Bobby Bonilla, Financial Genius? August 1, 2011
Posted by tomflesher in Baseball, Economics.Tags: annuity, Bobby Bonilla, compound interest, deferred compensation, finance, Mets
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When Bobby Bonilla signed a deferred compensation agreement in 2000, the Mets owed him $5.9 million dollars. Basically, the Mets got to hold on to the $6 million or so (and ended up spending it on payroll), but they had to pay Bonilla back a bit more in interest. His yearly payments are $1,193,248.20, which means that in absolute terms, the Mets are paying him $35,797,446 in total over the next 25 years. Of course, the $1.19 million Bonilla gets today is worth much more than the same-size payment he’ll get in 2036.
Bonilla’s arrangement mimics a financial instrument called an annuity, where a constant payment is made at specific time periods after a specific present sum is invested. The annuity formula is:
![Present Value =Payment \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]](http://s0.wp.com/latex.php?latex=Present+Value+%3DPayment+%5Ctimes+%5B%5Cfrac%7B1+-+%5Cfrac%7B1%7D%7B%281+%2B+r%29%5Et%7D%7D%7Br%7D%5D&bg=ffffff&fg=666666&s=0 "Present Value =Payment \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]")
where r is the annualized interest rate and t is the number of years of payment. Keep in mind, though, that the present value of the annuity isn’t $5.9 million – it’s $5.9 million compounded annually at some rate of interest agreed to by Bonilla and the team for the ten years between the deal and the first payout. In general, that means
![5900000\times(1 + r)^{10} = Payment \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]](http://s0.wp.com/latex.php?latex=5900000%5Ctimes%281+%2B+r%29%5E%7B10%7D+%3D+Payment+%5Ctimes+%5B%5Cfrac%7B1+-+%5Cfrac%7B1%7D%7B%281+%2B+r%29%5Et%7D%7D%7Br%7D%5D&bg=ffffff&fg=666666&s=0 "5900000\times(1 + r)^{10} = Payment \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]")
Since we know Bonilla’s payout, we can substitute in:
![5900000\times(1 + r)^{10} = 1193248.2 \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]](http://s0.wp.com/latex.php?latex=5900000%5Ctimes%281+%2B+r%29%5E%7B10%7D+%3D+1193248.2+%5Ctimes+%5B%5Cfrac%7B1+-+%5Cfrac%7B1%7D%7B%281+%2B+r%29%5Et%7D%7D%7Br%7D%5D&bg=ffffff&fg=666666&s=0 "5900000\times(1 + r)^{10} = 1193248.2 \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]")
and that solves out neatly to the 8% that the team and Bonilla agreed to. The math checks out so far.
At the time the deal was made, the 8% was 50 basis points (0.5%) below the Prime Rate, the reference rate used by banks in making loans. The average prime rate over the previous year was about 8.16%, and rates had hovered within 75 basis points since September of 1994*, so while interest rates are expected to move, it was very likely that rates would stay similar, at least in the short term. For the record, a 30-year fixed rate mortgage would have cost between 8.15% and 8.25%, so taking into account the long maturity of the loan, it wasn’t a bad deal.
Let’s look at how good a prediction it was. Annualizing prime rates, the Mets could have earned a (full prime) rate of return as follows:
So, the actual value of the $5.9 million on January 1, 2011, was $10,891,903.26, but the agreement pegged the value at
for a difference of about $1.85 million. Bobby’s already better off because historical interest rates didn’t keep up with 8%.
My biggest question is why the Mets agreed to an 8% interest rate then and there to be in effect for the next 35 years. Since I’m not a finance professional, I don’t know whether that’s an industry standard agreement or not, but it seems like the risk of setting an interest rate that far in the future would be far too high. What if the Mets had agreed to the 8% interest rate for ten years and then offered Bonilla a menu of financially equivalent options? All of them would rely on the payment formula:
where t is the number of periods and r is the newly figured interest rate.
