I initially created Baseball Graphs to develop new and better ways of presenting baseball statistics. The 2003 season was my first full-season attempt, and it turned out pretty well. I now spend a lot of my time creating and formatting the baseball stats at The Hardball Times.
Along the way, I've also picked up the writing bug. I spend most of my energy writing for THT, but sometimes I like to write about more geeky stuff, baseball research and things like that. That's what this blog is for.
I'm very interested in graphics and other information display, so I'll probably post links to creative stuff like that. I also plan to write historical articles that complement the historical graphs. And I have inexplicably developed an interest in baseball win-related stats, such as Bill James's Win Shares and something called Win Probability Added. So you can expect a few posts about that stuff too.
If you're interested, I've created a complex spreadsheet full of WPA logic, which you can download at ftp.baseballgraphs.com/wpa. If you'd like to read more about Win Shares, try these links:
Win Shares Intro
Let’s start with an economic statement. The marginal value of a player increases at a slower rate than his salary in the open market. This is the conclusion we came to in the first two “Money for Nothing” articles, and it’s something I’d like to explore further.
Remembering a couple of formulas: Net Win Shares Value is defined roughly as (WS*$300,000 minus salary). This is driven by our finding that the total major league salaries divided by total major league Win Shares equals about $300,000. When we applied that formula to all ballplayers in 2003, we found that the average Net Win Shares Value per player declined with salary according to this second formula: ($1,000,000 minus 2/3*Salary). In other words, the marginal value of every player’s salary dollar over $1 million was $333,333, on average. This relationship pretty much held true across all salary levels.
When I combined those two formulas, I came up with one that projects Win Shares as a function of salary: Projected Win Shares = (3 + (Salary/$900,000)). So Win Shares do increase with Salary, but at an alarmingly slow rate.
According to this formula, a player who was paid $10 million in 2003 created, on average, 14 Win Shares. I was stunned when I figured this out.
Now the 2003 Win Shares for players in this salary range ranged from one (Trevor Hoffman) to 34 (Todd Helton), so I’m not saying this is an accurate predictive formula. But it is an accurate representation of what happened with players and their salaries last year, on average.
Another interesting thing about this formula is that it seems to suggest that a replacement level for Win Shares is about three. If you paid a ballplayer the major league minimum of $300,000, you could expect, on average, three Win Shares from that player. There are a few problems with this. For instance, I included every player who played at all in 2003 in the database. But it may be worth exploring in the future.
As you can tell, this is such rich information that I hardly know where to start. But let me continue by re-posting the graph from Part One:
I could stare at this graph all day. In fact, I think I did stare at it all day. Last Monday. Or maybe it just seems that way.
As John Konstantin has mentioned in Part Two of this series, there is a pretty straight linear relationship between Salary and Net Win Shares Value. There is also a pretty consistent band around the fitted line. At the bottom, the band consists of those players who created virtually no Win Shares. In other words, their Net WS Value just about equalled their salary, only negative.
The upper boundary of the band, which includes Bonds, is about $6 million over the fitted line. It appears that, except for a couple of real outliers who are paid less than $1 million, like Pujols, the most you can expect in Net WS Value is $6 million more than projected. Now, that’s a lot, but it’s interesting that the band seems so consistent.
Let’s look at some specific teams. Here is the exact same graph for the Houston Astros. I’ve kept the graph format the same, and I’ve added circles for each player. The circle sizes represent the total number of Win Shares that each player contributed to the team.
I started with the Astros because they had a very good Net Value Year in 2003. They won 87 games with a payroll of about $76M. In total, their players delivered Net Win Shares Value of $9 million, vs. a predicted Net Win Shares Value of $1 million (that is, based on their salaries). These figures are based on the calculations quoted above.
Lance Berkman led the team in both Win Shares and Win Shares value, due to his $3.5M salary. But their higher-paid players also delivered more value than would have been expected given the size of their contracts.
Here’s another high-value team, the Minnesota Twins:
Every large salary that the Twins paid in 2003 came in below its predicted value (notably, these were all pitchers). But the Twins had relatively great years from most of their lower-paid players; their Win Shares leader was the since-traded A.J. I included all of Shannon Stewart’s Win Shares and salary in this graph because I didn’t know how to split his salary between teams.
Here are the Twins’ divisional rivals, the White Sox:
Again, I included total Win Shares and salary for Alomar and Everett, because I didn’t know how to split out their salaries between teams. Based on their salary structure, our formulas projected Net WS Value for the Chisox of ($2M), but they came in at almost $10M. Obviously, Esteban Loaiza made their year, financially.
