Bases in Baseball

First base

This is the most important one. Outs are baseball's currency, so getting on first any way you can goes a long way toward your team's success (as Billy Beane's A's famously exploited). Reaching first base prolongs the inning, tires out the pitcher, potentially allows earlier runners to advance, and represents a potential run based on how the following batters fare.

However, the team still has a long way to go to cash in the runner, needing either a well-placed extra-base hit or two or more of a single, a walk, a stolen base, a passed ball, or a wild pitch. Additionally, the runner is in constant jeopardy of being part of a double play on a ground ball.

Second base

Second base is squarely in scoring position, where most singles will score the runner.

A team with a runner on second and no outs can attempt to play small ball: sacrificing most of their potential for the inning in exchange for a reasonable shot of scoring a single run. This is accomplished by bunting, hitting ground balls behind the runner, or hitting sacrifice flies.

The runner is no longer much of a threat to be doubled off, aside from force outs at third, line-drive outs, or base-running blunders.

Second base's position on the field affects many things: It's the closest base to the outfielders who are returning batted balls to the infield. It's the hardest base to advance to on a fly ball (runners usually err on the side of returning to first on fly balls). It's the easiest to steal, given that the catcher has to throw roughly 127 feet, as opposed to 90 feet to the corner bases.

Getting there via the steal is a nice bonus, but you need to convert some huge percentage to make stealing a good strategy (I've discussed this in the past); the incremental base benefits the team much less than the cost of potentially turning a runner into an out.

Third base

There's an old baseball adage saying "Never make the first or third out at third base." The marginal benefit of third base over second is the smallest of any advancement.

Under the first scenario, a runner staying at second with no outs can often be converted into a run using small ball (as discussed above).

Under the second scenario, there aren't enough incremental ways to score from third with two outs over ways you would have still scored from second. Balls in play that could advance runners simply end the inning instead. However, there are a few extra ways to score from third, such as passed balls, wild pitches, or even stealing home.

Strasburg's Bat and Logical Fallacies

Stephen Strasburg's arm likely will be shut down in the middle of September as he recovers from Tommy John surgery. WaPo reporter Adam Kilgore today posed the question of whether Strasburg could be used as a pinch hitter, as he's shown prowess at the plate. Manager Davey Johnson quickly shot down this notion, citing injury risk.

I do not have the injury-per-at-bat data readily available, but this approach is insanely conservative. There were 185,254 plate appearances last year and perhaps only a handful of batting injuries. Maybe I could sell Davey some UFO attack insurance while we're at it.

Why does it matter whether Strasburg is pitching in the same game in which he appears at the plate? If batting is indeed so dangerous, why don't the Nats just concede his two at-bats per start and have the lead-off guy bat out of turn in place of Strasburg?

Managers have to balance both winning and saving their jobs. Davey won't marginally improve his chances of winning because he's afraid of having to answer for injuring Our Generation's Greatest Pitching Prospect, in — *gasp* — a game he wasn't pitching in.

On John Lannan and demoting the inferior player

Much has been made about how John Lannan is the highest-paid player to be optioned to the minor leagues before the season. His $5 million contract heads to Syracuse, while minimum-wager Ross Detwiler stays with the Nationals big club.

The contracts of both players are sunk costs, so they lose the same amount of money regardless of how the roster is arranged. If the big earner isn't among the best players, there's no reason to bring him up.

The Giants, meanwhile, have been going back and forth with their own horrible contract in Barry Zito, who is in the midst of his $126 million deal. They left him off the 2010 playoff roster and sent him to extended spring training this year, but he's coming back to the Majors in a few days.

General managers face some adverse incentives that often lead them to hold onto big money guys or first-round draft picks too long. Letting go of these guys is akin to admitting that they made a mistake.

Is the NFL the New NASCAR?

USA Today ran a front-page story today about how NASCAR's ratings and popularity have plummeted since Dale Earnhardt's death 10 years ago. No drivers have died since, and the article speculates that NASCAR has overemphasized its safety improvements, to the point that fans feel that the sport has lost its exciting edge.

I see some parallels with the NFL's recent crackdown on helmet-to-helmet hits this year. This is not to mention the longer-term increase of protections on receivers and quarterbacks via strict roughing the passer and pass interference penalties. All the while, the defense becomes increasingly marginalized.