One option would be to take the $12,737,657.48 as a lump sum, although that wouldn’t necessarily be a good idea for the Mets. (We know they’re cash strapped.)
The current prime rate is 3.25%, so if we took the lump sum $12,737,657.48 from the original agreement and reamortized it today at 2.75%, Bobby could receive a payment of $711,270.46 over the next 25 years. Similarly, at 2.75%, $1,047,789.14 per year for 15 years or $2,761,502.75 for five years would be equivalent options. Each has a different total cash outlay, but the discount rate means that each of them is worth the same $12,737,657.48 in 2011 dollars.
Bringing it all back, that’s why it’s a little silly to talk about the Mets paying $30 million to defer $6 million in compensation. It’s true that they’ll end up putting more dollars into Bonilla’s hands, but that simply represents Bonilla’s forebearing on the ability to invest that money at current interest rates. It doesn’t matter when you pay him – the money is worth the same amount, and that’s all that matters.
* Historical prime rates here, thanks to the St. Louis Fed and Federal Reserve Economic Data
Mets Fans, Meet Your New Closer July 17, 2011
Posted by tomflesher in Baseball, Economics.Tags: Bobby Parnell, closers, Francisco Rodriguez, Jason Isringhausen, Mets, Pedro Beato
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It’s been a while since the Mets traded Francisco Rodriguez, the 1982 model, to the Milwaukee Brewers. Mets manager Terry Collins has indicated that Rule 5 draft pick Pedro Beato, cranky old man Jason Isringhausen, and veteran Met Bobby Parnell are in competition for the closer role. Rodriguez had a reputation for being unpredictable, and watching him certainly gave that impression – he pitched wildly and emotionally.
I decided to dig out K-Rod’s stats for this year and figure out what his numbers looked like, using a couple of measures of control: his K/BB ratio (aka ‘control ratio’), his K/9 and BB/9, and then his batters faced per out (BFPO). If Rodriguez is unpredictable, then he should have a relatively high standard deviation for BFPO. With that in mind, if predictability is an important factor in selecting a closer, these stats are relevant for Beato, Isringhausen, and Parnell as well. Here they are, for 2011:
The best number overall is bolded. The best from among the three closer candidates is italicized.
Rodriguez had the best KBB and BB9, as well as the lowest standard deviation, but his BFPO was the highest in the group. Since he wasn’t walking many batters, that indicates that he was giving up a lot of hits or otherwise allowing lots of runners. That’s not good – it breeds high-pressure situations, some of which are bound to result in runs.
Beato had the lowest BFPO, but Parnell led all the other categories for current Mets as well as having a better K/9 than Rodriguez as well. Parnell’s BFPO was only .02 below Frankie’s, and was .15 higher than Beato’s (and about .05 greater than Izzy’s). Without a lot more data, it’s hard to compare these numbers meaningfully. However, over the course of 70 innings, that .15 differential adds up to 31.5 extra baserunners for Parnell above Beato. Parnell’s lower standard deviation means that those runners are going to be spread a bit more evenly than Beato’s, but it’s tough to distinguish the best choice. Isringhausen has been strong as a setup man, and Beato, as a rookie, is still unpredictable.
Parnell will probably come out of this with the closer’s job, but Collins would be a fool not to leave Isringhausen where he is.
RBIs with Two Outs July 4, 2011
Posted by tomflesher in Baseball, Economics.Tags: Boone Logan, Daniel Murphy, Hector Noesi, Jason Bay, Mets, Ramiro Pena, RBIs, Scott Hairston, statistics, Subway Series, two-out RBIs, Yankees
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Sunday’s Subway Series game between the Mets and Yankees ended with a bang – Jason Bay hit a single off Hector Noesi that brought home Scott Hairston. The tenth inning should have been over, but Ramiro Pena committed an error at shortstop that put Daniel Murphy on base for Boone Logan. Hairston’s run was unearned, but no matter – Noesi took the loss and the Mets won the game.
