What's a home run really worth?

In September, an old man’s fancy turns to the Greatest American Sport – greatest, that is, if you’re addicted to statistics. Mavens of Major League Baseball are poring over the numbers and chicken entrails to predict the playoffs.

How to size up hitters? The popular yardstick is the batting average – the share of times at bat that the player gets a hit, discounting an error or a fielder’s choice (when the other team lets the batter go to first while it throws out another player). The batting average is normally about one in four. As I write, the hottest hand is attached to Yordan Alvarez, designated hitter for Houston, who is merrily clicking along at .312. The Astros aren’t complaining: They’re leading the American League West, with 75 games won and 72 lost.

The batting average is easy to understand, but it misses the point. To win the game, you must cross home base more often than the rival. First base is just the first step.

What other yardsticks can we use? Well, the number of home runs is spectacular – Kyle Schwarber, a designated hitter for Philadelphia, has hit 44 so far, although the Phillies could use a few more: With a record of 82-65, they’re only second in the National League East, 4 games behind the Atlanta Braves. Maybe that’s because this statistic counts only some of the runs that the batter has set into motion. Even his single can be batted in later. So we should tally all his hits – singles, doubles, triples, and home runs, giving more weight to the hit that is closer to home, since it is more likely to become a run.

The slugging percentage fills the bill. It rewards a point for a single, two points for a double, three points for a triple, and four points for a home run. Thus weighted, the sum of hits can be compared to the number of at bats. In short, the slugging percentage is the hitter’s number of bases per at-bat. Alvarez of the Astros is slugging away this season at .593, or nearly three-fifths of a base per at-bat.

Slugger’s choice

Already you see the problem. In reality, the impact on the team’s score of a homer rather than a triple is greater than the impact of a double rather than a single. And yet the slugging percentage awards just one more point in either case. It also ignores walks and pitches that hit the batter, although these put him on base just as surely as a single.

Let’s add to the brew the on-base percentage. This is how often the player gets to base in a typical at-bat. Hits, walks, beanies, whatever works. Houston’s Alvarez sizzles at .428; 43% of his at-bats wind up on a base. As always, we will exclude base trips due to an error or a fielder’s choice. The idea is to gauge the batter’s skill, not his luck. (So why do we count beanies? Search me.) However, the on-base percentage strangely weights all base trips equally. A homer is worth no more than a single.

Back to the drawing board. Since the slugging percentage and the on-base percentage reflect different aspects of the batter’s performance, let’s add them together. That’s the On-Base Plus Slugging statistic. King of the stat is Babe Ruth, with a career value of 1.164. Breathing down his neck are Ted Williams (1.116) of the Boston Red Sox (the Yanks’ historical nemesis, though not this year, yet) and Damn Yankee Lou Gehrig (1.079).

The OPS may be the favorite batting statistic of aficionados of inside baseball. Unfortunately, just adding two statistics together makes no sense here. Why should the on-base percentage get the same weight as the slugging percentage? And what does the sum really mean?

OMG, another statistic

Maybe we should take another whack at the question. Our meta is a statistic that shows how much a batter contributes to the team’s runs. It considers two possibilities: He batted in runs himself; or he will be batted in later in the inning. Let’s look at the formula, then demystify it:

Chance of Runs = [Player’s runs batted in per Player at-bat] + [Team runs batted in per Team at-bat] * [Player’s slugging per Player's at-bat + Player's stolen bases per Player's at-bat]

Chance of Runs is the probability that the player generates a run. On the right-hand side of the equation, the first term is the probability that the player bats in a run. The second term is the probability that the player himself is batted in. This second term is the number of bases that the player reaches in a typical at bat, times the probability that someone else on the team will bat him in, in a typical at-bat.

Unlike my previous posts, this one subtracts the player's RBIs and at-bats to calculate the team's, to avoid double-counting. It also adds stolen bases. These changes are not trivial. On a team like the Nats, where most batters are as weak as kittens, an outstanding hitter like Abrams accounts for a respectable share of the team RBIs. Failing to exclude it boosts the calculated team RBIs per at-bat and consequently the player's Chance of Runs. Stolen Bases also matter for an Artful Dodger (apologies to LA) like Pete Crow-Armstrong of the Chicago Cubs. The center fielder has stolen 35 bases, and the night is still young. However, the formula excludes walks and beanies; it focuses on what the player achieves by his own bootstraps.

The table below lists the top 25 players in Major League Baseball in the current season up to September 7, using MLB’s official statistics. The standouts are Jordan Walker, right fielder of the St. Louis Cardinals, and Alvarez of the Astros. They exceeded a chance of one in four of sparking a run in an at-bat. All 25 players topped a chance of one in seven of an eventual run in a typical at-bat.

Of the 25 players, 9 are first basemen. This may reflect the fact that first base is one of the easier infield positions, leaving the player free time to hone his batting chops. On the other hand, shortstop may be the most demanding position on the diamond, and only two shortstops made the list of the top 25 hitters. CJ, of the bottom-feeding Nats, really is a magician.

