THE BOOK--Playing The Percentages In Baseball

If you accept the above, you can see why Win Shares severely undervalues starting pitchers.  Using Studes’ Win Shares database, since 2002 34% of all win shares goes to pitchers (starters and relievers).  Of those, IIRC, it’s split pretty much two-thirds one-third between SP/RP, meaning 11% for RP and 23% for SP.

To recap, I give 56% of the wins to nonpitchers, while Win Shares gives 66%.  I give 34% to SP, while Win Shares gives 23%.  We agree on relievers.

Thanks for this - I’ve been trying to piece together the methodology from many different posts, it’s great to have it all in one place.

Could you describe how you translate fielding runs into wins, and which defensive metrics you feel most confident in?

10.5 runs per win.

I use the Fans Scouting Report, UZR, and Dewan’s Plus/Minus.  In terms of weighting, it’s probably 40/35/25.

Is Dewan’s +- available anywhere for more than just the leaders and trailers?

By compiling for Dewan (of names on his ballot) the top 10 for each position from the Fans’ Scouting Report, I get two things: the James Handbook, and the not-for-redistribution Fielding Bible (as of mid-September).

I’m definitely bookmarking this. Thanks for posting this resource.

Could you show the exact formula you use to determine Win Percentage for pitchers? Take Tom Glavine, for example, who’s projected to post a 4.50 ERA and pitch 180 innings. Thanks.

Figure out the league average ERA, which in this case is 4.40.

Add up the two numbers to get your run environment: 8.90 earned runs per 9IP.  Divide by .92 to get that into total runs (including unearned).  That’s 9.67.

Use PythagenPat to get the exponent: 9.67^.28=1.89

W/L = (4.40/4.50)^1.89 = .958
W/(W+L) = .958/(.958+1) = .489

So, Tom Glavine would have a win% of .489.

Alright, I think I got it now. Thanks.

A comment on the positional values--specifically the -.5 for LF/RF and the -1.0 for 1B. Those were determined from your studies on players switching positions, right?

But here’s something I’ve been wondering about. Here are the approximate number of players who played at each position in 2007:
C, 120
SS, 130
2B, 140
CF, 160
3B, 165
1B, 175
RF, 210
LF, 245

It reflects the traditional def. spectrum almost perfectly, except for 1B. Why is that? The players who switch positions are a special subset of all players, because they already have the basic skills to play at each positions. But, if you consider all players, and asked them to play all positions ‘cold’, maybe they would do better in LF/RF than at 1B, because of the specialized skills needed at 1B, and the number of plays he is involved in. Maybe the ‘lag’ time of adapting to each new position should be given more weight in the def. spectrum determination.

That’s an interesting list.  Since a LF and RF are virtually identical, what would your count produce if you simply said “corner OF”?  If it’s more than 350 (double the 175 of 1B), I think you’ve got something.

I guess I could look at the source and figure that out by hand, but I’m not sure that the similarity in the skills needed to play LF and RF should be a way to mitigate or invalidate the idea I am suggesting. I mean, there are also similarities between 1B and 3B, and between SS and 2B. If LF and RF require almost identical skills, and that means that there are more players a team can/does choose from to put at those positions, that simply confirms that 1B is more unique. If you came at this knowing nothing about how each position does on offense, and the data I gave above, you might very well conclude that 1B is more ‘difficult’ than LF or RF for MLB players.

Sure, there are similarities among any pair, but by far the strongest is between LF and RF.  The amount of shared games at those positions tells you that too.

And the reason you have more players at those positions, is that they are 2 positions, not 1.  I just don’t see how counting Endy Chavez as a RF and as a LF tells you anything other than he played a corner OF.

Historically, does the .5 win gap between CF and 2B/3B hold? Going back more than twenty years, it seems that the skill sets required for each position, but especially 2B, have changed. Is this an accurate perception?

The problem with your line of analysis, Tango (IMO), is that a team needs to have a separate fielder at each position at any point in time. So, the position ‘utility’ advantage that a RF may be credited with (because he could also play LF), has to be balanced against the uniqueness of the skills needed to play 1B, (at a moment’s notice,which may be the main point in my analysis).

