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.

Schiano's New Kickoff Concept

Recently, Profootballtalk published an article discussing potential plans to eliminate an opening kickoff entirely (H/T to Abe Schwadron of TDDaily.com).

"Sean Gregory of TIME writes that one of the options being considered for replacing kickoffs entails giving the ball to the team that would have been kicking off at its own 30, automatically facing a fourth down and 15 yards to go. The team can then choose to punt or go for it, via fake punt or otherwise.

In other words, the kickoff would be replaced with the punt, and the onside kick would be replaced with a fourth-down conversion roughly half the distance of Ray Rice’s recent catch-and-run."

Obviously this concept piqued my curiosity, so I decided to run the numbers. Check out my two posts:

1) Goodell To Change Kickoff Rule? This gives an overview of the different probabilities and frequencies that would change.

2) Schiano's Suggested Kickoff Rule: When To Go For It? This looks at when it makes sense to attempt the 4th-and-15 and/or fake a punt.

Keith Goldner is the creator of Drive-By Football, and Chief Analyst at numberFire.com - The leading fantasy sports analytics platform.  Follow him on twitter @drivebyfootball or check out numberFire on Facebook. 

To Fake or Not To Fake: Fourth Down Decisions

After we wrote about Mike Tomlin's fake field goal decision in Week 9, it got me thinking about the general success rate of fakes versus typical fourth down attempts. Before moving forward, it should be noted that it is difficult to pull fake field goal and fake punts out of play-by-play data because they are not explicitly specified as such. So, you may be getting an aborted or bad snap or the field goal/punt formation may not have been recorded. We attempted to clean the data up as much as possible, which resulted in 213 fourth down fakes since 2000.

Similarly, we looked at the roughly 5500 fourth down normal go-for-it attempts. Granted, a lot of these will take place at the end of the game when teams are down by significant margins or must go for it in order to stay in the game, but that should not greatly affect their conversion rates. It may give us a sample bias, though, because those teams that are losing are typically worse offensively.

Fake attempts are exceedingly rare and given that there are only 200 or so attempts, we must be cautious of sample size issues. The most frequent fake attempts are on 4th-and-1 or 4th-and-2 which have happened about 30 times a piece. Compare that to over 2000 regular go-for-it attempts on 4th-and-1 and over 600 regular attempts on 4th-and-2.

Which Teams Should Run More?

If I read one more of these articles in the Baltimore Sun, I think I'm going to throw up.

...Ray Rice consistently ranks as one of the most productive and dynamic running backs in the NFL, capable of eluding defenders on the ground and through the air. He benefits from running behind bruising All-Pro fullback Vonta Leach, who's regarded as the most devastating lead blocker in the game. Yet, the Ravens have fallen to 19th overall in the NFL in rushing yards per game with an average of 104 yards per contest. And Rice ranks 12th on the rushing chart individually with 524 rushing yards...

The article goes on to add:

Blah blah blah. Run more blah. Need to find their identity blah blah.

Ok, I made that second part up. Actually, I have to give the author credit for attempting at least a surface level statistical analysis. But the fetish that sports columnists have with the running game has been one of the most enduring false narratives in the sport of football. It's time to put it to rest. I get that offenses have to run to keep defenses honest and to set up the passing game, but they don't have to run as often as they generally do to accomplish those things.

Let's take a look at offensive Expected Points Added per Play by play type. EPA/P accounts for all play outcomes--sacks, interceptions, fumbles, gains, losses, first down conversions, and so on--in other words, everything. Naturally, an offense would want to do more of the kinds of plays that gain them more and do less of the kinds of plays that gain less. Although this should be intuitively understood, zero-sum game theory proves that the optimum total production is when payoffs are equalized across strategy options.

Teams with high differences between pass payoffs and run payoffs should probably be running more often. And although you might think that teams with higher run payoffs than pass payoffs should be running more, that may not be true due to the passing paradox: Underdog teams that are poor at passing may need to do it more often to generate high variance outcomes.

The table below lists each offense's passing and running EPA per play, their total EPA per play, the difference between pass and run EPA/P, and their proportion of pass plays. I limited the analysis to 'normal football' where the score is relatively close and time is not yet a factor in play selection. The teams are ranked by the difference between pass and run payoffs. Teams at the top of the list should be passing more, and the teams at the (very) bottom should be running more. (Click on the table headers to sort.)

Running to Create a 'Manageable' 3rd Down Is Self-Defeating

Note: this is a companion article to last week's column at the Washington Post.

