THE BOOK--Playing The Percentages In Baseball

I’d like to see what MGL thinks of CC the rest of the way (a little more than a 1/3 of the season) for the Brewers...what did you have them projected at win-wise at the beginning of the season and what could we see them at with Sabathia?  Playoffs?

Victor does all the leg-work:
http://www.hardballtimes.com/main/article/evaluating-the-cc-sabathia-trade/

The numbers at the end for the draft picks in the table don’t seem to jibe with the article.  Also, it doesn’t look like he included the signing bonuses.

Overall, it seems that the trade was about right.

I’m surprised at the value of the draft picks, and will need to look into it some more.

I should add that this is an excellent article, and exactly what the mainstream should be doing in evaluating trades.

Unfortunately, we get what we get in the mainstream.

Good article, but I have a few nits to pick.

He’s got the surplus value of C.C. as his salary value based on wins above replacement - his actual salary.

Then he adds a few more million because C.C. will increase the Brewers expected win total.  I think he’s double counting, as his surplus value is what it is because C.C. is expected to win more games for you.

I’m OK with the playoff odds because the Brewers are in that sweet spot where a few marginal wins could be the difference, but isn’t the chance at playoff revenue already factored into the 4.8 million per marginal win that teams pay?

Thanks for the kind words Tango.  The study on draft pick values is here:
http://www.baseballprospectus.com/article.php?articleid=4368

Also, Nate did factor in signing bonuses in determining value.  Tango, do you think the draft values look high or low?

Sounded pretty high.

A few months ago, Dave Cameron had a great article about trading for someone for two months, and what the picks were worth at USSM (I linked to it here).  IIRC, you’d get something like an average player half the time, and nothing else otherwise. 

A player gets paid about one-third his free agent value over the first 6 years.  An average player would generate say 12 WAR, meaning that 8 of those WAR are “free”.

Hmmm… that’s about 32MM in surplus, which happens half the time, minus the signing bonus for the two players… so a bit over 10MM total.

I guess my initial instincts were wrong, and Victor (or Nate) probably has it right.

I came up with a win and a half, just with Sabathia replacing Bush in the rotation.

Much better than Sheehan’s piece, though:

http://www.baseballprospectus.com/article.php?articleid=7770

I cringed when reading it.

#37- I was debating about this too.  I don’t think it’s double counting because in trades like these, one team is going to be giving up a lot of surplus value to another team.  The reason they’re giving that up is because they feel the gain they’ll get with increased playoff odds is worth the prospects they’re trading.  Therefore I think to properly value a trade like this you have to factor in the increased playoff odds.  I am open to other opinions on this.

#40- if you factor in chaining I think you’ll get a similar figure to mine.

Re: Rally’s point that Victor is trying to refute.

It depends how BBTN presented the numbers.  I’ll have to dig it out and see, but the question is:
- did they present it in two steps, such that you have marginal dollar/wins value, and then an additional value beyond that of 950K per win, plus playoff $ per win, OR
- they simply said 950K per win, plus playoff $ per win

It would seem to me that it was the first step, and therefore, Victor is double-counting.

For example, I give a flat 4.4MM$ per win, and don’t consider playoffs.  But, if I were to consider playoffs, my 4.4MM$ would have to go down, if I’m also going to add an extra 35MM$ per playoff game.

So, this is what Rally is talking about I think, and if that is correct, then Victor is double-counting.

"It would seem to me that it was the first step,”

SECOND step is what I meant here…

"A player’s surplus value is equivalent to his win value in a dollar figure minus his salary.”

Does win value take into account the value of wins between an expected 90 win team and an expected 70 win team?  In other words, the subject of the last paragraph of your post?

Thanks MGL, glad you liked the article.  And I definitely agree a monte carlo type sim is definitely way to go for the playoff odds, but I didn’t quite have the necessary tools to do that.

At some point, someone is going to have to do a comprehensive study on how to properly add leverage (for lack of a better word) to marginal win value.  This touches on Melvin’s point in #1, but since we already have a half season of knowledge about the 2008 Brewers, we have a better idea about where those 2-2.5 wins that Sabathia adds are going to go. 

Obviously, the 89th, 90th, and 91st win for a team have a higher marginal value than an 83rd, 84th, and 85th win, due to the non-linear playoff odds increases at those win levels. 

Just as a reliever’s runs are worth more than a starter’s runs because of how a manager can choose to leverage those wins, I would argue that wins acquired in midseason are worth more than those acquired in the off-season, since they are far more likely to influence a playoff race. 