The final score was 3-2, and the interesting thing about the game was that all three of the Mets’ runs came with two outs. (My fiancée, Katie, suggested that this was unusual, and motivated most of the rest of this post.) In fact, so far, the Mets have had 347 RBIs (of 375 runs scored), and 147 of them have come with two outs. That’s about 42.4% of their RBIs. By contrast, only 1070 of 3274 plate appearances – 32.7% – come with two outs. (Less than a third of plate appearances come with two outs because of the double play, among other reasons.) The majority come with no men out (about 34.8%) with the remainder coming with one out. It seems like the high concentration of 2-out RBIs should be explained by the use of the sacrifice bunt, but the Mets have only had 31 sacrifice bunts this season – not nearly enough to account for the difference between 32.7% of plate appearances and 42.4% of RBIs.
Is that pattern common across baseball? So far, there have been 10,037 RBIs in Major League Baseball in the 2011 season. 3686 of them – about 36.7% – came with two outs. Excluding the Mets’ numbers, that’s 3539 out of 9690, or 36.5%. For the National League only, there were 1928 two-out RBIS of 5212 total, or 37%, with 1781 of 4865 (36.6%) of National League RBIs coming with two outs if you exclude the Mets. (Note that I’m defining ‘in the National League’ as ‘in National League parks,’ since what I’m interested in is whether the Mets’ concentration of RBIs can be partially explained by the rules requiring pitchers to bat.)
Assume that the Mets’ RBIs are drawn from the same distribution as all others’. Then, 95% of the time, I’d expect the proportion of RBIs that come with two outs to be within two standard errors of the National League’s proportion, excluding the Mets. (The ‘two standard errors’ comes from the fact that a t-distribution’s critical value for a large number of trials for 95% significance is 1.96. For less than an infinite number, two standard errors is a handy approximation.) For the Mets’ 347 RBIs, the standard error would be
Thus, 95% of the time, the Mets should be within the interval of (.366 – .052, .366+.052), or (.314, .418). Since, again, the Mets’ proportion is .424, the Mets are slightly outside the 95% confidence interval. That’s pretty close, and certainly could happen by chance, but it’s surprising nonetheless. The question then is whether this is due to some sort of strategy employed by the Mets’ management or to some sort of clutch playing ability by the Mets. Again, there’s more data to collect and crunch (as always).
Don Kelly, Utility King June 30, 2011
Posted by tomflesher in Baseball.Tags: Angel Pagan, Austin Jackson, Carlos Beltran, David Purcey, Don Kelly, Jason Bay, Justin Turner, Mets, Mike McCoy, position players pitching, Ronnie Paulino, Roy Halladay, Scott Hairston, Spectrum Club, Super utility dervish, Tigers, utility pitchers, utility player, utilityman, Wilson Valdez
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Super utility dervish Don Kelly is this year’s second inductee into the prestigious* Spectrum Club, which loyal readers if any will recognize as the group of players who have played both pitcher and designated hitter in a given season. Kelly pitched a perfect third of an inning (for those keeping score at home, that’s one out) against the Mets last night during a 16-9 Tigers loss.
Kelly’s lifetime pitching statistics: 0.1 IP, 0 R, 0 H, 0 E, 0 HR, 0 BB, 0 K, 1 BF. That batter was Scott Hairston, who flied out to Austin Jackson at center.
Kelly came in after David Purcey, the Tigers’ last arm in the bullpen, pitched the last out of the eighth and the first two of the ninth. In his one inning, Purcey gave up five hits, four runs (all of them earned), two walks (one intentional), and no strikeouts. Purcey’s ninth inning started promisingly when Justin Turner grounded out and Carlos Beltran flied out, but David then gave up a double to catcher Ronnie Paulino, walked Jason Bay, and then allowed Angel Pagan to double, scoring Paulino. At that point, Jim Leyland called on Kelly, who took care of Hairston to end the inning.
