keyboard_arrow_uptop

“He brings us that athletic dimension that we’ve been missing.”

“He’s can beat you in a bunch of different ways. That’s what we like about him.”

“He won’t clog up the bases.”

“He’s really fast.”

A confession: I reflexively recoil when I hear someone try to justify why someone is a good player by citing the fact that he’s fast. It’s not that I don’t get that speed on the basepaths has value to a team. In that weird part of the universe where everything else really is equal, I’d rather have a fast player than a slow one. The problem is that when I start hearing these arguments, it’s generally in the form of “Well, he’s not a very good hitter, but he’s fast. And his speed will cover for that fact that he’s not a good hitter.”

How much is speed worth anyway? Here at BP, we do have a baserunning metric (Base Running Runs, or BRR) that attempts to measure the additional runs that a player adds to a team by virtue of his performance on the basepaths above what we might expect from a league-average baserunner. For example, if a hitter goes from first to third on a single, he has “stolen” an extra base. Last year’s best baserunner by that metric was Matt Carpenter (seriously) checking in at 8.4 runs. (If you’re wondering how Carpenter, who’s no speed demon—seven career steals—won that title, it’s that he tended to be on base a lot when members of the Cardinals got hits, and he was adept at advancing.) If 8.4 runs is close to the upper limit, then why do people make such a big deal about speed? Sure, that’s nothing to sneeze at, but it’s also nothing to cough at.

It’s hard to study the effects of speed in isolation without knowing the rest of the context. A player could be an Olympic sprinter, but if he can’t get on base, what’s the point of his speed (other than as a pinch runner)? You can’t steal first base. Worse, there are plenty of players who survive in MLB basically because they are fast, despite their troubles as hitters. When we want to study the effect that fast players have on their team, we’re usually hamstrung by the fact that they are often subpar hitters, and that most certainly has an effect on the team’s overall output.

What if we could take a better hitter and plug in a Game Genie code that kept him the same hitter, but made him really fast. What would that do to a team?

Warning! Gory Mathematical Details Ahead!
For this article, I created a Monte Carlo Markov (MCM) simulator. (If anyone else has actually done this, you can appreciate the discordance between the length of that sentence and the length of that project.) For those unfamiliar, an MCM is a program that models some system that has multiple variables (like nine different hitters in a lineup) and multiple events (like 30-40 plate appearances for a standard game) and where one event affects the next in a meaningful way (a single means something different with a runner on third than with the bases empty). The computer knows that there are nine innings and a batting order and that after three outs, everything resets. It also knows that fast runners are more likely to try to steal (and be successful), to avoid hitting into a double play on a ground ball, to go first-to-third and second-to-home on singles, etc.

I didn’t write the model to be 100 percent complete. For example, no one bunts in this world. There are no pinch hitters, the pitcher is always league average (as is the opposing defense), and the other team doesn’t bat, so there’s no chance to make strategic decisions based on the score. It’s not perfect, but it can answer the question, “Over nine innings of ‘normal’ baseball facing an average set of circumstances, how much would a lineup with X characteristics score over 162 games?”

For the purposes of this exercise, I created a lineup that was a composite of what came out of each lineup spot in 2013. That is, a composite of everything that was done (by a non-pitcher) in the leadoff spot, the second spot, the third spot, and on down the line. Most of the time, in the leadoff spot, teams have a regular leadoff hitter, but they’ll use some pinch hitters, and some injury replacements for a couple days, and some guys who were thrown into blowouts to give the leadoff hitter a few innings off. Overall, though, this is a good representation of the “average” leadoff hitter.

I set everyone’s speed to league average. I should mention that I’m using my own home-brewed speed scores. In this case, zero is league average. I then simulated 10,000 games for that lineup. After that (actually, concurrently with that), I simulated 10,000 games, now with the leadoff hitter having turbo speed (1.5 on my scale, which would put him in the range of Dee Gordon and Craig Gentry from last year). Then, 10,000 games with the no. 1 hitter returned to normal and the no. 2 hitter getting the magic pill. Then I made a magical team where everyone was super-fast and called it the 1985 St. Louis Cardinals. I had the computer keep track of how many runs each “team” scored in nine innings.

After that, I did the same experiment, except I put lead weights on each hitter, in sequence, and brought his speed down to -1.5 (think, Victor Martinez and Adrian Gonzalez).