I’m not sure how much uniqueness is required for 1B.  I remember when Galaragga (or was it Floyd) went down, Larry Walker stepped right in, no problem.  This happens pretty much all the time.  Other than a sulking Gary Sheffield, I don’t see how any corner OF couldn’t make the transition to 1B.  I’d see the “learning curve” of 2B to LF along the same lines as RF to 1B.

***

I don’t know how the relationship of 2B/3B has evolved over time.  It’s possible that the 2B has been better in the 70s and 80s.  But, we won’t know until we study it.

what is replacement level in this system in terms of team wins (i.e. how many games does a replacement level team win)? thank you.

It’s right here where I say:

“since the average team wins 81, that sets the replacement team at...”

Any chance you can provide a real life example, or run through the numbers of a current player, perhaps one pitcher and one hitter in calculating WAR (and showing your work)?  Thanks.
vr, Xei

Shields:
http://www.insidethebook.com/ee/index.php/site/comments/sabermetric_moves_of_the_2008_pre_season/#422

Cano:
http://www.insidethebook.com/ee/index.php/site/comments/sabermetric_moves_of_the_2008_pre_season/#429

After looking over all this, you should put pen to paper, and try out a few players for yourself.  Let me know where exactly you are stuck.

I posted the following at USSM and am reposting here:
http://ussmariner.com/2008/02/06/calculating-wins-above-replacement/#comment-251472

The hard part of replacement level is deciding what that level is.

The easy part of average is that we know exactly what that level is: 4.8 runs per game in the recent past.

As I said, you can stick with average and ignore replacement completely.  Consider that the average payroll is 90MM of which around 12MM is required minimum payroll, leaving you with 78MM to play with for an average team (.500).  Presuming you allocate around 57% of your payroll to nonpitchers, that gives them 45MM to allocate for 9 full-time nonpitchers.

That means the average player will get 5MM per 162 games played.  Presume for the moment that each win (free agent, arbitration, pre-arb, on average) is worth $2.2MM per win.  (Plus of course every player gets his 400K minimum.)

So, this is what you get for a guy who plays 162 games:
$7.6MM +1 win above average (WAA)
$5.4MM +0 WAA
$3.2MM -1 WAA
$1.0MM -2 WAA
$0.4MM -2.27 WAA

And if he plays 81 games:
$5.1MM +1 win above average per 81 games (WAA)
$2.9MM +0 WAA
$0.7MM -1 WAA
$0.4MM -1.135 WAA

So, roughly speaking, a guy who is an average player for 162 games is equal to a guy who is +1 wins above average over 81 games.  How do you equate those two with 1 number, rather than necessitating carrying two numbers (his WAA, and his games played)?

Well, if you add .014 wins per game to each player, this is what you get:
First player: 0 wins above average + .014 * 162 = 2.27 wins
Second player: 1 wins above average + .014 * 81 = 2.13

As you can see, both roughly equal.  If you multiply the above numbers by $2.2MM per win, and then add $400K, you get:
2.27 * 2.2 + 0.400 = $5.4MM
2.13 * 2.2 + 0.400 = $5.1MM

And those are the numbers we got when we ONLY talked about average and never brought up replacement level.

So, both sides can go ahead and do what they want to do: use only average or use only replacement.  You end up at the exact same spot.

"That means the average player will get 5MM per 162 games played.  Presume for the moment that each win (free agent, arbitration, pre-arb, on average) is worth $2.2MM per win.  (Plus of course every player gets his 400K minimum.)”

Which assumes that an average player is worth two wins. I’m fine with that, but within the context of an average-only discussion, how do you come to the conclusion an average player is worth two wins without ever bringing up replacement level?

Gah, ignore that last post, I’m not thinking straight. I had meant to ask how we might go about getting the $2.2MM per win total without bringing up replacement level, but got confused in my head. The $5MM per 162 games obviously comes from 45/9. I’m an idiot.

Anthony/29: actually, you have a right to be skeptical.  After all, where in the world DID that $2.2MM per win come from anyway, if I ignore replacement level talk, altogether?

Each team rakes in $200MM in revenue, on average (6 billion / 30).  The question is how much impact does each win have on revenue.  If it’s 1%, that’s 2MM per win.  If it’s 2%, that’s 4MM per win.

If you go for the 1% rule, then teams, which are spending 78MM above the minimum, are paying for 39 wins above the minimum, on average.  This would imply that the minimum win level is 81 minus 39 = 42 (or .260 ball)

If you go for the 2% rule, then teams are paying for 78/4=19.5 wins above the minimum (or .380 ball).