That makes three utility pitchers thus far this year. Of the position players who pitched, Wilson Valdez, Mike McCoy and Don Kelly have each played at least three non-pitching positions. Valdez has played at second base, third base, and shortstop; McCoy has played second, third, shortstop, center field, and left field; and Kelly has played first, third, left, center, and right. They’re three of the four pitchers with fifty or more plate appearances. (Roy Halladay is the fourth, with exactly 50 PA this year.)
Over the course of his career, Kelly has been a utility ubermensch, playing every position except catcher. As a lifetime .242/.287/.341 hitter, Kelly needs to be versatile defensively to keep himself working. That’s essentially the same way Mike McCoy keeps his job. Kelly had never pitched professionally before.
*not a guarantee
Justin Turner Takes One For The Team June 23, 2011
Posted by tomflesher in Baseball, Economics.Tags: Athletics, Brad Ziegler, Charlie Morton, Dane Sardinha, hit by pitch, Jeff Francoeur, Justin Turner, Mariano Rivera, Mets, Oakland As
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The Mets’ Justin Turner quite literally took one for the team last night when he wasn’t trying to get hit, but, oops, managed to get plunked in the bottom of the 13th inning with the bases loaded. Brad Ziegler was the losing pitcher for Oakland. It was the first game-ending hit by pitch since last year, when Mariano Rivera nailed Jeff Francoeur for the loss in a September game.
In 185 plate appearances this year, Turner has been hit three times. The other two were both by Pittsburgh Pirates pitcher Charlie Morton, eleven days apart; Morton is not especially known for hitting batters, since he, too, has only been involved in three hit batsmen this year. (The third plunking was Dane Sardinha.) It was the Mets’ only go-ahead HBP this year, and the only one of this year’s six go-ahead hit batsmen to occur in extra innings.
Turner has a way about him. He’s hit ten go-ahead RBIs this year (and yes, a hit by pitch that forces in a run is an RBI), which accounts for a little over ten percent of the Mets’ 95 go-ahead RBIs. Only Carlos Beltran, with 13, has more. It’s also the Mets’ only game-ending RBI this year. I guess Turner will take what he can get.
Zambrano Back on the Horse May 27, 2011
Posted by tomflesher in Baseball.Tags: Carlos Zambrano, Chris Young, Cubs, Dan Haren, Mel Stottlemyre, Mets, Micah Owings, Pitchers batting
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Last night, Carlos Zambrano pitched on one day’s rest after pinch-hitting against the hapless Mets for two RBIs on Tuesday. We’ve talked about Zambrano’s pinch-hitting prowess before, but last night he was an awesome 3 for 3 from the plate, including a double. In fact, in 26 plate appearances, Zambrano’s got 9 hits for a .375 batting average and, since he has no walks, a .375 on-base percentage. Not only is that impressive, but I hear he can pitch, too.
I figured that was pretty impressive. It can’t be often that a pitcher gets three at-bats and hits for all of them, can it? It’s happened 450 times since 1919, including, surprisingly, once already this year. The Mets’ Chris Young managed a 3-for-3 night while notching the win against the Phillies back on April 5.
In recent memory, the most at-bats by a pitcher who hit each time was Dan Haren, who grabbed a 4-for-4 as a Diamondback against the Cardinals last year (also as the winning pitcher). Haren also gave up a whopping 7 runs, so he’s lucky he was hitting.
Micah Owings has had two games where he pitched and hit in all of at least 3 plate appearances, including a 4-for-4 from 2007 in which three of his 4 hits were doubles.
Finally, Mel Stottlemyre (in 1964) and two pitchers from the 1920s had 5-for-5 games. Stottlemyre’s two-hit gem included him hitting a double and pitching to a game score of 83.
Complete Game in a Non-Quality Start May 26, 2011
Posted by tomflesher in Baseball.Tags: Cheap Wins, complete games, Cubs, Dillon Gee, Edwin Jackson, Freddy Garcia, Mets, Pete Harnisch, quality starts
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Dillon Gee of the Mets was credited with a complete game in last night’s win over the Cubs. His line: 6 IP, 4 H, 4 R, 4 ER, 2 BB, 4 K, 0 HR, and 1 HBP, for a game score of 50. He qualified for a quality start under the Game Score definition, but not under the six-inning, three-run criterion. That makes it a form of Cheap Win, where a pitcher is credited with a win even though he didn’t pitch as effectively as expected.
