THE BOOK--Playing The Percentages In Baseball

Tango,

When you mean “playing time” in your WAR = playing time * (Talent-baseline), do you mean actual playing time or ideal playing time?

Ideal playing time:  Assuming I’d play Endy Chavez every day he was available, after factoring his age/injury history, I’d expect him to play 85% of the games.

Actual playing time:  Endy’s established role of reserve OF means we expect 50% playing time.

(This is just an example.)

I said:

“playing Time itself is a function of Talent over baseline (plus management stubborness).”

I would not consider the stubborness of management in the valuation of a player.

OK, I’ve thought it through and am ready to present a real life example.

Take the Marlins-Red Sox example of Hanley Ramirez.  For value, I’ll use my data at baseballprojection.com

Red Sox: http://www.baseballprojection.com/BOS2009p.htm

Marlins: http://www.baseballprojection.com/FLO2009p.htm

For this exercise, ignore contracts, years under contract, just look at one year differences.  It doesn’t matter if you think my projections are accurate or not, just pretend they are and see where this goes.

Considering them as average defenders, Hanley Ramirez is a 5.3 win player and Jed Lowrie is a 1.9.  Jon Lester comes in at 2.4, so a 2 for one is not fair to the Marlins.  Throw in Michael Bowden (1.2) and we’re close to even in WAR.

Since defense is even, just look at offensive runs above/below average.  Boston is 32 runs better with the switch of shortstops, and Florida is 32 runs worse.

On starting pitching, here’s what I do:  Start from best pitcher to worst, and add up the WAR until you get to 162 starts.  It may take 8-12 pitchers to get there, no team can expect to get through a season with only 5 starters.  The last pitcher will probably have to have is WAR prorated.  Taking Lester and Bowden away from the Red Sox, you give their starts to lessor pitchers.  This yields 143 WAR.  Putting them on the Marlins and displacing their worst pitchers gives the Marlins 106 WAR.

So the trade, even in the simple WAR calculation, yields -10 for Florida and +16 for Boston given real life roster situations.

How about if the Red Sox throw in Buccholz?  He’s projected at 2 WAR.  Repeating the calculation gives us 118 for the new Marlin rotation and 126 for the Red Sox.  That’s a 34 run gain for the Marlins over the starting point, a 33 runs loss for Boston, and we’ve now evened out the offensive gain.

This trade would be win neutral for the teams, but would show Boston giving up 4 players of 7.5 WAR for one Marlin of 5.3 WAR.

So maybe lopsided trades should lop off 0.4 wins in the calculation for each excess player for roster utility considerations?

I left out a step.  Assuming no trade, the rotation for Boston yields 159 Runs above replacement and Florida’s is 84.

And in a few spots I say WAR where I should have said runs above replacement.  Those instances should be obvious once you get past new year activities.

I’m probably not qualified to respond to this, but I think Rally is right. Unless something is off because of the playing time issue with Bowden and Lowrie projected to play a good portion of the time when in reality they might not be. Or would that not matter here? Not really sure, it’s 2:40 AM after all.

My comment at BTF:
The best case for valuing a 6 WAR player over 2 3-WAR players is that the 6-WAR player gives a team more ways to build a championship team. Let’s say the goal of the Red Sox is to assemble a 95-win true talent team*, so they will virtually always make the post-season. So they need 14 wins above average. That’s almost 1 WAA per regular player, which is what your 3 WAR players give you. It’s very hard, if not impossible, to be above average at every position (and 5 starters). Even a good farm system will not produce adequate players at certain positions for years at a time; the FA market will not always have players who meet your current needs. The market for baseball talent is not that liquid—there’s no Amazonbaseball.com where I can just order a 3-WAR shortstop and have him arrive in time for spring training. With a 4 WAA (6 WAR) player under contract, a team can carry a couple of average players, or sustain an injury, and still reach its goal. So for a rich and ambitious team, it makes a lot of sense to sign elite players.

That said, I think Tango is right that in practice, MLB salaries are linear, and teams don’t pay elite players more per win. Or the premium is small enough that it hardly matters. My guess is this is a function of injury risk: the downside of tying up so much payroll and talent in one fragile human is substantial. The odds that 2 3-WAR players will both sustain career-ending injuries is much smaller than the risk for 1 6-WAR player. In fact, if we knew how much teams paid to insure the elite players, and included that in their salary, we might find that teams do effectively pay proportionately more for their services.