I’m just guessing here, but if the marginal value of an off-season win acquisition is $5 million, I’d argue that the marginal value of an in-season win acquisition is probably closer to $7 or $8 million. 

I’d also argue that, because most teams use fiscal year accounting principles that don’t allow for money to roll from one year’s payroll to the next, we have to significantly discount the negative value of a mid-season acquisition’s salary.  It isn’t like Milwaukee is going to offset the additional salary they have to pay Sabathia by dumping an equivalent amount of money from the roster in order to stay under budget.  They’re simply expanding the budget with money that wasn’t previously available, and that budget expansion doesn’t devalue the rest of the team in any meaningful way. 

In the off-season, giving one player $4 million probably means that you’re not giving that $4 million to another player, and there’s a real opportunity cost there.  During the season, that same dynamic just doesn’t exist, and so we can’t hold the same opportunity cost against the new acquisition.

I think we can estimate the leveraged value of a marginal win pre-season just as we can mid-season, although obviously the pre-season estimate will have much more uncertainty.

I am not sure I understand your last point, David.  I know virtually nothing about economics.

Melvin, that quote is from the article, not from me.  Victor apparently treated those two things separately, I think.  The two things being one, the generic value of a marginal win, which is simply the average added revenue (minus some profit) that a marginal win provides to an average team, and two, the value of that win below or above that, based on the impact that marginal win has on a team getting into the post-season, and winning a pennant or WS.

You can combine those two things and treat them as one, or you can treat them separately.  It doesn’t matter.  The important thing is the total value of a marginal win to a team, which includes more fans/revenue based on more wins in a season and the bonus from making the post-season and winning a pennant or WS (a WS being much better than a pennant, I think).

Then again, although a player is worth, on average, X dollars (around 4-5 mil) as a FA per marginal win, simply because that is what they are getting paid (and we have to assume that the added revenue is at least that, on the average), that number varies greatly among teams, not only by virtue of each team’s playoff potential, but by virtue of all the nuances of their markets.

We know that, but we often forget that when we are discussing whether a signing or trade was “good” for a team.  For the Yankees to pay 8 mil for a marginal win is a completely different animal than for the Marlins to do the same thing.  Completely different. 

Now, if the Yankees pay 8 mil for a marginal win, and they could not have acquired another marginal win for any cheaper, and if that marginal win generates 10 mil in extra net revenue, then it was a good spend, obviously.  If the Marlins, on the other hand, spend 3 mil on a marginal win, which is less than the going rate and less than any other alternative, but that marginal win only provides an extra 2 mil in revenue, then the team did a stupid thing, at least fiscally-wise.

We generally evaluate trades and signings according to these very generic formulas (such as a marginal win is worth 4-5 mil in FA dollars), but that is a very bad way to do it.  The only thing that makes it a reasonable way to do it is that we assume that if a team pays 8 mil for a marginal win, it is because they mis-evaluated (overvalued) the player and that they could have gotten that same marginal win (not necessarily at the same position) for less than that, which is often, but not always, true.  We also make the assumption that, for example, if a team acquires a win for 3 mil, that is was a good deal and they did something smart, even if it loses money in the deal (as in the Marlins example above), because they were able to acquire a commodity at below market prices.

In Wong’s article, I have no idea if his values for the minor league players that CLE acquired are accurate (and obviously there is a great deal of uncertainty in those numbers no matter what), but the method for his analysis as well as his specific analysis of the value of CC, is spot on.

And it is exceedingly rare that any journalist even comes close to being correct in their analyses of trades and acquisitions.

I hate to pick on Joe or BP, but he has an article that analyzes the trade as well.

http://baseballprospectus.com/article.php?articleid=7770

The two have combined to allow 88 runs in 150 1/3 innings over 27 starts. That’s an RA of 5.27 and about 5 2/3 IP per start. Sabathia has allowed 54 runs in 122 1/3 innings (3.94 RA), averaging a bit more than 6 2/3 IP per start. That includes Sabathia’s clearly aberrational April; if you consider his true level to be what he’s done in his last 14 starts, it’s a 2.33 RA in 7 1/3 IP per. Regress that, split the difference—let’s not pretend we can predict player performance to two decimal places over half a season—and you can expect that Sabathia is about a 3.00 ERA pitcher giving you seven innings a start.

What a horrible way to figure player talent/value!  I might give it a pass if it were on ESPN.com or SI.com, but on BP, the supposed preeminent sabermetric site?  Come on!  Joe, get some help from someone on the staff that does these things (evaluating players, sabermetrically)!

Let’s see, first of all he is using each player’s 3 months of stats only.  That makes me want to throw up!