One of the common defenses of a run-heavy offense is that offenses need to make their third downs “manageable,” meaning short enough so that conversion is easier. The thinking goes that if an offense runs on either or both first and second down, it is relatively assured of shorter rather than longer distances on third down. At first look, this makes a lot of sense. After all, who wants to face third and long?

There are two problems with this argument. The first is that football is not a game of piling up first downs. The days of inching toward the goal line on 18-play drives are long gone if they ever existed at all. Football is, for the most part, a game of maximizing score differential, and the concept of Expected Points shows that NFL offenses are generally running too often on first and second down.

The second problem is that even if gaining a first down is the primary objective, running on first down is becoming a worse idea every year. The graph below shows that passing on first down leads to a conversion more often than running on first down. As usual, I limited the data to plays in ‘normal’ football situations, when the score is relatively close and time is not yet a factor at the end of either half.

Expect Even More Passing Yards, and Why It Matters

Remember the passing explosion to start the NFL season last year? Get ready for even more. 2011 was not a one-year blip but instead was part of an accelerating trend toward more potent and more frequent passing. This isn't statistical trivia either, as this trend has dramatic implications for how the game should be played.

Take a look at Adjusted Net Yards Per Attempt (courtesy of PFR), which with just one number incorporates passing efficiency, interceptions, and sacks. Since the dawn of the modern passing era, passing has become steadily more lucrative. But since 2004, the rate of increase in average ANY/A has accelerated. The 2011 season featured the most successful passing game ever.

For context, compare the graph above with the next one. This shows the same trend but for rushing yards per carry. There is a very shallow increasing trend since a trough in the mid 1990s, but it pales in comparison. The jump in net passing last year alone is larger than the increase in rushing over the entire period. (I've kept the scales of both graphs identical for a pure comparison.)

Identity Crisis

If there’s one meaningless word thrown around by football analysts in the last couple years, it has to be identity. “The Jets offense has an indentity crisis.” “The Ravens need to find their identity on offense.” “The Eagles have lost their offensive identity.”

Are we talking about professional football teams or teenagers trying to figure out whether to hang out with the jocks, dweebs, preppies, or wastoids?

Identity has replaced rhythm as the most meaningless word in the NFL. Remember those days when every broadcaster at one point in the game had to say, “The 49ers need a couple of completions here to get into a rhythm"?

What the hell does that even mean?

QB Sneak vs. RB Dive

In the NO-ATL game Sunday, ATL went for a risky 4th down and 1 conversion attempt in OT with just inches to go. They elected for a RB dive play rather than a QB sneak. (By dive play, I just mean a straight RB handoff directly between the tackles.) But all '4th and 1' situations are not equal--from 1.5 yards down to an inch to go.

QB sneaks seem more successful on inches-to-go situations than RB dives. We'd like to know if the data back this up. Unfortunately, the play descriptions don't note how long the 'and 1' is, whether it's a long yard or just inches. We'd expect to see more QB sneaks on the shorter distances and more RB dives on the longer distances, which bias the numbers because longer to go distances would naturally be tougher to convert. Still, we may be able to draw some inferences.

The table below lists the success rates for 3rd and 4th down runs with 1 yard to go. It breaks out plays by QBs, RBs, and FBs. QB scrambles on pass plays have been removed. Kneel downs and spikes are also removed. Plays inside the 10 yd line are removed due to field compression effects.

Almost Always Go for 2-Point Conversions?

In the Buccaneers-Redskins game this past Sunday, the Redskins were able to score a potentially game-tying touchdown at the end of regulation, only to fail to hit the extra point due to a mishandled snap. Gregg Easterbrook suggested the Redskins should have gone for the two-point conversion, which is a plausible strategy in many circumstances. But Easterbrook went on to add this little tidbit: "Rushing deuce attempts are about 65 percent successful in the NFL -- a better proposition than the 50/50 of advancing to overtime."

It's well established that 2-point conversion attempts are successful slightly less than 50% of the time, so could the 65% number for runs possibly be true? If so, what would that mean for NFL strategy?

There have been 718 2-point conversion attempts from 2000-2009, including playoff games. Overall, they've been successful 46.3% of the time. But this is slightly misleading because it includes aborted kick attempts. If we weed those out, along with some other mysterious plays, such as Josh McCown's kneel-down while trailing by 5 points in the final few seconds of the Cardinals-Vikings 2003 game, we get a different answer. For all normal 2-point conversions, the success rate is 47.9%.