Since the game was shortened by rain, Gee got a complete game, even though that usually involves 8 innings for the visiting pitcher on a losing team or 9 inning for a winning pitcher regardless. That made me wonder how many pitchers from the modern era, when complete games are less common than in previous years, have pitched complete games in non-quality starts.
A quality start, under the Game Score definition, is a start with less than 50 points. That represents that a pitcher had negative value for his team. It can’t be especially common, can it?
According to this list I queried from Baseball Reference, a non-quality start complete game hasnt been pitched since 2006 when Freddy Garcia pitched a rain-shortened 5-inning complete game for the White Sox to defeat the Blue Jays 6-4, with a game score of 42. The last nine-inning complete game non-quality start was Pete Harnisch with the Reds, who won a 10-6 slugfest in August of 2000 on 124 pitches with only one walk and three strikeouts. Aside from the six earned runs (all scored in the first three innings) it wasn’t a bad performance, somewhat reminiscent of Edwin Jackson‘s ugly but effective no-hitter last year.
Spitballing: Blanton in the Phillies’ Rotation February 25, 2011
Posted by tomflesher in Baseball.Tags: Adam Eaton, Chan Ho Park, Clif Lee, Cole Hamels, Joe Blanton, Kyle Kendrick, Mets, Mike Pelfrey, Phillies, R.A. Dickey, Roy Halladay, Roy Oswalt, Spitballing, Year of the Pitcher
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The Phillies have one of the best rotations, on paper, in baseball today. Although some people are measured in their optimism, including Jayson Stark, I think the important thing to remember is that we’re arguing over whether they’re “the best ever,” not if they’re going to be competitive. Rotations that bring this kind of excitement at the beginning of the year are few and far between. The Mets, for example, aren’t drawing this kind of expectation – guys like R.A. Dickey and Mike Pelfrey are solid, but they don’t have the deserved reputations of Roy Halladay, Roy Oswalt, Cliff Lee, Cole Hamels, and Joe Blanton.
I’m hardly the first to say it, but Joe Blanton seems to be the odd man out. He’ll be making about $8.5 million next year. Blanton faced 765 batters last year, fourth behind Halladay, Hamels, and Kyle Kendrick. Immediately behind Blanton was Jamie Moyer with 460 batters faced. For the record, the fifth-most-active pitcher faced 362 batters in 2009 (Chan Ho Park) and 478 in 2008 (Adam Eaton). Let’s take that number and adjust it to about 550 batters faced, since Blanton will get more starts than most fifth starters and he’ll stay in longer since he’s a proven quantity. In a normal year, the Phils face about 6200 batters, so that means Blanton’s 550 will be about 9% of the team’s total. (That figure is robust even in last year’s Year of the Pitcher with depressed numbers of batters faced.)
According to J.C. Bradbury’s Hot Stove Economics, this yields an average marginal revenue product of 3.15 million. This figure is based on the average rate that pitchers prevent runs and the average revenue of an MLB team. Obviously, Blanton is a better than the average pitcher (ignoring his negative Wins Above Replacement last year) and the Phillies make more money than most teams, but this is a pretty damning figure.
The other thing to take into account is that Blanton’s marginal wins aren’t worth as much to the Phillies now that they have a four-ace rotation. He won’t get every start and he won’t be a 20-game winner. Even if he were, he’ll be providing insurance wins – he might have an extra ten wins over a AAA-level replacement, but chances are that those wins won’t make the difference between making the playoffs and missing them when you figure in the Phillies’ solid bullpen and run production.
