BLUE THINK TANK

I have previously linked this article on Markov matrices as applied to baseball as a good read for the non-math geeks. Please read if you are unfamiliar with its concept.

I have discussed the value of the stolen base in 2 previous posts, on 3/30 and on 4/3. Using Dave Roberts' 04 regular season (38 out of 41) as an example, I calculated that Roberts' stolen bases were worth about 5 "expected" runs over the course of the season - not a whole lot.

In the second post, I stated that there is a difference between "winning" and "scoring runs". (The point is to win, whether by a run or 10 runs.) In a tight late inning game, the strategy is not necessarily outscoring your opponent by as many runs as possible; the team may try to eke out a single run to tie or win. So a stolen base, as with other situational plays, can make a big difference in the game's outcome.

Here is the historical "expected run matrix" for all games between 1999 and 2002, courtesy of TangoTiger. (Thanks, Tango!) It is basically the number of runs you "expect" to score given the out count and the runner situation.


Expected Runs, 99 - 02 Historical

Let's say that with no one else on, if a runner attempts to steal 2nd from 1st with 0 outs:

ExpectedRuns(0 out, runner on 1st) = 0.953
ExpectedRuns(0 out, runner on 2nd) = 1.189
Successful SB = 0.236 "expected runs" added

ExpectedRuns(0 out, runner on 1st) = 0.953
ExpectedRuns(1 out, no one one) = 0.297
Caught SB = 0.656 "expected runs" subtracted

In terms of "expected runs", a stolen base adds a mere 0.236 runs, while getting caught has a more severe penalty of minus 0.656 runs.

It's Game 4 of the ALCS, bottom of the 9th, Boston is a run down with 3 outs to go. Millar draws a walk. Runner on 1st with 0 outs. Dave Roberts enters the game as the pinch runner. A stolen base would add 0.236 "expected runs". Not a whole lot - But:

What is the probability of winning this game? How much would a stolen base help? To calculate this, I once again dug into TangoTiger's website. Here are some of the historical probabilities of scoring a certain number of runs given the out/base situation. I have it broken down another way:

Score zero runs -

Scoring 0 Runs, 99 - 02 Historical

Score a single run -

Scoring 1 Run, 99 - 02 Historical

Score 2 or more runs -

Scoring 2+ Runs, 99 - 02 Historical

(I realize that these numbers are historical "average" numbers and don't figure for the dominance of Rivera on the mound nor the strength of the batter, but they're worth looking at, nonetheless.)

In the bottom of the 9th while down by a single run with no outs and a runner at 1st, Boston can win the game if:

1) Boston scores 2 or more runs (win for sure)
2) Boston scores one run to tie (50/50 chance of winning in extra innings)

According to these charts:

WinPct(0 outs, runner on 1st) = ScoreTwoOrMoreRuns(Win) + (1/2)*ScoreOneRun(Tie)
WinPct(0 outs, runner on 1st) = 0.261 + (1/2)*0.176
WinPct(0 outs, runner on 1st) = 34.9%

Boston has a 34.9% chance of winning with no outs and a runner on 1st. Roberts attempts to steal 2nd. Had he been caught:

WinPct(1 out, no one on) = ScoreTwoOrMoreRuns(Win) + (1/2)*ScoreOneRun(Tie)
WinPct(1 out, no one on) = 0.072 + (1/2)*0.101
WinPct(1 out, no one on) = 12.2%

It's a good thing he wasn't caught. That's where Roberts' basestealing skills (92.7% success rate in 04) certainly factor in. He makes it under a close tag. Now the situation:

WinPct(0 outs, runner on 2nd) = ScoreTwoOrMoreRuns(Win) + (1/2)*ScoreOneRun(Tie)
WinPct(0 outs, runner on 2nd) = 0.284 + (1/2)*0.348
WinPct(0 outs, runner on 2nd) = 45.8%

Roberts' stolen base increased his team's chance of winning by almost 11%, which is substantial. Everyone knows what happened at this point. Dave Roberts - forever the folk hero in Beantown with a measly 0.236 "expected runs" gained.

