-Ed Novice softball team in league 480SBM04 - Adult Softball League Co-Ed Novice Mon, "Analyze This":

We're currently 1 game out of first place with the final two games of the season tonight, and if there's a tie for first, those teams involved enter a playoff for first in the league. I applied the MDS Model to our league to gauge the "true" win percentage for each team by runs scored/runs against (adjusted for strength of schedule):

Rank	Home Team	RF	RA	Pyth
1	We Are Here To Drink	200	80	0.842
2	Bunting for Pitches	181	85	0.800
3	Analyze This	170	87	0.773
4	Comic Relief	142	108	0.623
5	Pitch Better Have My Money	101	149	0.329
6	Pitches Get Stitches	72	125	0.267
7	Somerset Stephanie	74	146	0.224
8	Bright Futures Pediatrics	23	183	0.022

Here's the scenario: we're playing "Pitch Better Have My Money" twice, with the top 2 teams in the league, "We Are Here to Drink" and "Bunting for Pitches" also playing twice. If "Bunting for Pitches" can win one or both of those games and we sweep our series, we'll be tied in first place and will head to the playoff. 

So I calculated the odds of this happening, since that scenario is very straight forward. Using our Pyth ratings to project win probabilities, we have an 87.41% chance of beating our opponent in each game (favored by 4.93 runs in each game, with a 76.40% shot to sweep them 2-0). 

There's a 67.18% chance "Bunting for Pitches" beats "We Are Here to Drink" either once (in which case we would face "We Are Here to Drink") or twice (in which case we would face "Bunting for Pitches"). 

Assuming the two series are independent gives 67.18% * 76.40% = 51.33% chance of making the playoff.