*I know Tango thinks teams should shoot for c. 89 wins, but I don’t agree (nor, I’m fairly sure, do the Yankees or Red Sox).

I’ve thought about it some more and if the above example proved typical in lopsided player swaps, this formula would fit it:

A multiplayer package of total WAR = Y, consisting of X players

Y * 0.89 ^ (x-1) equals the WAR of a single great player that package equals.

I won’t say this should apply to salaries, just to trades.

From that formula, a 5.3 WAR player is equal to:

2 3.0 players
3 2.25 players
4 1.9 players
5 1.7 players

Good stuff Rally, just the basis for discussion I was looking for.

Ok, if for trade purposes:
5.3 = 3.0 + 3.0

Then what would be the equivalent here:
? + 0.7 = 3.0 + 3.0

I personally feel this discussion is too abstract. When going after a 6 WAR player, (or a 5 WAR player, what have you), there are other considerations at work. Generally that 5 WAR player is going to be an All-Star, which is going to add an iconic status to your team’s marketability that two 3 WAR players just aren’t going to give you. Yes, the bottom line is wins, but only insofar as those wins get you to the playoffs and give the ability to raise ticket prices and fill the stands. If you can get slightly less wins per season value out the transaction but can increase your marketability moreso then it is actually worth it. You also have to take into account what other players are in the organization. If you have two 3 WAR players on your roster but one of them plays the same position as say, a 2 WAR player, then getting the 5 WAR player and playing the 2 WAR player gives you more wins overall anyway.

Good question in #8.  Not sure how to handle that - obviously the formula breaks down.

A few thoughts:

1. If “replacement” is the 25th player on an average roster, then in a two-for-one trade, the team giving up two players will have to replace them with, at worst, a 24th and 25th best player. So the small difference between the 24th and 25th player would mean that 3 WAR + 3 WAR is really 3 wins above 25th best player plus 2.7 wins above 24th best player. You’d have to rank all 750 players in the league and put them in 25 buckets to determine the win value of each roster spot (ie the 25 worst players are replacement, the 26-50 worst equal the 24th spot etc).

2. There could be an opportunity cost for having to replace a roster spot with a replacement player. So, if replacement is 2 wins below average, then each roster spot given to a replacement player costs -2/25 wins = 0.08 wins. The team giving up one player loses 0.08 wins (reflected already in WAR) but the team giving up two players loses 0.16 wins.

3. Given that teams generally trade from strengths (ie willing to trade a 3 WAR SS because of a hot prospect at AAA), “replacement value” in a trading context might be halfway between real replacement and league average. Maybe it’s even league average. If it is, and replacement is -2 wins, then the 6.0 for 3.0 + 3.0 WAR trade is really 4.0 wins above average for 1.0 + 1.0 wins above average.

Doesn’t Rally’s analysis simply imply that the replacement level is too low? According to his projections, both the Marlins and Red Sox have 11 starting pitchers better than replacement. Overall, he projects about 350 starting pitchers to be above replacement level. If you upped the replacement level for pitchers by 5 runs, then Boston’s 4 players would total 6 WAR vs Hanley at 5.3.

When we’re talking about big-time free agents like Sabathia and Teixeira, it doesn’t matter much where we set the replacement level. But, it makes a pretty big difference when we’re talking about players who are relatively close to replacement level, like Bowden and Buccholz.

Replacement level may be set too low for starting pitchers.  I think I used a .400 winning percentage to set replacement level, but at that level there is a huge number of minor leaguers who project as better than the Livan Hernandezes and Sidney Ponsons of the world.

I agree with the view that replacement level is being set too low for purposes of evaluating trades made by contenders because the trade market is not perfectly liquid, and I think that we’re undervaluing roster spots.

One way the 6+0 combination in position players helps a team is that if they have a spare roster spot, they can platoon the 0 slot at very low additional cost.  In contrast, it’s not generally feasible to platoon 3 WAR players (there is almost always a better use for the money than hiring another 3 WAR player to play part time).

Teams face several problems in trading.  The other team will often have insights into their players which aren’t public information which can lead to adverse selection problems.  Also, fans value continuity to some degree, so there is a marketing cost to trading too frequently.  This is especially an issue with 6 WAR players (who are likely to have been at the center of marketing campaigns).