Then he wants to “discount April, because it was aberrational.” That makes me want to gouge out my eyes!

Then he makes no mention of the gargantuan difference between the AL and NL pitching this year (for example, an average pitcher in the AL is probably .3 runs in RA per 9 better than an average pitcher in the NL).

He also does not consider the significant injury risk of a pitcher, even in 3 months hence.

Hey, at least he regresses. 

Somehow, he actually comes up with the correct marginal value of Sabathia for the remaining months (2-2.5 wins), I think. 

He also says:

The marginal value of those wins could be astronomical, as there’s an excellent chance the Brewers will reach the postseason by that margin or less, and a postseason appearance pays off in direct and indirect revenues for years.

As I said, doing a Monte Carlo, you get an increase in around 16% for making the postseason.  You can call that whatever you want, but I don’t think you can call it “astronomical.”

He says that he does not think that Shapiro got enough for Sabathia, and that he thinks that he could have gotten more if he waited till closer to the deadline.  I don’t know if he could have done better by waiting (and CLE is a very smart organization), but I think he is overstating the value of a player (albeit a great one) who is going to be a FA in less than 3 months and already makes almost 9 mil a year.

What David was saying is that pre-season budgets are typically set, and so paying $4 million for player A means you have $4 million less to spend on other players. In contrast, he is saying that a mid-season acquisition for $4 million is unlikely to reduce next year’s spending by $4 million, and is essentially a (temporary) $4 million budget increase.

If you lose $4 million to spend on other players, it gives you less flexibility in the pre-season example, which means that the actual cost of that $4 million is much greater. Let’s say that a tremendous player does not exercise a player option for the last year of his contract after you’ve already tied up most of your budget—since you are already committed, you can’t make the move, which has massive costs.

In contrast, the $4 million spent on Sabathia won’t prevent them from obtaining other players (who are they likely to obtain at this point?) and likely won’t impact next year’s budget—that means that there is little chance that spending the money on Sabathia would hurt them in the longer run.

Posts #1 through #10 were moved to here from the “Sabermetrics in-season moves of 2008” thread.  Please read through those to catch up, before commenting.

Rally/Tango- so do you think the correct thing to do what be to just include the surplus value and playoff benefit and ignore the $950,000/win since surplus value already factors in the marginal $/win?

Victor - that seems about right to me.

I think it’s OK to include the playoff benefit here.  For a random team in the pre-season, the chance that Sabathia’s wins give you a better playoff chance should already be included in the surplus value, but since the Brewers are in a specific position, right on the playoff bubble, I think it makes sense to count it as an extra here.

There are 1000 marginal wins every season (.500 minus .294 times 162 times 30 equals 1000 ... I used .294 to get the nice rounded number of 1000, otherwise I’d normally use .300).

Each marginal win has a free agent dollar value of 4.4MM, giving us a total of 4.4 billion marginal$.

Now, the question is what happens if you split this 4.4 billion$ into two components: marginal wins, and playoff games.  There’s 8 teams each earning 35MM per playoff appearance, then that means the playoffs in all are worth 280 MM$. 

That leaves us with 4.1 billion marginal free agent dollars to spread out over the 1000 marginal wins, making each marginal win 4.1 MM$ for the regular season.

***

If MGL is saying that CC is adding 0.15 to the chances of the Brewers making the playoffs, then that’s 5.25MM added in bonus playoffs.

You had him at +2.2 wins, each of which is now worth 4.1MM, for a total of 9.0 for regular season play.

In all, that’s 14.25MM $.

On a straight 4.4MM, where we don’t care about the “sweet spot” of the playoffs, that’s 4.4x2.2= 9.68MM$. As you can see here, the additional value of the playoffs OVER RANDOM (not over not making it), is 14.25 minus 9.68 = 4.57MM.

Anyway, CC is earning 9MM this year, meaning aroud 4MM$ left to be paid.

His surplus value is 14.25 - 4 = 10.25MM.

However, you have chosen to figure his surplus value as his regular season value minus his regular season salary, which is 9.0 minus 4 = 5.0MM in surplus value.

You then have to add the playoff “bonus” of 5.25MM.

That gives you a final surplus value of 10.25MM.

What Rally was saying you were double-counting was the extra 950K per regular season win.

Rally/Tango- thanks, we’re on the same page now.

Minor quibble at best, but when you factor in inflation and everything you could just say NPV (Net Present Value) instead of Surplus Value.  Great article though!