It's sort of uncomfortable to speculate on where we stand on the trade-off between death and entertainment. The NFL has had an easier time favoring the latter, because, as Robin Hanson points out, the adverse health effects are often delayed beyond the player's retirement and thus less in the public view. I've always loved how he's framed the devastation:

Surely we can see football hurts players – we often see them carried off in on stretchers. But I wonder: would we accept this harm nearly as much if we saw it all up close? Players would suffer the same average loss if each season one out of ten players just dropped dead on the playing field! (A dead 25 year old player loses 55-25 = 30 years, which is ten times the three years life lost per player per season.)

Rethinking Pythagorean Winning Percentage

Baseball-reference.com describes Pythagorean winning percentage as "an estimate of a team's winning percentage given their runs scored and runs allowed. Developed by Bill James, it can tell you when teams were a bit lucky or unlucky." Click through for the formula.

An example is the 2009 Washington Nationals. The team finished 59-103. However, the Nationals scored 710 runs while allowing 874 runs, so their Pythagorean W-L is 66-96. The Baseball Reference folks would thus argue that bad luck cost the Nats 7 wins, which is a substantial number in comparison to their actual number of wins.

However, while winning is a function of runs scored and runs allowed, runs in the late innings are also partially a function of runs in earlier innings. Your team's run expectations in a given inning are highly sensitive to what's happened earler in the game.

Consider a game where your team is tied in the top of the seventh. And another where you're losing (or winning) by 10 runs. On average, you'll score more runs in the latter scenario, because both teams will insert inferior relief pitchers, saving their star bullpen guys for another day. Hell, they might even have a position player pitch. Losing by 15 or 5 is just as bad as losing by 10, so it makes sense to conserve baseball resources, even at the expense of the final score in a hopeless game. Any cheap runs you score in such situations won't do much to improve your winning percentage, but Pythagorean winning percentage has no way to account for this.

On the other hand, in a tied game, the other team will do everything possible to prevent you from scoring, because a run or two could mean the ballgame.

Of course, teams also conserve offensive resources in blowouts. Pinch runners and defensive replacements often swap in for the likes of Adam Dunn or Barry Bonds. I suppose it's possible a weaker offense could offset the effect of inferior pitching, or even trump it.

Additionally, batters could be trying less hard in blowouts, just wanting to get the game over with, but I don't think there's any evidence to support this (why not pad your batting average against bad pitchers?).

Proof that Washington Nationals Tickets Are Overpriced

Around the time that they set another record for lowest attendance, the Washington Nationals announced a "Buy 2 Get 2" promotion (see screen grab above once this link becomes obsolete) in which fans can get two full-season tickets free when they buy two in select sections (read: near or behind the foul poles).

At first, this seems like an arbitrage opportunity, or opportunity to make a profit with no risk. There are some time and money costs to reselling tickets, such as researching prices on StubHub or haggling with scalpers, but someone could theoretically make easy money just by selling each ticket for half of its face value. They just need to buy four tickets (two at face value and two free) from the Nationals for $60 and sell each ticket for a little more than $15.

The fact that someone couldn't expect to sell all these $30 Nats tickets for as little as $15 each, and thus make a profit, says a lot about the lack of demand and the sorry state of the franchise.

Using a Pitcher to Pinch Hit

Starting pitcher Jason Marquis pinch hit for the Washington Nationals in the fourth inning of last night's game and the fifth inning Monday, grounding out both times.

Marquis has a .201 lifetime batting average, but that comes with a paltry .516 OPS. In other words, he's just as weak a hitter as any other pitcher. Yet manager Jim Riggleman often uses starting pitchers to pinch hit if that day's starter is knocked out early in the game, in hopes of saving his bench players to pinch hit later.

If the Nationals' pitcher is being removed so early in the game, it's likely that he's been struggling and that the team is facing a large deficit. Therefore, Riggleman is sending up a pitcher to hit because it is a low-leverage situation (i.e., the at-bat has a small chance of affecting the outcome of the game).

Or so the thinking goes. Yet I have to wonder if the strategy is flawed.