Situational moves such as a stolen base can make a big difference in a close game, even though they may be worth little to overall run production during the course of the season.

EDIT: I finished this post in a hurry due to a dinner reservation on Saturday. As the commenters point out, there is plenty I am leaving out. Studes' article on "Win Expectancy" gives a more general (and better worded) description over at The Hardball Times.

Due to the current roster makeup, Nakamura is the probable candidate to be sent back back down to AAA when Antonio Perez returns from the DL. Before this happens, I would like to see Nakamura more at 3B. I would then occasionally rotate Valentin to the middle infield to rest Izturis or Kent. So for the time being until Perez returns, I would have Valentin rover around as a super sub, a la Hernandez last year. The side benefit is this:

As I commented over at The Fourth Outfielder the other day...

If Nakamura proves that he's capable of manning 3B everyday, the Dodgers would hold a trading chip in Valentin. For example, the Cubs just lost Garciaparra for a while with a torn left groin tendon, and could be looking for a stopgap replacement. Valentin is a better SS than a 3B, is familiar with Chicago, has a 1 year contract, and is capable with the bat unlike Neifi Perez, Garciaparra's probable replacement. So Valentin would be of greater value to the Cubs than to LA. If Valentin is indeed traded, LA can then bring up Oscar Robles, who looked good during ST and can be put on the ML roster with certain restrictions.

Let's run with the Cubs example for a bit. Their needs are where the Dodgers are strong. The Northsiders need a shortstop, relief pitching, and perhaps an outfielder to replace the production lost when Sosa and Alou departed. (Dodger rejects Hollandsworth and Burnitz now man the outfield.) So the Dodgers have what the Cubs need, but what would the Dodgers want in return?

Assuming no further injuries, the only possible "needs" for the Dodgers are a frontline starter (Doesn't everybody?) and a 1B if Choi stalls. This is obviously wishful thinking, but what would it take to pry either Prior or Zambrano? Weaver and Penny are both in their walk years, and blue chip prospects such as Jackson, Ketchner, and Billingsley are just that at this point - prospects. A package including Valentin, Werth, and Brazoban would be a serious starting offer - three needs filled cheaply, with two of them just starting to blossom. I would be willing to take back a bad contract (Remlinger) or two if it meant getting Prior.

Of course, the Cubbies aren't trading Prior or Zambrano, and can't trade Wood due to his no-trade clause, so it's a moot point. But I wouldn't be surprised if a small trade involving Valentin/ Repko/ Sanchez occured. According to the Cubs Reporter,, their farm is deep in pitching. Maybe a "need" trade isn't in the Dodgers' best interest. A long-term "opportunity" trade would work, too.

This is not meant to be a knock on Valentin, who has so far displayed an erratic glove and a power bat, as expected. He is, however, a mere one year stopgap who was signed prior to Nakamura becoming available. If Nakamura shows that he's capable of holding the 3B job, it would be in the Dodgers' best interest to see what the market offers for Valentin.

5/5/05 EDIT: Now that Valentin's out for at least 2 months with a knee injury, we'll see what Nakamura can do. So far, good glove, no hit...

Sample size.

Prior to tonight's game, Hee Seop Choi's OBP was .294 with a SLG of .311, which is downright abysmal for a 1B. In a move that showed Tracy's waning confidence last night, Choi was pulled in favor of Saenz against a RHP.

So far in tonights game, Choi is 4 for 4 with a HR. His OPS is now up to .775. That puts him about mid-pack amongst starting 1Bs, with a paycheck near the league minimum.

Choi's swing has improved since last year, when his hips would rotate way before his hands and be halfway to the visitors' dugout when he made contact, if at all. His current motion is still a bit long with the arms, and he still has a slight tendency to pull off to first base a la Ichiro. No matter, if Choi can ever improve to a point when he can consistently make contact, he would make a fine power bat with good plate discipline.

Who knows whether Choi is the next Paul Konerko or Billy Ashley, but at his salary and service time, the upside worth the gamble. Choi has had only 49 ABs this year. Give him a chance to figure it out.