Just a minor note, but the Brewers aren’t guaranteed a “Tier 3” pick for Sabathia. If he’s signed by a team that finished in the Top 15, the Brewers would receive that team’s 2nd round pick.

But overall, an excellent analysis. Thanks Victor for writing it and thanks to Tango and MGL for discussing it.

Re: draft and prospect values

I think both are probably too high, but since they’re on offsetting sides of the deal they may cancel and as a result the conclusion - that it’s an even deal - is reasonable.

Silver’s method to determine draft pick value is very good except he screwed up the conversion of WARP production to dollars.  He used a linear conversion and as a result came up with an “average” draft pick who produces 2 WARP/yr for 6 years as being worth 14M or something.  Except a 2 WARP/yr player is actually worthless because the replacement level is so low.  It’s really unfortunate he didn’t pick up on that when he wrote the article. 

Anyway, he did eventually fix his WARP to dollars conversion for subsequent FA analysis by using an exponential factor.  That’s how his MORP values are calculated. 

I know Tango has made a case that the true relationship between wins and money is linear, but in this case the relationship has be exponential or it just won’t work.  It may be because two wrongs - low replacement level for WARP and the exponential relationship - happen to make a “right”, but any WARP calculations without the exponential factor don’t really work.

When I calculated draft slot values a couple years ago I used the same process that he outlined in that article, but used his MORP calculations to determine the market values.  My values tended to be significantly lower and imo more reasonable.  Victor quotes values of 9M and 3M and mine were more in the 5M and 1.5M range.  Even with a couple of years of inflation I’d peg the value of those two picks as closer to 8-10M than the 16M used in the article.  And Jared makes a good point in #23 that if a protected team signs Sabathia than the value for those picks crashes as the difference between #18/#32 and #32/#60 is absolutely huge.

I also had a hard time buying Bryson, Green, and Jackson as worth 5, 7 and 1M.  I think maybe you didn’t discount hard enough for non-top 100 prospects. And honestly, I’m not even sure Bryson and Green are Top 200 prospects. 

Whenever I try to figure out the worth of prospect or draft slot I always try to double check against what common sense and baseball reality is trying to tell me.  Tim Beckham, the top ranked amatuer player, just signed for 6.15M.  Is his value really somewhere between Bryson and Green’s?  Would a “smart” organization actually be willing to buy Tyler Green for 6.5M because that’s 500k under market price?  I really don’t think so.

And maybe a clearer way to look at that is to see if all the monetary values being used make sense in relation to each other.  If LaPorta is worth 23.5M, then does it make sense that the other 3 guys are worth 13M?  I wouldn’t trade LaPorta for those 3 guys and a couple more Bryson’s.  Is LaPorta at 23.5M really only 3x as valuable as Tyler Green, a guy on very few people’s radars, at 7M?  I don’t think that passes the “reasonableness” test for me.

Maybe their values are “right” and LaPorta is being way undervalued, but I don’t think the relative weights are right.  I’d be more comfortable with those 3 guys valued more in the 5-6M range than the 13M range.

Which is a long way of getting to where I started - it probably is an “even” trade, but more in the 30M range than the 35M range.

The value of lower prospects is going to be zero in a strictly linear method, because they are below replacement level.  Take any one at random, the odds are less than 50% he even makes the big leagues.

My method for calculating the value of lower prospects is this: 

1. Do a projection
2. Do percentile projections (like Pecota’s, I’m working on these for CHONE.
3. Figure value over replacement at each 10th percentile.  Minimum value is zero.
4. Add them up and divide by 9.

For a good player, he’ll be above replacement at even the 10th percentile, so his value won’t be any different (at least not much, maybe rounding) than looking at his mean projection.

For a scrub, he may only have value above replacement at the 80th or 90th percentile.

I know Tango has made a case that the true relationship between wins and money is linear, but in this case the relationship has be exponential or it just won’t work.  It may be because two wrongs - low replacement level for WARP and the exponential relationship - happen to make a “right”, but any WARP calculations without the exponential factor don’t really work.

That’s exactly correct.  I proved this in a post last year.  Because of the ridiculously low replacement level of WARP (wrong 1) you need an exponential factor (wrong 2) to realign it properly.

Here’s the proof to the two wrongs make a right:
http://www.insidethebook.com/ee/index.php/site/comments/supervorp/#9

Read through to comment 12.

Also this is a good link:
http://www.insidethebook.com/ee/index.php/site/comments/do_teams_pay_more_for_top_end_talent/

Philly- that is some good stuff you have posted.  I wasn’t aware that Silver calculated those values linearly, I’ll have to look back at your draft study.  And i’m not quite sure we have a definite answer on valuing lower rated prospects, but it’s something I’m trying to look into.

