Optimizing a Swim Meet: Traveling Salesmen and Asexual Mutants

You wouldn't think there is much to swimming analytics. Compared to sports like baseball or football, swimming is extremely deterministic. Swimmers tend to have a certain speed in each stroke, and they vary only slightly around that tendency from meet to meet. There are no interactions with teammates, collisions with opponents, or bouncing balls to worry about. But it turns out that there's more to aquametrics than meets the eye.

My kids are on a summer swim team in the local league. It's a great activity--exercise, a bit of healthy competition, and all four of my kids and step-kids are on the same team for one season out of the year. It's a lot of fun for everyone.

It's complicated, though. There are five age groups for both boys and girls for a total of ten competition groups. There are 4 strokes (fly, back, breast, and freestyle). Each swimmer is assigned to one of three classes for each stroke. The A class has the faster kids, the B class the next faster kids, and the C class has the rest. First, second, and third place in each stroke-class (for each age/gender group) earn points for the team. The A, B, and C classes all count equally, in the spirit of the league. It's 5 points for a 1st, 3 for a 2nd, and 1 for a 3rd, regardless of class. This way, nearly everyone's performance can affect the outcome of the meet.

There's only one strategic variable in the meet. Each swimmer can only swim in 3 of the 4 stroke events in the meet. In other words, each swimmer has to skip one of the four strokes for the day. The manager of each team seeds the meet a couple days beforehand. You'd think that the best strategy is to have each swimmer participate in their 3 best strokes. But that's not the case.

Do Those Who Deny Advanced Statistics Even Watch the Game?

Stochastic Football

We understand your hostility. Maybe we're dangerous. Would it comfort you if I guaranteed that we are dangerous? And maybe we're dangerous to you. Do you prize your memory, your experience? Do you have knockdown, drag-out fights about what just happened, what you saw, what you know? Are you infected with certainty? Does this, this quote to follow, does it resonate within you, move you to potency, make you want to pressure wash something?

Inaction breeds doubt and fear. Action breeds confidence and courage. If you want to conquer fear, do not sit home and think about it. Go out and get busy. —Dale Carnegie

Joint Statistical Meetings

I've been invited to speak at the Joint Statistical Meetings this year, an annual event hosted primarily by the American Statistical Association. It will take place August 3-8 in Montreal. The theme of the talk is Big Data in Sports. My talk is scheduled for Monday the 5th. So if you'll be in Montreal for the conference, please come by and say hi.

Gagnez le jour, Alouettes!

Exploring the Causes of a Sack Pt. 1

A guest post by David Giller. Born and raised in Swampscott, MA, David attended Vanderbilt University where he was the starting longsnapper for the Commodores. He graduated summa cum laude with a degree in economics/corporate finance. David currently works as a business analyst for a Bain Capital Ventures portfolio company.

I would first like to thank Brian for his suggestion to post my study here in an effort to spark some interesting conversation and obtain some valuable takeaways. My post contains the results of a recent study I put together which focuses on the causes of sacks in NFL games. Although it is fairly detailed, I believe there are still areas of further development, some of which have been explored in an appendix to this initial study and will be coming in the second installment of this post.

As a disclaimer, the number of sacks were provided from an official source; however, the timing of the sacks, count of offensive blockers/defensive rushers was determined from my individual film study.The full piece is attached in a link, however, I have included some highlights below.

Point / Counterpoint on Rodgers' Extension

Today we're going to try a new format here at ANS--a debate between me and myself on the market value of Aaron Rodgers' recent contract extension. Rodgers recently signed a deal adding 5 years to his current contract. This will pay him roughly $21M per season over the next 3 years. See if you can figure out which Brian has the right idea and why they get different results.

Brian 1: Rodgers' new deal is a fantastic bargain. He's one of the truly elite QBs in the league today, and guys like that don't grow on trees. But more scientifically, just look at this super scatterplot I made of all veteran/free-agent QBs. The chart plots Expected Points Added (EPA) per Game versus adjusted salary cap hit. Both measures are averaged over the veteran periods of each player's contracts. I added an Ordinary Least Squares (OLS) best-fit regression line to illustrate my point (r=0.46, p=0.002).

Rodgers' production, measured by his career average Expected Points Added (EPA) per game is far higher than the trend line says would be worth his $21M/yr cost. The vertical distance between his new contract numbers, $21M/yr and about 11 EPA/G illustrates the surplus performance the Packers will likely get from Rodgers.

(This plot includes for all free-agent or veteran extensions since 2006. Cap figures are averaged for each player's career and, to account for cap inflation, are adjusted for overall league cap ceiling by season. Only seasons with 7 or more starts were included.)

How Much Money is a Sack Worth?

I realize it's draft season but I'm still working on building a salary database and combining it with performance statistics. Most of the work in this type of analysis is building the data, but it's harder than it might seem at first. Salary data might use one kind of player identifier while performance statistics use another. Merging them and creating a flat data file to play with is more than half the battle. There's still more I need to do. First up will be segregating free agent years from rookie contract years. But for now, here's some trivia.

Offenses get all the attention, so I thought I'd toy around with what I have so far on defense. Sacks are one of the most visible and tangible defensive statistics. I took the primary sack makers, defined as DTs, DEs or LBs who have averaged over one sack per season in their career, and plotted their career average sack rate against their average cap hit.

A few notes about the data: Only those years with cap hits greater than $1M were included as a crude way to focus on every-down starters. Additionally, only seasons where the player had 7 or more game appearances were included. The data ranges back as far as 2006 for whoever I had salary data for. Cap hit was adjusted for salary cap inflation--All cap hits are in $2012 cap dollars. Lastly, 'sacks per season' is extrapolated for each player to full 16-game seasons.

Cade Massey on Flipping Coins and the NFL Draft

Readers of this site will recall the name Case Massey. Along with fellow noted economist Richard Thaler, he co-authored the Massey-Thaler draft study titled The Loser's Curse. The paper found that, under the previous CBA, "surplus" draft value peaked with picks in the late first round and early second round. Surplus value was defined as the expected performance value above which a team could expect by spending an equivalent amount on a veteran free agent.

Massey has continued research into the draft. His presentation at the 2012 MIT Sloan Sports Analytics Conference outlines his recent findings. (I recommend using IE to view the presentation. Chrome didn't play nice with the video.) The slides from the brief can be viewed here.

If I understand things correctly, Massey has found that:

EPA Production and Cap Value, Skill Positions

I've been playing around with the connection between player value and production, and I thought I'd post some interesting observations.

As a measure of production I used Expected Points Added (EPA)--actually EPA per game to account for injury shortened seasons. For the measure of player value, I used cap hit. Cap value is useful because it boils down the complexity of many NFL contracts into one number. It can be tricky, though, as many contracts can be quite uneven from year to year in terms of cap value. For cap management and player-incentive purposes a 4-yr/$40M will often diverge far from a steady $10M per year cap hit. To account for this, I averaged each players' per year cap hit for the full period ('06-'12) and plotted against each player's EPA/G. The purpose of doing this is to see what level of production teams expect per $1M of salary. Is there a solid connection between true production and salary?

There are assumptions and limitations inherent in this analysis. Player production is dependent on the abilities of their teammates. WRs and TEs rely on their QBs to get them the ball, and some will have better passers and some will have worse, and vice versa. RBs are dependent on their line and scheme. But over the league as a whole, these considerations would (ideally) balance out. Put simply, for every Larry Fitzgerald being victimized by the offense around him, there's a Brandon Lloyd benefitting from being on a great offense.

The chart below plots offense skill position production by annual average cap hit. Each position is color coded.