Now look at the success rate broken out by play type:

The Linebackers' Dilemma

Say there are two inside linebackers on the same team, John Andrew and Dan Farley. They’re considered equally good players, and both are in a contract year. Their team is good, and one of the early favorites to go deep in the playoffs this season. Each one has some choices to make over the course of the upcoming season.

Both Andrew and Farley want a big payday. In order to get as big a contract as possible, they need a lot of gaudy numbers to point to—lots of sacks, QB hits, forced fumbles. Millions of dollars are on the table, and the temptation is strong. However, leading their defense to a successful year and going deep in the playoffs will increase their values too. But that can only happen if both Andrew and Farley play selflessly and put their team first.

On any given play, a LB can either guess at the play call, trying to get a sack or stuff a run. Or, he can play his responsibility within his scheme by reading and reacting, doing exactly what the coordinator expects him to do. In other words, he can do what his team is counting on him to do, or he can gamble trying to make a play himself, exposing his team to giving up big gains.

World Cup Penalty Kicks, Wimbledon Serves, and Intuitive Algebra

Maybe June should be "other sport month" here at Advanced NFL Stats. Except for Albert Haynesworth's principled, valiant stand against being forced to play defensive tackle a foot and a half to the right from where he is accustomed, there's not much going on in the NFL. Fortunately, there's plenty of other sports going on, including the world's biggest events in soccer and tennis.

Soccer and tennis offer two of the best examples of simple two-strategy zero-sum game theory. Soccer offers us the penalty kick, when a player kicks to the left or right extreme side of the goal so hard that the goalkeeper must simultaneously guess a direction to lunge. Tennis gives us the serve, where the server aims for either the extreme forehand or backhand side of his opponent's service box. Both examples give us the opportunity to examine how well experts are able to approximate the optimum strategy mix.

Run-Pass Imbalance In the Red Zone--1st Downs

Just before halftime in last year's Super Bowl, on first and goal from the one, Kurt Warner threw the ball directly into the arms of James Harrison who rumbled 100 yards for a touchdown. With so little time left in the half, passing was the obvious call, but that play highlights the dangers of passing so close to the goal line.

Game theory tells us that when payoffs for strategies are unequal, the strategy with the higher payoff should be chosen more often. We've seen that between the 20 yard lines payoffs for passes are consistently higher than for runs on 1st down, but inside the 20 running becomes more lucrative. Now let's take a look at the red zone in more detail, where the stakes get higher and the field gets shorter. On 1st downs in the red zone, should offenses run or pass more often, or do they already strike the right balance?

Run-Pass Imbalance on 2nd and 3rd Downs

I've recently been looking at the imbalance in the payoffs for running and passing on first downs. The results suggested that most teams should generally pass more often outside the red zone and run more often inside the 10-yard line. What about 2nd and 3rd downs?

Game theory tells us that when the payoffs for two strategy options are unequal, the strategy option with the higher payoff should be selected more often. As the opponent adjusts to counter the new mix of strategies, the payoff of the favored option will decline while the unfavored option becomes more lucrative. Eventually, the payoffs for both options equalize, and at this point the overall payoffs are optimum. In two-player zero-sum games this is known as the minimax, or more generally as the Nash Equilibrium.

I used Expected Points (EP) to value the payoff of each play. Expected Points measures the net point advantage that the play result gives to an offense. It captures the value of yardage gained and lost, first downs, sacks, penalties, turnovers, and everything else in terms of equivalent point value. The change in EP resulting from a play is called Expected Points Added (EPA).

One of the things EP does not measure is the time value of a play. In situations when a team has a significant lead, the true value of a run includes the time burned off the clock. To a team behind late in a game, pass attempts have more value because they are more likely to stop the clock. For this reason I only include plays in the first and third quarters and when the score is within 10 points. This excludes trash-time plays and plays affected by the clock.

Defensive Run-Pass Balance

I've been writing a lot about offensive run-pass balance lately, recommending that most teams should pass more often. So far I've ignored half of the equation--Defensive strategies matter too.

Unlike offensive play choices which are discrete defined options (such as either run or pass), defenses have a continuum of options ranging from a prevent defense to a goal-line stand. Defenses don't have to commit to one or the other. Instead, they can bias their strategy anywhere from 100% pass to 100% run.

With play-by-play data, we know what option an offense chose. Unfortunately, without coach's film of every game and an intimate knowledge of a teams' defensive schemes and intentions, it's nearly impossible to know where on the continuum a defense stood on any given play.