Instead, let’s say Blanton goes to the White Sox, just to pick a team. Jake Peavy and Edwin Jackson combined for 765 batters faced, so plug Blanton in for Freddy Garcia with 671 batters faced – a worst-case scenario. That would be 10.85 % of the batters faced, bringing him up to about 3.8 million. In this case, though, you have a team who finished 6 games back and missed the playoffs. If you replace Garcia with Blanton, you stand a very good chance to make the playoffs. That’s another way of saying that the Phillies’ 6-game lead over Atlanta (the NL wild card team) was worth less than the Twins’ 6-game lead over the White Sox (when neither team had as many wins as the AL wild card).
Economists would refer to this as a diminishing marginal returns situation – when you have fewer wins, around the middle of the pack, each additional win is worth a little less. This captures the idea that taking a 110-win team and giving them 111 wins would cost a lot of money and not yield much extra benefit, but a 90-win team making 91 wins might let them overtake another team.
The upshot of all of this? Trade Blanton for prospects. Rely on the bullpen and develop a future starter. Roy Halladay won’t be competitive forever.
Adventures in the Mets Bullpen: One-Run No-Decisions and Vulture Wins July 19, 2010
Posted by tomflesher in Baseball.Tags: Francisco Rodriguez, Jason Stark, Johan Santana, Mets, one-run no-decisions, Phil Cuzzi, Phil Cuzzi's hissyfit, Randy Wels, Roy Halladay, Ted Lilly, Tyler Clippard, vulture wins, Yovani Gallardo
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A close cousin of the Tough Loss discussed earlier is what Jayson Stark of ESPN calls the Criminally Unsupported Start. Stark defines a CUS as a start in which the pitcher pitches 6 or more innings but the offense scores one run or less in support. Johan Santana didn’t fit that definition last night, but he was close: he left the game with a 2-1 lead after 8 innings pitched and ended up with a no-decision. (A friend of mine liked to call that “the ol’ Roy Halladay” back when Doc was pitching in Toronto.) Just as he was the centerpiece of Jayson Stark’s CUS standings back in 2007, Santana currently leads the league in starts with 6.0 or more innings pitched, at most one run allowed, and no decision. He has six such games, and no other pitcher has more than four. (Yovani Gallardo, however, has a respectable 3.)
In all of 2009, no one hit the six-game mark in one-run no-decisions. Surprisingly, this year the Mets aren’t leading the league in these one-run no-decisions – the Cubs are, led by Randy Wells and his impressive 4, along with Ted Lilly with 3.
Francisco Rodriguez also picked up his third Vulture Win of the year last night. A vulture win is the combination of a blown save and a win in the same game. Usually, that happens when a hometown closer blows the save in the top of the 9th and his teammates score in the bottom for the win. Frankie blew the save in the bottom of the 9th last night, but they left him in to pitch the bottom of the 10th and he held on (despite Phil Cuzzi’s hissyfit and some questionable umpiring going in both directions). Tyler Clippard leads the league in vulture wins this year with four.
Santana the Late-Blooming Hitter July 7, 2010
Posted by tomflesher in Baseball.Tags: Brewers, Dave Eiland, home runs, Jason Jennings, Johan Santana, Mets, Pitchers batting, Yovani Gallardo
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Last night, Johan Santana hit his first home run in his 87th career game as a batter. (Granted, he’s played far more than that many games because he played a few years in the American League.) Out of curiosity, I checked Baseball-Reference.com’s Play Index to see how many home runs have been hit by pitchers in their first 87 games as batters.
Since 1961, there have been 431 home runs (although the Play Index only lists games starting at 1970, so that may or may not be accurate). Four pitchers have hit home runs in their first games, including Yankee pitching coach Dave Eiland in 1992 and Rockies pitcher Jason Jennings. Like Johan, Jennings pitched a complete game shutout for the win that night.
The all-time leader in home runs by a pitcher in the first 87 games (how’s that for esoteric?) is Yovani Gallardo, who’s in his fourth season pitching for the Brewers. He’s hit seven of them, and as of July 4 he’s only hit in 71 games. He’s got a lot of time to pick up the pace and possibly hit the triple-digit mark when he gets back from the disabled list some time after July 20.