So, figure out how much each win generates to the bottom line, and that’s the figure to use.  I’d be surprised if the outcome of that is not close to $2.0-$2.5MM per win.

wes, I’m going to continue the discussion here:
http://www.insidethebook.com/ee/index.php/site/comments/spread_in_talent/#12

All the Pythag related posts have been, or will be, moved here:
http://www.insidethebook.com/ee/index.php/site/comments/more_than_you_probably_ever_wanted_to_know_about_the_pythagorean_method/

I suggest reading the main article in that blog, that goes in-depth as to Pythag.

Thanks for posting this.

I wanted to give running the numbers myself a shot, and I’ve recently been mulling over how bad Julio Lugo’s ‘07 campaign was. So, I figured, why not? I pulled out my handy-dandy cellphone calculator and came up with the following:  his .283 wOBA had him roughly as a -3 hitter, he gets +.5 for being a SS, I have him as an average fielder +0, +2.25, full time player.  So I get him at -.25 WAR in ‘07 or to be kind, a smidgen below replacement.  Does that seem right to everyone?

He was in the AL, so he gets +2.5 for replacement level, making his PERFORMANCE last year, according to your post, a replacement level performance.

***

Note though that even if you perform at a replacement level doesn’t mean that you are a replacement level.  The former is a sample, and the latter is a true.  Just remember that all performances are a sample of the true, and therefore a performance is a mix of the true and random variation around that true.

Whoops. I should have double checked with the formula at the top of the page before posting.

To take this one step further…

If I’m interested in getting a rough estimate of what a players dollar value was for a specific year and comparing it with his actual salary for that same year, would using WAR and your salary chart(s) be a decent way of approaching this.  For example, if Joe Schmoe was a 3 WAR player in ‘07 and his ‘07 salary was $8 million, would it be fair to look at your ‘07 salary chart and come to the conclusion that in ‘07 his net value was $4 million?

Yes, if he were a free agent.

Is it possible, when calculating batting RAA to just use league average positional wOBA instead of league average wOBA and just skip giving the positional adjustments?  Or will this still understate the defensive differences between corner and middle positions?

You don’t want to use positional averages, because this will force the average player at each position to be equals.

If you’ve been reading my stuff on the matter, you will see that I think it’s ridiculous to presume that the average 3B = average 2B, when considering hitting and fielding.  The avg 2B is very close in fielding to the average 3B, but the average 3B is a much better hitter.  To equate them each and every year is sloppy work.  These players aren’t paid the same, and we shouldn’t pretend that they are the same.

Or look at the DH.  Case closed right there.

Our job is to model reality.  Making the average quarterback = average offensive tackle is not reality.  And neither is all the gobbledygook that the avg 2B = avg 3B forces upon us.

Do a search on “positional adjustments” in this blog.

Could you explain how it is you’d do it with a closer?

Is it: WAR * LI or W% * LI?

Or something else.

Never mind. I dug up it in of your other posts/comments:

For relievers, there’s an extra adjustment.  You need to figure out his Leverage Index (assume 2.0 for a closer and 1.3 for a setup guy).  You give him bonus WAR for his wins above .570 (.560 for AL, .580 for NL), multiplied by his LI minus 1.

So, Rivera gets 2.4 WAR in this case.

Save yourself a step there for closers - two minus one is one. So

(.660-.560) * 72/9

Gets you to .8 just the same.

Well, that’s assuming a closer’s leverage is 2. If it’s something different, than that would not work out If I’m using projections for an upcoming season, then you would be correct. Doesn’t really matter, though. I’m just dumping this into a spreadsheet.

To Colin: What’s your e-mail? I’ve been meaning to ask you something, but I couldn’t find your e-mail address at your blog.

Tom, you’re supposed to implement leverage for other relievers, too, right? In your original post, you only mention adjusting for leverage for closers, but in the comment that I quoted, you say all relievers.

Thanks

WAR spreadsheet:
http://www.footballsfuture.com/phpBB2/viewtopic.php?t=241928

Hyl: If you are using 2.0 for closers, and 1.3 for one setup man, you should use 0.7 for other relievers.  The overall average needs to be 1.00.

