Tuesday, January 26, 2010

Ruining the Thome Signing with a Bunch of Math

There's going to be a lot of discussion about Jim Thome's potential value to the Twins in 2010 - how he can platoon with Delmon Young, rest Justin Morneau occasionally, be a presence in the clubhouse and provide a nice late-inning option for manager Ron Gardenhire. Just scroll down those blogs over there on the lower right, and you'll get plenty of solid analysis on all these aspects.

But I want to concentrate on just how valuable a bench bat is when used in late-inning situations? I've wondered about this since 2002 and 2003 when that role was often filled by Bobby Kielty. I remember writing about a quote from Ron Gardenhire stating that he thought Kielty was more valuable as a bench option than an everyday player, because that one 9th inning at-bat could be in a more valuable spot.

That's the kind of statement that makes disciples of advanced metrics like WAR throw up in their mouth a little bit. But it's also the kind of statement that makes disciples of advanced metrics like WPA applaud. Because it is undoubtedly true that a late inning at-bat can be much more valuable than an early inning at-bat. What isn't clear is how much more valuable, and whether it really makes sense to reserve a player for just those situations.

So with Thome joining the club, I crunched a few numbers for your digestion and comments. Let's start with a scenario. Imagine a player on the home team leading off an inning with a home run. How much does that home run really help the ball club?

The answer depends on the score and the inning. And you can see it in the graph below:


That axis at the bottom is innings. So if you look at the dark blue line (which represents when the home team trails by a run), it shows that if the home run leads off the first inning, it improves the teams chances to win by just over 10%. But if it happens in the ninth inning (where it ties the game), it improves the team's chance to win by over 45%. Think about that: the same hit, in the same situation but in a later inning, is four times more valuable in the ninth inning than in the first inning.

The temptation for people studying players is to write this finding off. After all, there's plenty of evidence that players aren't clutch. Thome can't choose to hit that home run late in the game as opposed to when it has less value. So from a player's perspective, when trying to determine their overall value, we focus on the raw numbers and not when it happened.

But we aren't really studying the player in this case - we're studying the manager. And the manager DOES get to make a choice. He gets to choose the best situation in which his bench players get to bat. Thome might not be more clutch in that position, but he's significantly more likely to hit a right-handed pitcher silly than Brendan Harris. If he hits a home run in that ninth inning of a one run game, it's more valuable than if he had hit a lead off home run in the first, third and fifth innings combined.

Of course, the chart also shows that it's significantly different if the game isn't a tie game or the home team isn't losing by just one run. If the home team is winning, putting that slugger in late innings to jack a ball into the right field bleachers doesn't add much, as the game is almost decided. That's fine - so keep in the defensive specialist. And if the home team is down by two runs, it's actually considerably more valuable to hit that lead off home run in the eighth inning than in the ninth, since it gives your team more time to come back.

So just how often do baseball games enter the ninth inning fairly close? Below you'll see some numbers for games between 1977 and 2006. I'm afraid I don't have percentages for you, but you can see close games are the most common occurrence, but not necessarily overwhelmingly so.



Finally, I should mention that I only charted the value increase of a specific outcome: a lead off home run. What if he struck out instead. I suspect that the difference isn't quite as pronounced with other outcomes, but the trend is similar. An out in the ninth inning of a one-run game is more important than an out in the second inning.

No matter what outcome you choose, in the late innings success counts more and failure hurts more. Either way, the manager wants to have a very good hitter available.

And now, he's got one.

17 comments:

Anonymous said...

This is a good signing. I just hope it doesn't preclude getting infield help. I also hope it doesn't mean that Delmon doesn't get his PT. I know a lot are down on him, but I think he's going to take a major stride forward this year. If he's a pinch hitter, an occasional sub for Mauer and Kubel, as well as insurance against an OF injury, I like it.

Jack Ungerleider said...

It's interesting that based on some of the early handicapping of this situation that it has come to be. After all Thome was known to be looking for a gig where he would be the DH. Maybe after the comments from Ozzie in the Chicago Media, Thome realizes that his preferred team doesn't want him back and a full time DH role is only available on a team with little or no potential to get him one last shot at another ring. So like another 40 year old athlete he decides to go to the rival. Maybe to prove a point.

Jeff B said...

I'm growing more concerned about the outfield defense, especially a lack of defensive replacement in the late innings. An OF of Kubel, Span, Cuddyer just won't track down all those gappers like we have grown accustomed to seeing. Then again, maybe Target Field won't necessitate such speed and coverage.

TT said...

"After all, there's plenty of evidence that players aren't clutch."

Actually there is very little evidence "players aren't clutch". Since you can't measure it, you assume it doesn't exist or at least doesn't matter. But you should remember that isn't really true.

"So from a player's perspective, when trying to determine their overall value, we focus on the raw numbers and not when it happened."

Which is the fundamental failing of modern statistical baseball analysis. Rather than trying to understand what happened, it is trying to predict what will happen in some alternative universe. Because very little of what happens in baseball is actually random, the result if a lot of poor analysis that is little more than interesting speculation.

Bryz said...

That's the kind of statement that makes disciples of advanced metrics like WAR throw up in their mouth a little bit. But it's also the kind of statement that makes disciples of advanced metrics like WPA applaud.

This is very interesting. If Thome is used as a pinch hitter, he'll likely accumulate a very low WAR but could either have a high or low WPA (depending on how successful he is). However, if he's mainly a full time player, then he could have a high WAR but middle of the pack WPA. Which one is more valuable to a team?