Still, it may be useful to see how often a team was run against or passed against, and see how successful each play type was. The table below lists each defense's proportion of passes faced on first downs. Also listed is the average success of each type of play as measured by Expected Points Added (EPA). The difference in average success between passes-against and runs-against roughly measures the imbalance in play selection.

2009 Team-Specific Run-Pass Balance

Recently I've been looking at run-pass balance on first downs based on a principle of game theory. When strategy mixes are optimized, the two strategies will ideally produce equal payoffs. If they aren't equal, then the better strategy should be selected until the opponent responds with his own counter-strategy. Results suggested that, in the NFL overall, the gains by passing on first down exceed those by running. In turn, this suggests that offenses should pass more often than they currently do.

However, every team has its own relative ability between passing and running. You can't just tell the 2009 Raiders to start passing more often. Their running game may actually be superior to their passing game in terms of expected payoffs, so while most teams should be passing more frequently, it's possible a minority of teams should be running more often.

(Much) More on 1st and 10 Run-Pass Balance

In a recent article I presented evidence that offenses should generally pass more often on first down. Accounting for both the potential gains and the potential risks of each type of play, passing tends to lead to a greater net point advantage than does running. The analysis was based on a concept known as Expected Points, which measures the average point advantage an offense can expect given a down-distance-field position situation.

Expected Points incorporates all the various factors such as turnovers, yardage gains, sacks, incompletions, first down conversions, scoring, and so on. But I thought it would be helpful to dig deeper to investigate how and why passing appears more advantageous. In this article, I'll present a series of graphs comparing running and passing on first down, each one looking at a different facet of the game.

Offenses Run Too Often On 1st Down

NFL offenses generally run too often on 1st down. Accounting for the relative gains of each play type, and accounting for the risks of turnovers, offenses should pass more. There is currently an imbalance, where teams are too often running directly into defenses that are expecting runs.

Game theory tells us that when there are two strategy options, like run and pass, the expected payoffs for both options should be equal. You really don't need game theory to intuitively understand this. If one option yields a better payoff, then it should be chosen until the opponent responds with a strategy change of his own. Eventually, as the opponent responds, the payoffs for the two options equalize. The point at which the strategy mix equalizes payoffs is known as the minimax, or sometimes called the Nash equilibrium. The resulting strategy mix, or run-pass balance in this case, produces the best overall, long-run payoff.

When there are two strategy options and one of them yields a much higher payoff, it tells us two things. In this case, passing is more lucrative than running on 1st down, and this tells us: 1) offenses should be passing more often, and 2) for now, defenses should continue to be more biased toward stopping the run.

Onside Kicks

With 4 minutes left in the first quarter of last week's Cardinals-Seahawks game, Arizona's Neil Rackers booted a short but high 'pooch' kick that was quickly recovered by the kicking team. The kick recovery was worth a very considerable +0.12 WP. The Cardinals went on to score a touchdown, taking a 14-0 lead. How smart are onside gambles like this?

Onside kicks in the NFL are successful 26% of the time. It’s true, but it’s also very misleading. Onside kick success rates are very dependent on whether the receiving team is expecting one.

Full Review of Game Theory Run-Pass Balance Study

A new paper on game theory and run-pass balance in the NFL, Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League, says that offenses run too often and play calling is too predictable. The authors, Kenneth Kovash and Steven Levitt, construct a success metric to value the outcome of NFL runs and passes from the 2002-2005 seasons. Then using regression models, they estimate and compare the values of a typical run and a typical pass. They also construct a regression to test if play calls can be predicted to any degree based on the previous play call.

Game Theory

Game theory tells us that in a 2-player zero-sum game, if both players are playing the optimum mix of strategies, the long-term average payoff from each strategy will be the same. If you have two general strategy options, like run or pass, you can’t just choose one of them all the time. That would make the defense’s job pretty easy. So you need some sort of unpredictable mix of strategies. The question is, what’s the optimum ratio?

A New Academic Study on Game Theory and Run-Pass Balance

There’s a new study on run-pass balance based on game theory minimax equilibrium. The study is called Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League and it’s from Kenneth Kovash and Steven Levitt (of Freakonomics fame).

The authors created their own version of  Expected Points as their measure of play success. Using a giant regression model that accounts for all sorts of confounding variables, they find passes lead to more success than runs. Game theory would say that, ideally, both strategies should yield the same amount of success.