You can try to be a bit more conservative, and make it 1.8 for closers, 1.2 for first setup guy, 1.0 for second setup guy, and 0.7 for everyone else.

pontifexexmachina at hotmail.com

There’s another WAR calculator available here:

http://home.comcast.net/~briankaat/statsite.html

Although I have made some refinements recently, and should probably release another version of it.

Alright, thanks Tom. Surprised you read FF!

And I didn’t know exactly what to use for other types of relievers, so I guessed 1.1. I’ll change it, though.

I see all

If you look at some Fangraphs team pages for relievers, you will see that the team-average for starters and relievers all hover around 1.00 (0.98 for starters and 1.04 for relievers).

Doing the calculations now, you should use 0.80 for the “other relievers” LI, from my post #37.

For a closers WAR, should be using pLI or gmLI?

I’ve been using pLI, but I’ve been thinking using gmLI would be the more correct thing to do. For example, you have a guy like Todd Jones, who has been thrust into pretty low leverage situations (1.22 pLI). Being a “Tigers fan”, of course I’ve noticed that he always gets himself into trouble (higher lev situations) because, well, he’s not very good, so he has a 1.51 pLI.

Should they really be rewarded for that?

inLI would be better than gmLI, if for no other reason that if you have multi-inning games, then when your offense takes over in the middle, you’ve got a “new” game for the next inning.

LI is not about “rewarding” but simply is a reflection of what’s on the ground.  So, try to keep that in mind. The LI simply reflects how much fire he’s been facing, whether he was the arsonist or not.

Also note that it may not be the pitcher who is getting himself into trouble but his fielders.

If you can give me a better idea of the exact question you are trying to answer, I’ll give you a more appropriate answer.

I’d say Todd Jones has been killing himself with his mediocre everything.

You say:

that is, while he is not responsible for the LI he finds himself in, he is responsible for his talent that allows him to take advantage of the extra leverage (sort of like Ozzie Smith gets to play SS and reaps the benefit of all the extra opps).

If we use pLI, which if I understand it correctly, is just the leverage in which he pitches in, then you’ll have cases where it’s not really a “pitcher’s talent that allows him to take advantage of the extra leverage”, it’s the exact opposite, like Todd Jones, he’s pitching himself into those situations because he’s not very good (yeah, I’m sure there are cases where a reliever’s defense fails him)).

I’m not sure if I completely made myself understood there.

If the explanation is:

LI is not about “rewarding” but simply is a reflection of what’s on the ground.  So, try to keep that in mind. The LI simply reflects how much fire he’s been facing, whether he was the arsonist or not.

Then I can perfectly understand that. I might have just misunderstood what the point of accounting for leverage was.

We just want to account for the extra wins (or losses!) based upon a reliever’s utilization. If a reliever with a true-talent 5 RA is consistently pitching in 2 LI situations, he’s costing his team more than a similar pitcher who is only in 1 LI situations. This is true regardless of whether or not he’s digging his own grave or not.

Over a long enough period of time, you won’t find a pitcher who is bad enough to consistently pitch himself into high-leverage situations without him giving up lots of runs, so its not really an issue.

Alright, thanks.

Quick question about projections using the WAR, specifically replacement level.  I understand the reason for differing replacement levels in the AL and the NL - the average AL player is better than the average NL player.  I’m fairly certain that I’m correct on that, but I could be misunderstanding something.

Now say I’m projecting Adam Dunn and he’s 1.5 WAA (or whatever, just throwing a number out there).  He plays in the NL so his true projection would be 3.5 WAR.  Seems straightforward to me.

But what about a guy like Mark Teixeira?  He’s played most of his career in the AL, but his most recent season of games (besides the last week with LAA) has been in the NL.  If he’s 2.5 WAA (or whatever number you get) based on his projections, what is his projected WAR for 2009 - 4.5? 5.0? greater than the first but less than the second?

My guess that when converting to WAA to WAR we would give him more than 2.0 wins (as at least some of his projection is based on AL numbers), but less than 2.5 (because he’s been in the NL for the last season), but I feel like I’m missing something here.  Or I could be completely off on the whole thing.

You are deadon.  I think I used 2.25 for him.  But, you would simply use the weighted average of whatever he did.