I hope I’m not double-posting it:

I did answer at BTF and it went something like this:
If you ask about the money team is willing to pay, I think, based on the signings of the last few years, that 2 - 3 WAR players (without special injury concerns, discounts for home team and any other special case) are payed around their value (mean value per win). 5+ WAR players are also payed around their value, but that is win value of the top revenue teams, so they should get a bit more per projected win. (This is distorted when some 3 WAR players who had shown signs that they can give for a period of time 5+ WAR performance get payed as 5+ WAR players. these contracts really hurt teams. Also, when certain type (CF, SP is in relatively short supply, but there are a number of 2 - 3 WAR players (and larger number of teams who need them), they will usually get paid more than they deserve (think all the SPs in 2005 except Byrd).
Second view of value, what should the team give up for superstar player. The value of 6 WAR player versus two 3 WAR players depends on a specific team. If the team has nearly as good player at one position who is currently on the bench, and the other 3 WAR player plays the same position as 6 WAR player, then this trade is almost 3 win upgrade for that team (of course, than comes the question of who additional players are included and what other trades are available for one of two nearly identical players).
If team A is thinking about a trade which would transfer two positions from 3 WAR + 3 WAR to 6 WAR + 0 WAR, usefulness of the trade depends on the position of the team. If the team is a clear favourite (5+ wins over the second best in the division) then they shouldn’t make the deal - injury to one of the 3 WAR players still leaves them as favourites, but injury to 6 WAR player pulls them back into the pack. If the team is out of the contention, it’s of no consequence, they shouldn’t do it if they have to significantly overpay. If the team feels they may be in the hunt for playoff spot in 3 - 4 years, and the player should stay around 6 WAR and under team control for 5+ years (Hanley with his new deal), then this trade would make a serious statement and very good starting point (except if they have to significantly overpay, but sometimes even then, to show to the public and to other players they hope to get in following years that they are serious). If the team is in contention for playoff spot, then this trade should be made because of the opportunity it provides for the team to get better. I’ll show it analyzing this proposed trade.
For the purpose of this analysis, let’s assume that Hanley is true 6 WAR player and that Lester and Lowrie are true 3 WAR players, that all will stay that way for 5+ years and that over next few years Lester and Lowrie will be together payed roughly the same as Hanley on his new, very team -friendly contract. Trading L&L for Hanley leaves Boston with 3 WAR upgrade at SS and a hole in the rotation. They can plug that hole internally or externally. They can put one of their young pitchers that they think will be between 0 and 1 WAR. They can sign someone like Wolf who should be good enough for 1 - 2 WAR at some (low for Boston) cost. Or, they can sign Love, at high cost, who should give them 3+ WAR. If they go with someone who gives them 0 - 1 war, they can evaluate situation at the deadline and if they are close to the playoff spot, they can trade for some impact pitcher (Harden, Johnson, if he suddenly pitches like his old self,...) who could then be full 2 win upgrade over the rest of the season. Yes, that would cost, but the main advantage of 3+3 for 6 trade is in the opportunity to improve the team. Now, if Boston has another 0 - 1 WAR pitcher in the rotation, than this trade may not be as effective, because then they will only use this opportunity if they sign Love now and get an ace at the deadline. (But if they expect not to have less that 2 WAR starter in 2010, 2011 and later, than this trade gives them opportunity to improve for those years, like if they sigh Love now, and that second 0 WAR pitcher is a prospect who should be 2 WAR player in 2010 or will be replaced by 2 WAR prospect in 2010.)
To acquire that opportunity to improve, team should be willing to overpay - so with L&L they should send someone like 2 prospects who are a good bet to play in the majors, but who should be 2 WAR players, maybe peak at 3 WAR; or one such player and one player who might be 5+ WAR, but with low chance of making it (lower than Hanley, maybe like that guy they gave Texas for Gagne), and maybe some of those classic C prospects - reliever with excellent stuff who can’t find strike zone or outfielder with great tools and zero results.
By following this strategy, team overpays for 6 WAR player and has additional costs, but if they can get the playoff spot it is worth it. So, for NYY, BOS, TB it should be good trade - they are close enough. For every team in NL West except the Padres it should be a good trade. Probably also for Mets and Phillies, I think they are close enough.
Now, if players are worth 4.5 and 1.5 WAR, teams in the playoff hunt should still do it, but overpay less (it’s easier to upgrade over 1.5 WAR player than over 3 WAR player, so the opportunity value of the trade is lower), and if players are worth 4.5 and 3 WAR the trade should be made only if it is followed by love’s signing and if Sox think they have a real chance to reach playoffs with the trade (and they should send at most one player who should reach majors and be average and 1 - 2 classic C prospects).