Apparently runners attempt more stolen bases against sinkerballers. According to an article written by Tony Jackson at LA Daily News on April 24, 2005:

Running game: Dodgers catcher Jason Phillips worked with bullpen coach/catching instructor Jon Debus over the weekend on controlling the opposition's running game, a season-long bugaboo. Phillips entered Sunday's game having thrown out just two of the 14 runners who had attempted to steal on him. ....
"We have three sinkerball guys, and teams notoriously run on sinkerballers just to avoid the double play," Phillips said. "It's not even trying to steal a base, per se. And the other thing is that sinkerballers rarely use the slide step (to hold runners close) because it throws off their sinker to some extent because they can't get out front. And, a sinkerball always challenges a catcher (throwing out runners) because the ball is always down in the zone."

Just about everything Phillips says makes sense. The intricacies of baseball...the more you know, the more there is to learn.

As a follow-up to the previous article:

To visually see the relationship between line drives given up (pitching) and fielding efficiency (defense), I ran a linear regression and plotted a graph for all NL teams during the 04 season. The data is courtesy of the Hardball Times. LA is the blue dot.


r sq = 0.279, stan err = 0.008

The relationship is straightforward: the less line drives your pitcher gives up, the more likely the fielders will turn balls hit in play into outs. The black line is the best-of-fit trend line using a simple linear regression model.

Some thoughts:

1) Park effects for balls put in play are not incorporated. To my understanding, Dodger Stadum traditionally suppresses doubles and triples.
2) The lowest line drive rate given up was 17.9% by Milwaukee, and the highest was 19.5% by Houston. The difference is only 1.6%.
3) The highest fielding efficiency was 71.1% by LA and St. Louis, and the lowest was 67.8% by Colorado. The difference is only 4.7%.

Over a full 162 game season, the differences are small.

Given a line drive rate, a team above the trend line made more outs than predicted, and hence was a superior fielding team. Likewise, a team below the trend line was an inferior fielding team.

Note how good the Dodgers' defense was last year. Despite the pitchers giving up more line drives than the average team, the fielding efficiency is tied for the highest. So this supports the notion that LA had the best defense in the NL last year. In stark contrast are is Milwaukee, who at 69.5% fielding and 17.9% line drive rate would make them the worst fielding team.

Let's look at the current season, after 13 games. (I know, sample size...) For comparison, the trend line from the 04 season is included as the red line.


r sq = 0.218, stan err = 0.023

As expected, the R squared value is lower than in the 04 season, and the standard error is higher than the 04 season. That's 13 games versus 162 games in a nutshell, a greater range of values:

1) The lowest line drive rate given up is currently 13% by LA, while the highest is 20.9% by the Cubs. That's a difference of 7.9%.
2) The highest fielding efficiency is 75.8% by Florida, while the lowest is 66% by Arizona. That's a difference of 9.8%.

By the way, the Yankees over in the AL are giving up a line drive rate of 21.1%, while their fielding efficiency is only 64.3%. That is easily the worst combination in the majors, and no wonder they're 5-9 while giving up 6.5 runs a game.

According to this graph, the Dodgers' fielding efficiency so far has been subpar in relation to last year's team and also in relationship to the 04 trend line. Even though LA has the second highest fielding efficiency, one can see from the graph that given the low opponent line drive rate, the efficiency rate has not been stellar, even though LA may be perched above the 05 trend line. Again, sample size and park effect at work...

I think the biggest culprit so far is from having so many new position starters this year, especially the infield. The rotation, with 3 sinkerballers, is inducing more groundballs (1.3 groundout/flyout so far) than last year, and the corner infielders have been especially shaky. Valentin, usually a shortstop, is playing 3B. While 1B Choi has looked decent with the glove, his lack of a bat has meant significant playing time for Grabowski/ Saenz/ Nakamura, not exactly a stellar trio with a 1B glove. Even Izturis has looked shaky at times.

Once again, the sample size is small, so the numbers might be very raw. The park effect for balls in play is not incorporated. However, as the season progresses it's reasonable to think that the infield will improve by repetition and familiarity. It had better, given that the pitchers have so far given up line drives 13% of the time and that last year's NL rate ranged from 17.9% to 19.5%; the 13% rate is almost certain to shoot up by a bunch.