The weight would be PA*yearFactor
such that the yearFactor is 5 in 2008, 4 in 2007, and 3 in 2006.  Add it up for his AL time, add it up for his NL time, and compare.  If 80% of his weight was NL, then he gets 80% of 2.0 and 20% of 2.5

Question in regard to post #7:

Does the league era change for starters and relievers, or is it just the era in a given league/year/park for all pitchers?

Thanks.

All pitchers.

2 more in regard to posts 34-40…

1) Say you have a bad closer - can he have a “negative bonus”?  For example, if his WP is .500 in 45IP, would his WAR be

(.500-.460)*45/9 + (.500-.560)*45/9*(2.0-1) =
2 + (-3) = -1

2) If you apply the 0.8 to all other relivers, do you calculate a bonus for them as well? For example, a would a .480 “other reliever” just be

(.480-.460)*45/9 = 1

or would there be some other adjustment.

Thanks a bunch.

I wouldn’t give a negative bonus, just like I wouldn’t make any fielder (position plus fielding value) be any worse than -2 wins.  Simply put, I’m not going to punish the player because the manager doesn’t put him in a better situation.

***

As for the relievers, you’ve given me something to think about.  Let me get back to you on that.

bumping

I thought about posting this in the “Sabermetric Moves 2009” thread, but I thought this one could always use a bump.

I’m just messing with some other people’s offensive player projections and converting the raw projections to wOBA and then bRAA as detailed here by Tango and Stat Corner.

For calculating RV/PA, bRAA, etc. what’s a good league wOBA to use (for the AL, in this example) without doing a projections of the whole league and getting it from there (I’m not using park factors, as I’m just doing a home-brew). In the post above, you use .338 for lgwOBA, but I assume that’s just a “plug-in” to be replaced. Should I use .338, or last year’s AL-average .339, or am I making too much out of nothing?

You can use anything between .335 and .340.  Ideally, the wOBA equation would be calibrated each year so that wOBA = OBP at the league level.

In any case, you are just talking about a run or two difference (and it’ll work out pretty much the same for all the regulars).  So, don’t sweat it.

Hey Tango, was wondering does a lower run scoring environment affect the 10.5 number and if so would lower offensive numbers like last years offset it enough to make a difference? Thanks.

It seems to me that you are benchmarking offense based on replacement but benchmarking defense off AVERAGE--UZR is a measure against an average MLB defender, not replacement level. Is there a rationale for this?

#56 My understanding is a replacement level player is still (at least) an average fielder at his position.  If the player is so bad with the bat, he’s not going to play at all unless he can defend.

That makes sense, but forgive me if I doubt it as a Nationals fan who spent a good bit of last summer watching Paul Lo Duca play first, Ronnie Belliard play SS, and Wily Mo Pena play baseball!

The runs per win is roughly equal to 1.5*(RPG+2)

So, if you score 5 runs per 27 outs, the runs per win converter is 1.5 times 7 or 10.5

If it’s 4.667, then it’s 10.

As it turns out, we are extremely close to 10 these days.

Tom, do you still use the same replacement-level and positional adjustment as the ones that are stated in the original post?

See bold part in post #1:

http://www.insidethebook.com/ee/index.php/site/comments/uzr_positional_adjustments_revised_with_2008_uzr/

So with the non closer reliever (the setup up guy with the LI of 1.30 and the other guys at .70) do we do it like this?

(Replacement Level - Pitcher Win Pct) * IP/9 * (LI - 1)

And bonus or no bonus for relievers?  And at what level would the bonus kick in.....it wouldnt be the same as the .580 for NL Closers right?

The easiest thing is just to use an LI that is halfway between the LI that his talent deserves and 1.  So, Mo get’s 1.5.  Some schmoe gets 0.75.

Newsday linked to this thread:

http://www.newsday.com/sports/columnists/ny-spken226079211mar22,0,2188090.column?page=2&track=rss

Thanks Ken…

Where can I find Rally’s historical Total Zone numbers? I can’t seem to find them, unless he doesn’t have them available and I’m confusing it with the minor league Totalzone.

They are at his site, plus will be at the new b-r.com

http://www.baseballProjection.com

Rally published Total-Zone data from 1956-2007 on Hardball Times last year:

http://www.hardballtimes.com/images/uploads/tz19562007.xls

I wish that he hadn’t combined the stints of players who played on more than one team during the same season. It would be nice to be able to link these to the fielding tables in the BDB database.