Suppose the Nationals have five bench players, not including the backup catcher (who is rarely sent into the game, because if the other catcher gets injured and the backup is no longer available, the team is in deep trouble). More often than not, Riggleman's strategy would give plate appearances to Marquis and four or fewer of these bench players, when he could no doubt expect better results from plate appearances from five or fewer bench players instead.

The latter combination would give the Nationals a better shot at being in a close game in the late innings, which would justify the risk of using up all the bench players. A run scored in the fourth inning counts just as much as a run scored in the ninth. A surplus of bench players in the ninth inning does the team no good if it's trailing by four runs. Even if Riggleman does blow through his whole bench, it's unclear that having Marquis possibly pinch hit in the ninth is worse than having him for sure pinch hit in the early innings.

Perverse Incentives for Pittsburgh Pirates

I've already blasted this Slate article all over Facebook and Twitter, but it's worth posting here as well.

Baseball's revenue sharing system was designed to try to help baseball's poorest teams by forcing the richer teams to pay them millions of dollars a year. However, this weakens a team's incentives to win games and become more profitable, as all additional money earned by winning is partially offset by a drop in income from revenue sharing.

The phenomenon is similar to welfare or unemployment insurance. Someone who collects $400 a month in welfare would only become $600 a month better off by taking a $1,000-a-month job, not to mention the time and effort required to work the job.

The Benefits of Drafting Too High

It was as if a big new market-moving Wall Street money manager had sprung into being, and bought shares only in vegetarian restaurants, or electric car manufacturers. With a difference. A revaluation in the stock market has consequences for companies and for money managers. The pieces of paper don't particularly care what you think of their intrinsic value. A revaluation in the market for baseball players resonates in the lives of young men. It was as if a signal had radiated out from the Oakland A's draft room and sought, laserlike, those guys who for their whole careers had seen their accomplishments understood with an asterisk. The footnote at the bottom of the page said, "He'll never go anywhere because he doesn't look like a big league ballplayer."

- Michael Lewis' Moneyball


I am re-reading Lewis' 2004 classic, which explains how the Oakland A's had so much success in the early 2000s despite a paltry payroll because they evaluated players differently. The A's won with misshapen players who couldn't run or field very well but who had a knack for getting on base.

Many of the players the A's were interested in before the 2002 amateur draft didn't see themselves getting drafted until the fifteenth round or later. One could argue that the A's should indeed have waited till these later rounds to draft these kids, because no other team was going to take them anyway.

Instead, the A's called these kids and told them how well they would fit into the Oakland system, so much so that the A's would be selecting them in the first or second rounds. They would be offered a signing bonus that was absurdly higher than what they were expected yet up to a million dollars less than other high draft picks would typically receive.

Either method would help the A's acquire valuable players that no one else really wanted, but it's clear that the latter gave these youngsters a credible reason to believe in themselves and thus devote the effort to becoming big league ballplayers.

The Decline of Stephen Strasburg Mania

I recently wrote about the absurdly high ticket demand for Stephen Strasburg starts, but it seems like the hysteria has ended.

After an incredible beginning to his career, Strasburg has regressed to the mean a bit, being pulled from one start minutes before the game, spending a stint on the disabled list, and getting shelled against the Florida Marlins. While Strasburg's first few starts were sold out, his appearance Sunday drew a paltry 21,695 fans to Nationals Park.

I like to track prices on StubHub, a secondary ticket market, because it says so much about anticipated demand by the scalpers looking to turn a profit and actual demand by the fans as game time draws near. A few hours before Sunday's game, there were hundreds of tickets under $5 still available (many for only a few cents), as the resellers tried desperately to recoup any small percentage of what they paid for the tickets.

It's hard to imagine the market to see Stephen Strasburg will ever return to its early form, even if he continues to be an incredible pitcher. Ever wonder why many venues don't raise ticket prices, even when they know an event will easily sell out? One reason is insurance: for whatever reason (recession, bad weather, etc.), the venue could have made a mistake and ended up with a half-empty house.

But this mistake would be perpetually punished: it's not much fun to see a sporting event or concert surrounded by a sea of empty seats, which serve as a reminder that other people no longer think that this event is much fun. It's difficult to convince yourself that attendance is down because of the economy and not because the team sucks or baseball is boring. Today's attendance can very much be a factor of yesterday's attendance, which has such a large influence on how people perceive an event.