Baseball Prospectus came out with a slew of numbers on 4/19/05. Instead of rattling off that the Dodgers are 11 and 2 due to outscoring their opponents 88 to 51, I want to see what the team is doing with the bat and the glove. Due to the small sample size, I'll call these "tendencies" instead of "statistics." First, I'll analyze pitching and defense.

The team ERA is 3.58 after 13 games, good for sixth best in the majors.

According to Baseball Prospectus:

Defensive Efficiency:
defined as: 1 - (hits -HR -reach on error)/(PA -K -BB -HBP -HR)

In the first 12 games, LA is 2nd in the majors at 0.7399, behind Florida at 0.7645. MLB.com uses a slightly different formula and also lists Florida and LA as #1 and #2. The current Dodgers defensive efficiency rating is actually higher than last year's 0.7178, when LA led the majors.

By the way, Florida's league-leading 1.79 ERA is not a surprise, given their terrific defense and dominant pitching. (0.98 WHIP, 1st in MLB) They look like a major contender despite their "measly" 8-6 record, considering that their bats will rebound.

Fielding Percentage (from MLB.com):
0.979, 22nd in the majors

I can't emphasize sample size enough here. It's only 11 errors! With 3 less, the Dodgers' fielding percentage would have been 0.985, which is mid-pack. The high fielding efficiency more than compensates this anomaly. Besides, the 2 biggest culprits (Izturis with 3, Valentin with 4) surely will improve.

Also, courtesy of Hardball Times:

Opponent Strikeout Rate:
4.83 K per 9 innings , lowest in MLB. (average is 6.51)

Tha ball has gone into play a lot, and the defense has apparently gobbled up the chances, according to the defense efficienty rating.

But the defense is not solely responsible for the sixth best ERA in the majors.

Opponent Line Drive Rate:
12.7%, lowest in MLB (average is 17.3%)

The Dodger pitchers are not generating many swing-and-misses, but so far have been successful in generating soft outs. Perhaps this is somewhat due to:

1) flat out luck (probable)
2) playing games against weak lineups (somewhat unlikely)
3) having pitchers that the NL hasn't seen (Lowe, Schmoll, Carlyle, Wunsch, etc.)

This is worrisome, since you would expect a return to "norm", especially if the hitters are not swinging and missing. Eventually they will make good contact.

Still, the pitchers have held its own without ace SP (Penny), stud closer (Gagne), and versatile swingman (Alvarez). Those are three guys with historically high strikeout rates, and hopefully will balance out the "line drive luck" that the Dodgers have been enjoying. Barring further injuries, the pitching staff looks to be in good shape in the future months as everyone gets healty.

This is an offshoot of some comments off a game thread in Dodger Logs. This is how I would cast various roles in the "Major League" movies with current and former Dodgers.

Premise :

A mish-mash band of unknown misfits overcome all odds to win the World Series despite efforts by ownership to trim payroll to $0 and raze Dodger Stadium to replace it with high-rise condos.

Starring :

Tom Goodwin as Willie Mays Hayes
"You may run like Mays, but you hit like sh*t." - Tracy to Goodwin

David Ross as Rube Baker
"They're gonna send me to Pittsburgh, and I don't even live there."

Steve Howe as "Wild Thing" Rick Vaughn
Reason? There's a strong possibility that Howe has also played in the California Penal League.

Hee Seop Choi as Pedro Cerrano (Major League 2 Pacifist Monk)
"I no walk, I swing now."

Milton Bradley as Hiroshi "Kamikaze" Tanaka
"You have no ... MARBLES!" - Milton to Hee Seop

Gary Sheffield as Jack Parkman
"I'm the only winner on this team. The rest of 'em, they're losers. Either by choice, or by birth."

Vin Scully as Harry Doyle
" You know, I used to hate Sheffield when he was with the Marlins. It's amazing how a new uniform can change your attitude about a guy. He's STILL a d*ck! "

And Introducing:

Jamie McCourt as Rachel Phelps
"First Class? Stick that fat Mexican in Coach!" - unconfirmed quote regarding Valenzuela

Last Minute Script Change -

The nude cardboard cutout of Jamie McCourt has been replaced by a cutout of Mrs. Lima, in the interest of public decency.