The table also suggests that home runs are not the alpha and omega of baseball. Schwarber, king of homers, ranks only 16th on the Chance statistic.

As statistics go, mine is undoubtedly a swing and a miss. For instance, it assumes that the increase in the chance of a run is the same for a homer rather than a triple as for a double rather than a single. More tinkering in the garage is on the agenda. My only excuse for Chance is that it's easy to interpret. And it keeps me off the streets at night. – Leon Taylor, Seymour, Indiana tayloralmaty@gmail.com

Rank Player Team Chance Position
1 Jordan Walker STL 0.259 RF
2 Yordan Alvarez HOU 0.251 DH
3 James Wood WASH 0.242 RF
4 Junior Caminero TB 0.233 3B
5 Max Muncy LAD 0.232 3B
6 CJ Abrams WASH 0.229 SS
7 Brandon Lowe PIT 0.228 2B
8 Manny Machado SD 0.211 3B
9 Miguel Vargas CWS 0.207 3B
10 Sal Stewart CINCY 0.197 1B
11 Luis Garcia NYY 0.192 1B
12 Willson Contreras BOS 0.183 1B
13 Pete Crow-Armstrong CHC 0.183 CF
14 Pete Alonso BALT 0.177 1B
15 Ben Rice NYY 0.172 DH
16 Kyle Schwarber PHI 0.170 DH
17 Rafael Devers SF 0.168 1B
18 Hunter Goodman COL 0.167 C
19 Dilson Dingler DET 0.164 C
20 Shohei Ohtani LAD 0.162 1B
21 Kazuma Okamoto TOR 0.161 3B
22 Colson Montgomery CWS 0.161 SS
23 Bryce Harper PHI 0.160 1B
24 Muneta Murakami CWS 0.160 1B
25 Matt Olson ATL 0.144 1B

Is Social Security a scam?