(A nod goes to Russ Roberts, who discussed many of these ideas in his class a few years ago.)

Arbitraging Strasburg

Just for the heck of it, I listed my tickets to Tuesday's Nationals game on StubHub at a 300% markup.

Stephen Strasburg is scheduled to pitch, and our season ticket seats are right by the Nationals bullpen. To my surprise, the tickets sold within a few hours.

I once had a professor say that you can benefit if you enjoy things that few other people do.

For us, our quirk is that we enjoy the games in which Stephen Strasburg doesn't pitch. We like it when the games are less crowded, which means shorter lines and less of a crunch heading to the Metro after the game. Plus, we've already seen him a few times.

We'll happily sell our tickets to the Strasburg games, because other people value them so much more than we do. I won't quite be able to go to other games for free because of the Strasburg proceeds, but selling those games will sure put a dent into my season ticket bill.

There are teams that sell out every game, and there are teams that nearly can't give away seats. But the Nats have a strange situation on their hands, in that Strasburg gives them an attendance jolt every 5 days. In fact, I think the day after his debut represented the largest drop-off in ticket sales between games in major league history.

Note how people like me can take advantage of this phenomenon, but the Nationals can't. They can't triple their prices every five days, or invalidate cheap ticket sales that occurred months ago.

I hope I'm not costing myself hundreds of dollars by writing about this, but such is the price of ego. Let's just hope the kid doesn't get hurt!

Why Are Baseball Seats Filled So Unevenly?

CC photo courtesy of ttarasiuk on Flickr.

I often see scenes similar to the above photo at Nationals Park.

Notice the lower sections of seats, closest to the field. The ones to the left and center are nearly full, followed by two sections that are nearly empty, followed by sections to the right that are nearly full.

This is puzzling at first, but it makes perfect sense once you consult the seating and pricing guide. The seats in the far right of the photo are the pink seats in the guide. They are $10 cheaper than the seats next to them in the mostly empty sections, which are at the cutoff of the higher pricing zone.

The tradeoffs of seat pricing zones are intriguing. One extreme is general admission, where everyone pays the same price. On the other extreme, Nationals Park and other sports stadiums probably have the highest number of pricing zones of any event where tickets are sold, yet there are still numerous instances where seats that are mere feet from each other cost substantially different prices.

The advantage of pricing zones is obvious: a seat right behind home plate shouldn't be the same price as a seat in the nosebleeds. So why aren't there hundreds of price zones, instead of dozens? Transactions costs would be way too high. Or, in non-economist speak: it would be too much of a hassle.

What if the Best Teams Drafted First?

I am in the midst of reading the thoroughly depressing "The Elusive Quest for Growth" by William Easterly, which details how various attempts to help developing countries escape poverty have failed because of misaligned incentives.

For example, giving the most foreign aid to the poorest countries gives Third World leaders incentives to keep their subjects in poverty and therefore acquire even more aid. Alternatively, giving aid conditional on political or economic reforms doesn't work; when poor governments become increasingly corrupt, donors don't have the heart to stop giving aid. And on and on.

That got me to thinking: Do we try to improve the worst sports teams in the same incentive-perverting way that we're trying to help the poorest countries?

Professional sports leagues award draft picks in the reverse order of the teams' standings the previous year (there are some technicalities, such as the NBA's draft lottery and baseball's draft pick compensation for lost free agents, but the point remains the same). The idea is that the worst teams get first choice at the top rookies, thus enabling them to become competitive in the near future.

If the reverse-order draft did nothing to change teams' behavior, it would be an admirable policy. But statistical research has suggested that teams might be losing on purpose to improve their draft standings. For instance, each year the worst baseball teams trade away many of their best players in July and give ample big-league playing time to unpolished young prospects who otherwise would be kept in the minors.

I wonder if the Washington Nationals wish they had won a few more games during their horrid 2008 campaign. Because they didn't, and therefore finished dead last, they were awarded the No. 1 pick the next year and thus the rights to rookie phenom Stephen Strasburg. And all the sellouts, merchandise sales, and national media exposure that came with him. I'm sure they're devastated.