Here are some noteworthy numbers from some ex-Dodgers.

David Ross just hit his 2nd HR, raising his OPS to 1.287 in 6 games for PIT.
Kaz Ishii has an ERA of 3.29 in 2 starts for NYM.
Hideo Nomo gave up only 1 run in 6 innings for Tampa Bay.
Shawn Green has an OBP of .432 after 10 games for the Dbacks.

To make myself clear...


(courtesy of MIT OCW 15.075)

A season is a 162 games, not 8.

Choi (.158 BA), Drew (.125 BA), and Erickson (12.4 6ERA) deserve some patience.

EDIT: Ross hit another HR and bunted a single. Go figure...

The easy answer is not resigning Beltre. However, Beltre chose to sign elsewhere; such is the reality of free agency. Rather, what irks me is how the team chose to replace Beltre's production in the lineup. To quote Depodesta from a Dodger Thoughts interview:

"Our biggest fear was being left standing without a chair when the music stopped"

Depodesta called this an "audible", but this sure sounds like a scramble to me. I warned against that scenario in the Dodgers Forum way back in last October, and sure enough, it happened. Boras timed the Beltre signing beautifully. Glaus and Koskie, the other big-name FA 3Bs, had already signed, forcing LA to look for offensive production elsewhere. The premier position FAs left were catcher Varitek (no chance), 1B Delgado (LA was set on Choi), and the overpriced Boras clients such as Beltran, Drew, and Magglio.

Perhaps I should have called this post "The Beltre Hangover".


1) Giving J. D. Drew a Player Opt-Out Clause

Drew is a potential top 10 player when healthy, and may be worth $55 million over 5 years, if not more. My main gripe is the out clause. (See an earlier post for an explanation of its value - eerily similar to Beltre's contract) I just can't root for a player who will opt out 2 years if he performs well, or possibly saddle the team payroll for 5 years if he underperforms. Small upside, big downside.

Kent is a massive upgrade over Cora for a relatively low price at 2B, as is Phillips over Ross/Bako at catcher. Drew may be able to match Beltre's production, but he is NOT a massive upgrade over Green given the $55 million contract with an ugly clause versus $16 million for 1 year, especially figuring in the $10 million sent to AZ in the Green trade.


2) Trading RF Shawn Green

In itself, trading Green and $10 million for catching prospect Navarro and a handful of B prospects is not bad. Who knows how an aging Green will perform in 2005: .199 BA with RISP in 2004 or .970 OPS in 2001. Besides, the trade shored up a minor league system thin in catchers, and freed up some 2005 payroll to sign SPs - the biggest priority off the offseason, in my opinion. But I do not like this trade because it was made necessary by the Drew signing, which was in turn made necessary by the Beltre fallout. Trading Green to a division rival with a stadium that is kind to decent power hitters is not a good idea, either.

One could say that Green waived his no-trade clause for an extension; I would say that Arizona pursued him because they were reasonably sure that they were one of the few teams willing to extend Green's contract and take on a decent RF in the middle of their lineup. (It helps that Green's former agent runs the Dbacks now.) Hence they were probably the only serious bidder for Green's services. When you are forced to make a move, chances are that you won't get equal value in return.


3) Resigning Elmer Dessens

This isn't the worst signing in LA history. Afterall, it's only a small one year deal. Who knows, maybe I don't like anyone named Elmer. But let's face it, this is the same guy who got bumped from the rotation of the worst team in baseball last year. Alvarez, when healthy, is clearly the better swingman. Dessens came up golden the other day, and I hope that he continues to be serviceable filling in for the pitchers on the DL. But I think he was resigned because:

1) He is the only Mexican player in a large Mexican market.
2) He is a Depodesta acquisition.

Neither of these reasons translate to performance on the field.

It felt like 10/2/04 all over again.

The Giants spent much of the offseason addressing their weaknesses in the bullpen and on defense, and it happened again.