Talk about alternative facts. A purple post (and I do mean purple, as in prose) is making the rounds in Indiana, among Hoosiers Against Braun (including me): 'We've taken trillions from Social Security...." *Sigh*. Neither Republicans nor Democrats have robbed or are robbing the Social Security trust funds. No one is taking trillions from the funds. Yes, they are within a decade of insolvency, but that's because Americans are growing old. Congress is not to blame, aside from dithering rather than biting the bullet and either raising taxes or cutting benefits to fix the problem. The last time that Congress formally borrowed from, or for, Social Security was December 1982, in the Reagan years. The Old-Age and Survivors Insurance Trust Fund, which is conventional Social Security, was nearly depleted. To save the fund, Congress passed emergency legislation. OASI borrowed $17.5 billion from the Disability Trust Fund and the Medicare Hospital Insurance Trust Fund to pay benefits. All three of these funds are part of Social Security or Medicare. The borrowing occurred because, due to stagflation arising from high oil prices (sound familiar?), the funds were having trouble paying benefits on time, so Congress took money out of the disability and Medicare funds, which had a surplus at the time, to bail out OASI. By law, OASI had to pay back the loans by 1989 with interest. They were actually paid off by 1986. And that was it, sports fans. Congress' authority to play this shell game with Social Security and Medicare money ran out in 1987. I am drawing upon notes by the historian's office at Social Security: Social Security History https://www.ssa.gov/history/interfundnote.html The claim that Congress has stolen (excuse me: "borrowed") trillions from Social Security is not documented, for a good reason: It is hogwash. The Social Security trust funds do rely on Social Security tax revenues, which are invested in Treasury securities to earn interest. However -- and this is the vital point -- Social Security is pay-as-you-go. Taxes from current workers and their employers pay for current retirees. No, it is not true that your benefits come out of the taxes that you and your boss paid. The crisis of the moment is that current tax revenues are falling short of current benefits. This is because Americans are aging: The number of retirees is growing more rapidly than the number of workers, so the number of retirees financed by a worker is growing. The number of workers supporting each beneficiary has fallen from 5 in 1960 to 2.7 today: Social Security History https://share.google/702ITYdP9IF4cCzrf. In fact, in 1940, it was 159! Who’s paying your bills? While the trust funds still had a $2.8 trillion surplus at the end of 2023, Social Security projects insolvency in the OASI fund by 2035. This crisis is not because Republicans or Democrats have raided Social Security. It is just demographics. Although OASI is headed for the rocks, the disability fund DI is to remain solvent until 2098. It would seem to make sense to transfer funds from the disability fund to OASI, but this is illegal. Anyway, the combined Social Security funds -- OASI + DI -- are to remain solvent only until 2035. Over the rest of the century, Social Security would be able to cover only 83% of promised benefits. To make Social Security whole, Congress must either cut benefits or raise taxes or both. Estimates at the moment are that an increase in the Social Security tax of 3.5% would enable current benefits to continue until 2098. The payroll tax now on workers and bosses is 7.65%, so this would be a hefty chunk of change. Understandably, Congress keeps putting off resolving this predicament, especially in an election year like 2026. The Social Security administration has suggested that raising the retirement age right now would postpone insolvency for several years, but there doesn't seem to be much enthusiasm on Capitol Hill for this sensible idea. Another intriguing idea is to let the trust funds invest in private securities that earn more interest than Treasury securities do. But critics correctly object that private securities are less safe than securities from the US government, which still has a superb (if no longer spotless) record for paying its bills. Nailing billionaires I see proposals to save Social Security by taxing billionaires. That would change the nature of Social Security, which was meant to pay for itself. Congress can do it, of course; and as far as I'm concerned, it makes sense to treat social insurance as an endowment for everyone rather than as a means-tested program (which is what we do today), since we all are prone to good and bad luck. (A “means-tested program” is one that pays you benefits only if you qualify. For example, Medicaid pays benefits to the poor, although the definition of poverty varies from one state to another. Medicare pays benefits to the old.) Milton Friedman proposed a negative income tax that was seriously considered from 1969 to 1972 when Richard Nixon was President. Even today, it lives on in the form of the Earned Income Tax Credit. But there would be a battle royale if anyone proposed to replace Social Security, Medicaid, Medicare, what is now Temporary Assistance to Needy Families, and the other social insurance programs with a pure negative income tax. For example, Social Security recipients feel that they have earned their benefits by paying Social Security taxes, although in reality there is no close relationship between the taxes you paid and the benefits you receive. And maybe that's one reason for Bernie Sanders’ proposal to pay for Social Security, the Social Security Expansion Act, by soaking the mega-rich: They don’t “work,” the argument goes, so why should they receive benefits paid by workers? At first glance, this is a tempting proposal. Sanders would lift the current maximum of $160,200 of annual income on those who pay Social Security taxes. In other words, today, a billionaire pays the same amount in Social Security taxes as someone who earns $160,200. In principle, taxing the billionaire at a rate commensurate to his income could greatly increase tax revenues and even benefits for most Americans, according to Sanders. Social-Security-Expansion-Act-one-pager-Final.pdf https://share.google/B4EQ6xuUj2bCtcgeM One problem with the argument is that millionaires and billionaires have enough money to pack up their bags and take off for friendlier countries. The United States would lose billions of dollars of income and of tax revenues – money that could feed the hungry, heal the sick, and educate the kids. But boy, we’d sure get even with those billionaires! Would we lose so many of the rich, as they vote with their feet, as to offset the tax revenues gained by taxing the rich who stay? The answer is not clear. The most relevant case study is the United Kingdom’s reform of “non-dom” status last year. For centuries, the UK had taxed only residents. If you were a British citizen living outside of the UK, you were taxed only on the foreign income that you brought into the commonwealth. That policy changed last year. The UK now taxes all income earned by citizens regardless of where they live. The Adam Smith Institute, which favors free markets, estimates this this would cost the economy 111 billion euros over a decade as the rich flee to low-tax jurisdictions like Dubai, Switzerland, and Italy. But the UK Treasury estimates that it would gain 30 billion euros, because the rich choose to live where life is good and where they have social roots: Not only taxes matter. Clearly, we have a lot to learn about how the rich choose their locations. Examining the UK's non-dom regime - LSE https://share.google/F13eRjXb7V4N1rqWq ; Why the super-rich are leaving Britain https://share.google/6n2WLeLonpUXrt1Vk Is your Congressional representative a dollar burglar? A last note about thieves on Capitol Hill. Many years ago, when the trust funds were running an annual surplus, Congress would temporarily borrow from the surplus, in a technical sense. But since 2010, the Social Security trust funds have been in deficit every year. Their annual costs exceed their annual revenues. It's like your credit card; if you don't pay off the balance each month, your available credit will shrink. Since there is no longer any annual surplus, Congress cannot legally tap into the trust funds now. Not for trillions. Not for one blessed dollar. I will expand on this point a bit. The Social Security Act of 1935 requires the IRS to send Social Security tax revenues to the Treasury (Section 807a). When Social Security has an annual surplus, the Treasury will hold that cash in general funds and then exchange it for special Treasury securities, which Social Security holds. In that sense, Treasury borrows from Social Security for the general fund, not for specific programs. Social Security earns interest on the securities -- and cashes them in when it needs the funds. It is thus, to say the least, highly misleading to assert that Congress has stolen funds from Social Security. Social Security does get the use of the funds, with interest. In any event, even this point is moot, because Social Security no longer runs an annual surplus. Many readers said the Treasury securities given to Social Security in exchange for payroll tax revenues were worthless IOUs. In reality, the Treasury has always made good on the securities. There is a reason why the Treasury has a sterling reputation for paying its bills: The value of the dollar as a currency trusted the world over, depends on it. This FAQ from Social Security may clear things up: Trust Fund Data. https://www.ssa.gov/OACT/ProgData/funds.html – Leon Taylor, Seymour, Indiana