"MIL (Increased their chances of making post by 16%, by acquiring CC.)”

What did you peg the value of that trade at in wins for the Brewers?  2?  I assume you had him replacing McClung?

Sorry, I see that my questions were already answered in the proceeding thread.

I may have missed it, but I didn’t notice anyone mentioning the value of the Sabathia trade insofar as improving the odds of the Brewers doing better IN the playoffs.  I have the trade improving their odds of winning the first round alone at around 6%.  That has to have some kind of dollar value.

Sure, not only is any addition going to improve your chances once you are in the post, the addition of a #1 or #2 starter is going to greatly improve your chances as compared to a position player of similar WAR value.

Went to dig up some of my relevent draft stuff from last year.

This post addresses Jared’s point in #23 about the possibility of a protected team signing a type A FA.

http://sonsofsamhorn.net/index.php?showtopic=21417

In the 2007 draft there were 17 type A’s, which was a lot, but only 6 returned a 1st rd pick.  Those teams on average recived picks #21 and #40.  I valued those two picks at ~13M in 2007 FA dollars.

The other 11 type A’s were signed by teams with protected firsts or by teams that had signed multiple type A’s.  Those compensatory picks averaged out to be #39 and #88.  I valued those picks at 4.7M.  That’s roughly a 2/3 reduction in value simply because the “wrong” team signed the player (wrong from the perspective of the team getting the picks).  There can be a wide range of compensation amognst type A FAs.

Now that draft had an unusually big group of comp picks under the older CBA and Sabathia would likley be the highest ranked FA this winter so his compensation wouldn’t get bumped down as far as some of those other guys, but it’s definitely true that not all type A’s return the same compensation.

For the 2008 draft it looks like there were only 5 type A’s signed.

Glavine: #18/#33
Hunter: #27/#31
Cordero: #32/#53
Rowand: #34/#51
Linebrink: #35/#54

Again this year less than half of the type A’s actually returned a 1st.  The Mets really did well getting 18/33 when the system max is 16/31.  It sure beats 3x/5x that the teams who lost Cordero, Rowand and Linebrink got.

This post has a full set of values for slots #1-244 based on 2007 FA data and the 1987-1994 drafts.

http://sonsofsamhorn.net/index.php?showtopic=19514

The values are actually higher than what I posted in #24.  I think I mistakenly pulled up the 2006 report.  The 2007 values for a late 1st and an early supp pick were more like 9M/3M.  That’s actually pretty close to what Silver initially reported.  And now that I notice that I do remember getting a chuckle over the fact that even by “fixing” Silver’s mistaken process that the two answers weren’t that much different.

Suppan is actually the worst pitcher on the team, but they are heavily invested in him and don’t realize how bad he is.

CC adds around 2 wins, depending upon whom he replaces and how that affects the “chaining” of the relievers and rest of the starters.

MGL, what do you have CC’s WAR at then?  If he’s adding 2 wins for 1/2 a season, then you have him at about 4 WAR?  I know there is the question of who he replaces and things like that, but I was just curious.  I guess it’s best to look at these things through a database projection system where you can just put CC in for Suppan or McClung and see the post-season expectancy increase.

I just remember you talking a lot last year (and when Abreu was traded to the Yankees) about how these kind of mid-season trades don’t really help teams out that much.  I guess because it’s CC and because it’s 1/2 of the season (and not a 1/3 like at the trading deadline), things are different.  Would you say that’s the reason why CC has a decent-sized impact on the Brewers this year?

I have CC as around 5 WAR, in the NL which has substantially worse pitching this year.  But that depends on the definition of a replacement pitcher.

He adds 2 wins to the Brewers because he is not replacing a replacement pitcher, whoever it is he replaces.

He is a premier player of course.  Lots of trades involve players who are considered impact players but are only 3 WAR (sometimes less).  Trade for a player who is 3 WAR at the trade deadline and assuming that he replaces a better than replacement level player, you are often talking about a less than one win impact!

Also, the average person thinks a player like CC is worth 6 or 7 wins in less than half a season.

Plus, the Brewers are in a fairly unique situation whereby they are literally on the cusp of making the post.  Harden, assuming he stays reasonably healthy, is a better pitcher than CC, yet he only adds 5% or so to the Cubs chances of making the post, because they already were almost a lock.  Of course, if he lasts that long without getting hurt, he substantially increases their chances withing the post, as a #1 starter (although he will be considered #2 behind Zambrano, but he is MUCH better of course).