What did the Washington Wizards do this past year to deserve the No. 1 pick in the NBA Draft? From The Washington Post:

Grunfeld sat in the back room to watch the Ping-Pong balls bounce in favor of a franchise that finished 26-56 last season, enduring a trying campaign. Abe Pollin died of a rare brain disease in November; star point guard Gilbert Arenas was suspended for the final 50 games and received a felony gun conviction after bringing guns to the locker room in a dispute with teammate Javaris Crittenton; and Grunfeld detonated the roster with a flurry of trades at the deadline that shipped out former all-stars Antawn Jamison and Caron Butler, as well as Brendan Haywood and DeShawn Stevenson.

Setting aside the death of team owner Pollin, none of the above is behavior that the NBA or its fans want to encourage. Yet the team was rewarded with the No. 1 pick.

So while corrupt leaders end up with more foreign aid, incompetent team owners or upper management end up with top draft picks. How could these systems be improved?

In his book, Easterly suggests that the most aid should go to countries that have implemented the most economic reforms, not the ones who promise to implement them, thus making their commitment to improve credible.

In that spirit, why not give the highest draft picks to the best teams, rewarding them for winning? Or, for a less-extreme solution, why not make the draft order random? Either approach would remove the incentive to lose.

Of course, bad teams would suffer. After the losses began to mount, maybe the teams' management would be replaced by more competent personnel. Maybe teams that can't draw many fans will improve their on-field product, move to more lucrative markets, or go bankrupt.

Are these outcomes really that bad?

Fudging the Numbers: NHL Edition

In the NHL, each player's impact on the team's salary cap is based on the average annual value of his contract. Just as government officials and corporate executives often use creative accounting to meet certain fiscal goals, sports team aren't immune from trying to game the system.

In this case, players want large contracts, but NHL teams don't want large impacts on their salary caps. The New Jersey Devils attempted such a compromise by signing Ilya Kovalchuk to a 17-year deal, which is unheard of in professional sports and has since been voided by the league. Follow the link to the original story for more details, but the gist is below:

The contract was rejected because years of low salary at the end of the deal were added for the sole purpose of lowering the cap hit. The person added that it was determined that neither the Devils nor Kovalchuk believe he will play the final years of the deal at those terms. The All-Star was slated to earn only $550,000 in each of the last five seasons of the contract that was to run through the 2026-27 season, when Kovalchuk will be 44.

Kovalchuk was to earn $98.5 million of the $102 million in the first 11 years of the deal.

...

The Devils would have absorbed an annual salary-cap hit of $6 million - the average amount per season. That number was brought down because of the extended years at low salary at the end.

Nationals Win Me Over. Reluctantly.

In March, I had my run-in with the Washington Nationals ticket office, after which point I said I wouldn't buy season tickets because, as I wrote later:

"I can't give you the satisfaction of saying you talked the crazy blogger guy into buying season tickets after all."

Well, since that time, Sharon and I have attended several games this season. I finally caved and bought a flex plan, which involves getting tickets to three games in order to get a fourth free.

I should have already done this several times over this season, as we go so often and the Nats have become Sharon's favorite team.

I guess my love of baseball and desire to economize on ticket purchases, as well as Sharon's inexplicable fandom of relief pitcher Tyler Clippard, have won out over my pride. You win, Nationals ticketing office.

Parity by Division

Major League Baseball has six divisions. All six divisions have won the World Series since 2001:

NL West: D'Backs ('01)
NL Central: Cardinals ('06)
NL East: Marlins ('03), Phillies ('08)
AL West: Angels ('02)
AL Central: White Sox ('05)
AL East: Red Sox ('04 and '07), Yankees ('09)

In fact, from '01 to '06, there were six Series. All six divisions won once.

The NBA also has six divisions. No team currently in the Northwest Division has won a championship since the Thunder (who were then the Seattle Sonics) won in 1979.

Is the "Choking" Effect in Sports Real?

There's an interesting discussion over at the Sabermetric Research blog about whether a "choking" effect exists in soccer:

Gier Jordet, a professor at the Norwegian School of Sport Sciences in Oslo, reports that, when the score is tied, penalty kick shooters succeed at a 90% rate. But when the shooter's team is behind by a goal, and presumably there's more pressure, he succeeds only 60% of the time.

I made a similar point in the comments on the SR blog post, but I'm not too surprised that teams perform worse when they're losing.