Here’s a team for whom most everything went financially right in 2003:
As John Konstantin pointed out in the second article of this series, they were one of the most successful teams last year in value realization. According to our formulae, the Braves “should” have had a Net WS Value of ($28M). Instead, they had a Net WS Value of ($5M). Virtually every player was above the fitted line, but Giles, Furcal, Lopez and Sheffield really stood out.
Here’s the opposite sort of outcome, from the Braves’ division “rivals”:
I realize, looking at this graph, that I should have made the parameters of these graphs constant. The circle sizes are misleading, when comparing across graphs. Anyway, most everything went wrong for the Mets in 2003, until they were forced to start playing the kids.
And how about the Mets’ crosstown rivals?
If you obtained every one of your players in the open market, and they performed about average compared to their salaries, you’d have to pay something like $200 million in order to win 100 games. Even the Yankees didn’t spend that much. Although most of their larger contracts were relatively valuable, the Yankees had a lot of below-par contracts in the $2M to $8M range. The keys to their financial success were Soriano, Johnson and Posada.
What are the themes here?
1. Virtually every successful team, even the Yankees, had players who were paid less than $1 million but who delivered significant value. Without these players, you can’t buy your way to the top.
2. You will make mistakes with your large contracts. You should expect them.
3. Pitchers are much more likely to be expensive mistakes than everyday players.
I could create these graphs for every team, but I’ve got to stop at some point. If you’d like to see a financial graph for a specific team, let me know.
More to come!
Great job, studes. These graphs are just about the coolest thing I’ve seen in awhile.
I do agree that you should make parameters the same for all teams. Compare R. Alomar on the White Sox (small circle, well below the line) to R. Alomar on the Mets (medium circle, on the line.)
Great catch, Buford. Actually, I had loaded the incorrect data for Alomar in the White Sox graph (Everett, too). I’ve corrected it.
Next time, I’ll keep the X and Y axes the same, as well. Unfortunately, it’s kind of hard to standardize the circle sizes. I’ll have to work on that.
Great work, studes! Has anyone broken apart the salary data for traded players? I’ve been meaning to, maybe based on something like plate appearances or innings pitched, but haven’t gotten around to it yet. This would make a big difference for someone like Jeremy Burnitz, who basically split his plate appearances with the Mets and Dodgers and should probably we counted as $6 mil per team, rather than the $12 mil as shown in the Mets chart above.
We’re leaving something out of these analyses: the opportunity cost of running players out on the field. For instance, although the Mets blew a ton of money on Vaughn, at least they got to put someone else out there (Phillips) who generated some win shares. Meanwhile, in Philly, Mesa managed to suck while both costing a lot of money and taking valuable playing time.
Here’s another way to think about it: as a GM, you’ve got three primary resources available to you. Your budget, approximately 4,300 offensive outs, and approximately 1,450 defensive innings. The budget varies from team to team, but the other resources do not.
So, here’s a suggestion. Let’s say the average team wins 81 games, and that those 243 win shares get split something like 50/40/10 between hitting, pitching, and defense. (Feel free to substitute your own percentages.) So, you’d expect each “average” batterto contribute ~0.028 WS per out. If we assume the average OBP to be 0.340, that’d be ~0.01 WS per PA. Similar calculations would give us ~0.067 WS per IP, and ~0.002 WS per defensive inning in the field.
Feel free to refine those calculations, but if applied broadly you’d end up with something like Win Shares Above Average per Dollar. I think doing so would give you another interesting perspective, and might also illuminate which GMs / field managers are best at dealing with contract mistakes.
Great point, David. I’ve been thinking that WSAA is another way to go with this analysis, and you’ve articulated why.
Guys like Mo Vaughn or Trevor Hoffman, who were injured most of the year, would have close to zero WSAAs, and their salaries wouldn’t look so bad. Of course, there are problems with looking at the data only this way ($16M is a lot for someone who doesn’t play, as the Mets’ insurance company would attest), but it does yield its own insights.
Once I finish (oy!) with the WSAA approach, I’ll come back to salaries.
I found this very interesting, especially the fact that a Win Share seems to be valued at $300,000, the major-league minimum salary. But that got me thinking. Since you have a price floor, can we truly say that total Win Shares/total salaries tells us how the baseball market values Win Shares? The first $300K is a given. Teams show what they value by the amount they pay over $300K. I’d be interested in seeing the results if you tried it like this:
NWSV = (total salaries - (300,000*number of players))/Win Shares.
I would think that this would temper the slope of the line. I won’t be surprised if there’s a good reason not to think of it this way, but I’m curious.
Thanks.
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