Anonymous said...

Wow, great breakdown - and one that makes me feel better about the signing. My frustration pretty much only stems from the Twins/Gardy routinely taking the bat out of the hands of Kubel, who I feel like has earned the chance to settle in somewhere as much as the big names. If Thome is here to provide that 45% lift in the 9th, awesome. If he's here to do much else, I'm very meh.

Anonymous said...

How do you hit a leadoff homerun in the 1st inning, up by one or two?

writerjoel said...

Thome on the bench means that Young/Kubel are in the line-up. So Thome will come into play as a pinch-hitter for whoever is playing second (Punto) or third (Harris).

The flip-side is that you need a defensive replacement.

Or that one of the other two (Pridie, Tolbert, Casilla are the current options) would be put in for Thome if he drew a walk.

That's also the BIG factor of Thome coming off the bench. He can draw the base-on-balls. He may hit a homer, he may strikeout, and one other plus -- he can hit the fly-ball sacrifice out.

Kubel/Young play the part of 4th outfielder. Pridie (or someone) is a phone call away to come up if someone goes down on the field.

JfW said...
This comment has been removed by the author.
JfW said...

Which is the fundamental failing of modern statistical baseball analysis. Rather than trying to understand what happened, it is trying to predict what will happen in some alternative universe.

Well, especially when looking at the possible impact player signings, forward looking 'alternative universe' stuff is all that's really usefull as looking backwards simply isn't so much.

BeefMaster said...

Jeff B - It's likely that Jason Pridie will still be on the roster as the reserve outfielder. The word on him is that he's a competent center fielder and well above average at the corners, so he should be able to serve as a defensive replacement.

TT - Perhaps a better way for John to phrase his sentence would have been "There's virtually no evidence that players are clutch." I believe that would address your objection.

TT said...

"Well, especially when looking at the possible impact player signings, forward looking 'alternative universe' stuff is all that's really usefull as looking backwards simply isn't so much."

Not really. Understanding why something happened can be just as important as projecting what results might have been in some alternative universe. The results only tell us so much anyway.

"There's virtually no evidence that players are clutch."

To say "there is little statistical evidence that players are clutch" is somewhat true.

There is, however, an awful lot of anecdotal evidence for some players doing better in pressure situations than others.Observing human behavior in other situations where they are under pressure, it would be odd if baseball players were immune.

BeefMaster said...

There is, however, an awful lot of anecdotal evidence for some players doing better in pressure situations than others.

To borrow a phrase from the realm of statistics, the plural of "anecdote" is not "data". I'll grant that some players have shown an ability come through in the clutch, and I am not a complete clutch denier, but I also think that relying on anecdotal evidence is a sketchy proposition, at best - we tend to have selective memories in situations like this, remembering more epic successes or failures while forgetting ones that aren't as obviously notable.

Observing human behavior in other situations where they are under pressure, it would be odd if baseball players were immune.

I'd certainly agree with this, but with a big caveat - baseball is a sport that has a lot of pressure situations (every at-bat is at least somewhat a pressure situation, in my experience), so it's likely that most major league players already are very good at dealing with pressure situations. The difference in handling pressure between "clutch" and "non-clutch" players is probably more like the difference between the 99th and 90th percentiles of stress management, not the 99th and 50th.

Anonymous said...

I'm not worried about getting Thome at bats -- that would mean we didn't have one significant injury at 1B, DH, or OF -- which would be great! But unlikely. As last year's playoffs showed, we are one injury away from starting Brendan Harris or Jose Morales at DH (see game 1 and game 3 against the Yankees). Thome is worth it for injury insurance alone.

Not to mention that with Gomez gone, we had no plan B for the Delmon Young experiment, and now we can play Kubel in LF if we have to, with Thome taking over at DH. But again, if Young plays so great we never want to rest him, all the better! If our only need is to pinch hit for Punto, things will be looking good! (Or best of all, we don't even need to pinch hit for Punto, because we already have a big lead!)

John said...

Thanks for the comments everyone. This morning I was feeling like a real dumbass for staying up til 12:30 to finish that post. It's nice to see it generated some discussion.

TT said...

"relying on anecdotal evidence is a sketchy proposition, at best - we tend to have selective memories in situations like this, remembering more epic successes or failures while forgetting ones that aren't as obviously notable."

I agree, but that is more a "how well do we recognize it" question than a "does it exist".

"so it's likely that most major league players already are very good at dealing with pressure situations. "

People adapt to constant "pressure situations" as a new normal, but there are still situations with the game on the line where some players are going to do better than others. One of the problems with capturing those situations statistically is just that - they are by necessity a small sample size.

John - Despite my predictable complaints, I think this was a good presentation of why "context matters". If Thome adds just one more win there won't be a tie this year.

Anonymous - "Thome is worth it for injury insurance alone. "

Well said, the Twins are not going to get through the year without having significant plate appearances from its bench. Without Thome, the bench is long on defense and short on bat. The one thing that worry's me is that if they sign Crede, that is no longer true. Harris is the only backup infielder on the bench.

David said...

Good point by Anonymous #2 about being up before having a single at bat.

Also, I must be missing something, because it seems like a home team 9th inning leadoff home run wins a game that was tied. Shouldn't that be a 100% improvend chance of winning?