On average, bad teams spend a larger portion of the game trailing. It's reasonable to assume that they would therefore get more penalty kicks in such situations than good teams would, thus making them overrepresented in the "behind by one goal" sample. If bad teams also have inferior penalty kickers, it's no surprise that they do worse.

Similarly, if your team is playing against an outstanding goalie, you're more likely to be trailing at any given moment than you would be otherwise. In such situations, the outstanding goalie is also more likely to block your penalty kicks.

If we could control for these factors (say, if we had 100 observations of penalty kicks by one team against a certain goalie) and still observed the choking effect, I'd be more convinced.

Am I a Baseball Keynesian?

The blog Bayes Ball cites my post among several theories attempting to explain the recent trend of perfect games. He then conducts a careful analysis using the Poisson distribution, which is perfect for studying events that are extremely rare (in this case, perfect games) but have many, many chances of occurring (there are thousands of regular season games each year). His analysis shows that a season with two perfect games is well within reason.

After reading the post, I had a few protests. For instance, if Jim Joyce gets the call right, we'd have three perfect games this year, and the Poisson analysis goes out the window.

Even if we let Joyce's call stand, I speculated that a season with three games in which the pitcher gets the first 26 batters out would still be exceedingly rare by historical standards, and we'd have to start questioning the assumption that the dominance of pitching relative to hitting hasn't changed much in the past few decades.

In my previous post, I argued that the string of perfect games in fact did demonstrate a change in favor of pitching. I even suggested that baseball should change its rules (like adjusting the height of the mound or the dimensions of the strike zone) to restore the historical rates of success and failure between batters and pitchers.

But after a while, I was forced to wonder: What if I had spotted a trend where there wasn't one? What if I had advocated that we fix a problem that doesn't exist?

There is a connection to macroeconomic policy. To keep the economy on track between the undesirable extremes of too much unemployment or too much inflation, the federal government often modifies monetary policy (such as changes to the interest rates) or fiscal policy (such as changes to taxation and government spending).

The chief advocate of such tools was John Maynard Keynes, who is regarded as a hero among most economists but whose theories are generally dismissed among the George Mason economics faculty and students.

One has to wonder how often we are tempted to implement macroeconomic policy changes in response to economic news that might just be the result of statistical fluctuation. Perhaps action is occasionally warranted to rebalance both baseball and the economy, but we should think twice before moving in the fences and allowing each batter five strikes, or introducing stimulus programs and holding down interest rates.

How Has the Price of Madden Games Held Stable?

In the middle of last July, I preordered Madden NFL 10 for Wii, paying $46.99.

The Wii version was vastly inferior to the PS3 and X-Box versions, but that's another matter. As far as Wii football went, it was top of the line: new features and updated rosters. It was released right before the NFL season.

It is now the middle of June, 11 months later. The Super Bowl was played four months ago. A new version of Madden comes out in two months. There is probably less interest in football video gaming now, when football isn't in season.

Yet Madden NFL 10 still sells for ... $46.99.

Is anyone else surprised that the price hasn't dropped? Is Electronic Arts maximizing its profits with this price? People can evade the high price by buying used copies of the game or Madden games from prior years (Madden 09, for instance, is only $18.73).

Perhaps EA's stable-pricing policy encourages people to buy the game when it comes out, because they have seen year after year that the price isn't going to drop a few months later. These additional sales could more than offset the sales that EA is losing by not lowering its price in the interim months between seasons.

Can you think of any other goods that behave this way, with new versions coming out every year? What happens to the price of cars the month before the new models come out?

Optimal Time to Rest Position Players

Major League Baseball teams play 162 games in about 180 days. With a few exceptions (such as players named Ripken or Gehrig), position players need a day off every so often to stay sharp.

For Wednesday's afternoon game, Dodgers manager Joe Torre rested four of his eight starting position players against the Diamondbacks: Rafael Furcal, Manny Ramirez, Casey Blake, and Russell Martin (all of whom, ironically, later played, as the game went 14 innings and the Dodgers needed pinch hitters). Managers often rest older players en masse in day games after the team played the night before.

Would splitting up the days off, by instead resting one starter each game, lead to more wins? Is it better to significantly reduce your chances of winning one game or slightly reduce your chances of winning four games?

I don't have a clue how someone would go about answering this question empirically.