The results:

Hitter Made Super Fast

Runs Scored per 162 games

Difference from baseline

None

687.0

***

1st

697.7

10.7

2nd

701.2

14.2

3rd

702.5

15.5

4th

699.6

12.6

5th

705.0

18.0

6th

688.7

1.7

7th

701.9

14.9

8th

689.1

2.1

9th

695.3

8.3

Everyone!

762.1

75.1

Hitter Made Super Slow

Runs Scored per 162 games

Difference from baseline

None

687.0

***

1st

691.4

4.4 [sic] – I don’t know either

2nd

680.7

-6.3

3rd

678.2

-8.8

4th

683.5

-4.5

5th

684.3

-2.7

6th

685.4

-1.6

7th

682.1

-4.9

8th

684.7

-2.3

9th

682.8

-4.2

Everyone!

629.7

-57.3

It looks as though adding speed to a player does more than does taking speed away. It’s actually nice to have a fast player, especially one who hits like a regular middle-of-the-order hitter. The effect was 18 runs—nearly two wins—for a no. 5 hitter. However, it also seems that adding speed all over the lineup doesn’t produce what the sum of the parts would suggest. There’s an upper limit to how much speed can influence the game. On the flip side, a team where everyone is slow actually suffers more than one might imagine based on the sum of its parts. One base-clogger might not be as much of a problem, but a whole team of them would be.

But here’s a question. How much of that spread between different spots in the batting order (the same upgrade produced very different results throughout the lineup) was because of the ability of a certain lineup spot to leverage speed versus a certain type of hitter to leverage speed? To look at that issue, I created a second set of simulations. I created a composite league-average hitter from 2013 (excluding pitchers hitting) and cloned him nine times over. This way, it’s always the same hitter over and over. Once again, I started with a baseline where everyone is also a league-average runner and then went through and ran a simulation in which each of the nine batting order positions was given the gift of speed. (Then, after that, each was given lead weights to walk around with.) Again, 10,000 games per simulation.

Hitter Made Super Fast

Runs Scored per 162 games

Difference from baseline

None

659.4

***

1st

670.6

11.2

2nd

676.7

17.3

3rd

676.2

16.8

4th

666.5

7.1

5th

671.6

12.2

6th

670.9

11.5

7th

667.3

7.9

8th

663.6

4.2

9th

669.3

9.9

Everyone!

733.8

74.4

Hitter Made Super Slow

Runs Scored per 162 games

Difference from baseline

None

659.4

***

1st

658.2

-1.2

2nd

659.3

-0.1

3rd

653.2

-6.2

4th

659.5

0.1

5th

666.5

6.1

6th

658.7

-0.7

7th

655.4

-4.0

8th

664.9

5.5

9th

663.6

4.2

Everyone!

610.9

-48.5

It looks like a good amount of the variation in outcomes can be explained by the fact that speed just plays better in some lineup positions than others…at least in our abstract world. It also looks like that the best place in the lineup for speed is not in the leadoff spot (where the manager usually sticks the fast guy), but in the second and third spots. It also looks like robbing this lineup of speed does little to affect outcomes. In some cases, the lineup does a little better.

Speed—Better Than a Keanu Reeves Movie!
I wouldn’t swear to these values down to the third decimal place. It’s much more a way to look at the effects of speed in general. We can see that if we attach speed to a league-average hitter, it can make a big difference (assuming that our fast guy has other league-average hitters around him). If he hits like your average no. 3 or no. 5 hitter, he’s probably on base a lot to take advantage of his speed. Of course, there aren’t a lot of prototype no. 3 hitters who have elite speed. We also don’t often get to see those fast guys hitting in the no. 3 spot, so we don’t really have the sample size to sustain any intelligent guesses about what that would look like or potentially be worth to a team.

But there are some takeaway lessons from this work. One is that standard practice of demanding that a leadoff hitter be fast (and sometimes having that be his only qualification) is actually not a good one. All else equal, speed actually plays better in the second spot in the lineup. Additionally, speed doesn’t seem to play as well at the bottom of the lineup. Now, that’s not to say that all fast guys should hit second. The loss of production at the plate that a team takes from having the fast guy hit second (and get more PAs) and having a better hitter who is slower hit down in the lineup might be bigger than the gain from getting the speed guy into an optimal place.