The Giants' bullpen imploded as Hermanson and company morphed into Benitez. The Giants' defense failed them as Ransom morphed into Ellison.

It's only 7 games into a 162, but a massive comeback win in the home opener against the Archnemesis is sweet.

1) Trading away SP Kaz Ishii for C Jason Phillips

A Phillips trade had been rumored in December, and this trade fell into Depodesta's lap when Trachsel went down. At first, I was skeptical. (and not because I am opposed to trading a SP for a backup C...) LA looked thin in the rotation to start the season - Odalis and Alvarez suffered setbacks during ST, and Penny was unable/unwilling to air it out. Phillips had a dismal .624 OPS in 2004 after a solid 2003 season, which is strangely Ross-esque. Then I read the following article, written by Tom Meagher of the Fourth Outfielder:

http://www.hardballtimes.com/main/article/all-batted-ball-types-all-the-time/

"How rough was Jason Phillips' season? He had fewer singles than his batted ball types would suggest, but he also had fewer doubles, fewer triples, and fewer home runs...perhaps he just had the unluckiest season in baseball. "

Phillips should be a solid starting catcher, will cost near the league minimum this year, and is a huge roster upgrade over Ross, who, to quote Lasorda, "couldn't hit water if he fell out of a boat." As for Ishii, his 13-8 W/L record last year is not indicative of his performance; he enjoyed the best run support of any NL SP. The trade also makes it likely that the two blue chip prospects, Navarro and Martin, are not rushed to the bigs. So this trade is perfect for the roster, for the short term and the long term.

Plus I won't be chugging Pepto once every five days. Many thanks to the Mets!

2) Signing 2B Jeff Kent

Back in December, I posted this on the Dodgers forum just after Kent signed a 2 year $17 million contract with LA. I did this to throw some sense to the critics who were harping that LA signed a surly, slow-footed, pornstached, redneck former Giant with a propensity for popping wheelies on his bike. I compared Kent to Finley and concluded that Kent was the better fit for the Dodgers.

Finley ended up signing with Anaheim (that's right, NOT LAAofA) for a few bucks less than expected, but I think my point is still valid. Finley is nowhere near the upgrade over Werth/Bradley/Green(now Drew) as Kent is over Cora. LA upgraded from a #8 slap hitter to a cleanup hitter with a mere 2 year commitment. All this with a minimal downgrade on defense, to boot.

I know that it's only six games into the season, but I'd say he's gaining a few fans with his leadership, defensive play, and his 1.275 OPS.


3) Tie - Resigning RP Alvarez/Acquiring 3B Nakamura

Alvarez resigned with LA over the offseason for 2 years, $4 million. The portly one-time ace has found a nice niche as the swingman for LA, and provides veteran leadership to a bullpen where, outside of Gagne, is rather inexperienced. I realize that "experience" means nothing to a hitter facing a 95MPH fastball, but.... Alvarez is a 13 year veteran who provides versatility out of the pen, and is effective right-handed batters. Plus that "Fat Boy" gag last year...classic.

Nakamura, who recently got called up to the majors, could be a find. If not, it's no big deal - his contract is a "mere" $500,000. Beltre left a huge hole at 3B, and Valentin is a one year stopgap. (I know it's only 4 games into the season, but 3 errors in the first six games... although Jose is on fire with the bat) Will Nakamura pan out? I think he's capable, and if so, he would help the lineup overall - he has 5 Gold Gloves in Japan. Valentin would then fill in/platoon at 3B, SS, LF, and perhaps 2B - a la Jose Hernandez last year. That would be ideal.

I was reading an article dated 4/4/05 in the Fourth Outfielder where J. D. Drew's opt-out clause is discussed in comparison to Aramis Ramirez's similar clause. The article basically states that Drew's opt-out clause is nowhere near as bad as Aramis'. It seems as though that there was quite a disagreement between the readers on which is worse. (I am comment #29, by the way, dated 4/6/05.) Studes also commented on the article and gave his own thoughts in The Hardball Times on 4/7/05.

I would like to expand on what I stated in the Fourth Outfielder: the player opt-out clause has a significant value, and its value can be estimated.