Say, however, that a manager has two players whom he plans to hit first and second. He considers them to be roughly equal to one another in their hitting prowess, but one is faster than the other. The manager should actually hit the fast guy second. There’s also the curious finding that adding speed affects a lineup more significantly than taking it away. In fact, inserting more speed and taking away speed appeared to have two entirely different effects on a lineup.

Finally, let’s remember that while some of these numbers per 162 games are gaudy, this represents the effect of a player suddenly waking up with truly elite speed (or with truly heavy weights tied to his legs). The nice thing about this model is that it can be re-programmed. For example, suppose that instead of a speed score of 1.5 on my scale, our hitter was only a (very respectable) 1.0. Would he still get all of the benefits? Just some? The major strength of the MCM approach is that it allows us to look (at least somewhat) at how the pieces of a lineup interact with one another (and they do!). Indeed, we saw that just changing the lineup spot of the fast runner (backed up by otherwise cloned hitters) made a big difference over the course of a year. Structure matters. It’s tempting to want to say “Smith is worth three wins a year, so plugging him into Team X’s lineup will make them three wins better.” We need to be a bit more careful than that.

You need to be logged in to comment. Login or Subscribe
paulcl
7/08
It's weird that super-slow runners lead to more runs scored than average runners when batting 5th, 8th or 9th. Possible causes I can think of: 1) The average runners try to steal too much and lose value by getting caught, whereas the super-slow guys never try to steal. 2) It's just random noise and would disappear if you ran the simulation more times. 3) There's a bug in the simulation. Any others?
lichtman
7/08
Yes, that last chart is completely implausible.
lichtman
7/08
Russell, I think that you are suffering from severe sample size problems. 10,000 games is not nearly enough, I don't think, to smooth those out the random fluctuations. For example, if you put 9 league average players in a lineup, why would speed affect any spot more than another? And slow players adding runs? Come on! You may even have a bug or bugs in your model.
cmaczkow
7/08
Agree completely. Going by the final two (cloned player) charts, a super-slow runner in the 8 spot is worth 1.3 runs more than a super-fast runner! I wonder if this hints at something about our assumptions given a player's speed. I mean, we can all agree that it's better to be fast than slow, right? (Right? I hope?) But I'm wondering if the simulation is somehow overstating the risks that faster players take on the basepaths. Perhaps the super-slow group is assumed to never, ever try for the extra base or take ANY other risks, while the super-fast group is assumed to take so many risks that the payoffs are totally negated?
lichtman
7/08
It entirely depends what Russell put in the MC simulation. Obviously one can program a fast runner being too risky but that is not what happens in reality (fast runners have +5 to +10 baserunning linear weights), so that would be a programming mistake. So remember, we are not finding out anything about actual fast and slow base runners with this simulations, only what Russell's simulation does with them. Now, he should be making sure that his fast and slow runners do what they do in reality, which is easy enough to find out. Simply look at all players with low and high speed scores and see how often they take the extra base, get thrown out, etc. I can tell you from the work I have done with base running linear weights that fast runners do NOT get thrown out on the bases very often. In fact, no one gets thrown out very often. The fast runners get their edge from taking the extra base and don't give back much if anything from getting thrown out.
TangoTiger1
7/09
10,000 games is not enough. You need one million games to get the rounding error to under 1 run per 162 games. Overall though, you can run a model here, add +.15 or subtract .15 runs to each of the values in the chart, and you will find a change of 0.4 runs per game as the impact of speed in terms of taking the extra base. http://tangotiger.net/markov.html Of course, speed comes into play in hitting and fielding and basestealing. When we talk about speed for hitting, it turns say a guy with a .300 wOBA into a .330 wOBA because of his speed, etc. So, you have to be careful how you frame the discussion. You may find this old article by Tom Tippett interesting: http://207.56.97.150/articles/ichiro.htm
lichtman
7/09
The assumption here is that the faster the player, the more extra bases he takes, the more he advances on outs, and the fewer double plays he runs into on the bases, including getting thrown out on the bases. So the model has to reflect that. It is fair to use that model to see how speed (fast or slow) is leveraged in the various slots in the order. It is not possible for a slow player to gain runs regardless of the slot in the order, as in the last chart, since the model is supposed to assume that faster = more value. So there must be something wrong with the model. As well, as I already noted, if all the players in the order have the same batting profile, there should be little to no difference in the value of speed regardless of the batting slot since the order is a loop and not a line with endpoints. So, again, something is wrong with the model.