To me, a player opt-out clause is similar to a financial option, which is a product traded in the derivative market, my former field of study and work. (Many thanks to Prof. Cox for the pleasant naps during his option theory class) Here is a quick summary.

http://www.riskglossary.com/articles/option.htm

After two years in LA, Drew has the right to void the last three years ($33 mil) of his contract if he believes that he can get a higher offer in the open market. Logic would dictate that the option would not be exercised otherwise. In effect, Drew has a "European call option" with a strike price of $33 million.

For the sake of simplicity, let's say there are two 50/50 possible scenarios in two years: Drew has played marvelously for two years and his market value has climbed to $46 million, or he has been ineffective/injured and his value has sunk to $20 million.


A Simple Binomial Option Model

If Drew signs a contract for $46 million in the open market, then he will have pocketed an additional $13 million. If his worth drops to $20 million, Drew still earns $33 million in LA and loses nothing.

What is the value of this option? Let's assume that the annual interest rate is about 4%. I'm going to skip a lot of numbers and say that this option is worth about $7 million, or $7.24 million to be exact.

If we were to use a trinomial model - say there is a 33%/33%/33% chance of being a $46 mil/$33/$20 player - the option is worth about $5 million. Not as much, but still significant.

I realize that these values are based on an extremely simple model, but the numbers are still significant. (A better way would be to determine a historical distribution for contract fluctuations amongst similar players and then value the option, in spirit with a Black-Scholes model.) The point I want to make is this: a five year $55 million contract with a player opt-out clause after two years is about equivalent to a five year $55 million contract sans the clause and WITH AN ADDITIONAL $5 TO $7 MILLION UPFRONT. Put another way, this is in essense a 5 year contract worth about $62 million, with $17 to $18 million in the first year.

(drum roll....)

That's essentially Beltre's contract from Seattle. To refresh everyone's memory, Beltre turned down the Dodgers' six year $60 million offer for Seattle's front-loaded five year $64 million offer. ($17 million or so in the first year) Depodesta then signed Drew to replace Beltre's production in the lineup. Hindsight is 20/20, but Depodesta lost out on Beltre and replaced him by signing Drew, overpaying to a point where the $ amounts were, in essense, similar.

No wonder Scott Boras was reportedly cautious during Beltre's Seattle press conference when asked about the Dodgers. I wouldn't be surprised if he probably had this scenario lined up all along - take Beltre elsewhere, offer Drew and his "Moneyball" numbers to LA. I believe that Depodesta got taken here. Love him or hate him, Boras is pretty good.

I need to throw in a big caveat regarding my previous post evaluating the value of the stolen base. Using the Markov process, i calculated that stolen bases have a minimal effect on runs scored over a season. What naturally follows is that the more runs you score versus runs allowed, the more games you would expect to win. (the famous Pythagorean Theorem of Baseball)

BUT BEWARE! Runs do not equal actual wins.

All runs are not equal. A run that ties a game in the ninth is more significant than a run while down by 10.

Boston is down by a run in the bottom of the ninth in Game 4 of the ALCS. Kevin Millar leads off the inning with a walk. Francona ponders how to give his team the best chance to win, and chooses pinch-run Dave Roberts and his 92.7% 04 SB rate for the snail-like Millar. Roberts successfully steals 2nd, and scores on an RBI single. Game is tied, and eventually won in extra innings.

The Markovian value of Roberts’ stolen base is a mere 0.231 expected runs. That contribution, however, was the critical run that saved the game.

The following article is a good read on changes of managerial strategy at various stages of the game.

http://ite.pubs.informs.org/Vol5No1/Bickel/

To quote the article:

The types of strategies that maximize expected runs may not be the same as those that maximize the probability of winning late in the game. It is for this reason that baseball strategy changes as the game progresses ... The objective of baseball is to win, not to score runs.

If the game is close, the managerial decisions in the late innings may not optimize runs scored versus runs allowed. At such times, going for a single run can be the best chance of winning the game, whether by a sacrifice bunt, hit and run, or a stolen base - "expected" runs be damned.