Dollar Value of a Run

by Schaefer on May 18, 2009 12:25 AM PDT Comment 6 comments

Since we can estimate how many dollars a win is worth in baseball, is it possible to determine the dollar value of a specific run? I'm not talking about a run in the more abstact sense, like "Ichiro is X runs above replacement, which equates to X wins," because that would theoretically be easy to convert from $/win to $/run. I mean if you look at a play in a specific game, can you determine how much money that run was worth? Or is this difficult because of the variable amount of runs it takes to win a specific game?

Example: A pitcher intentionally beans a hitter. Let's say the run value of a HBP is around .3 runs. From that, can you determine how many dollars the pitcher cost his team by hitting the guy?

I'm curious because this would be an interesting way to address the question, "how stupid is it to 'retaliate' or 'stand up for your teammate' by hitting an opposing team's player?" I don't know much about the math behind WPA and related stats, so any details people would be willing to share would be helpful. Thanks.

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If I'm not mistaken, that would just be some form of $$ of WPA.

Because if the team is losing 20-0 in the bottom of the 9th, and some guy hits a solo homer, it’s value is ~$0.01, and the run was essentially irrelevant. Leverage is already included. That’s not “runs” though.

At the same time, if leverage is not taken into account, that would just be WPA/LI.

I do not know if WPA or WPA/LI converts into runs, but I think if it does that would be the only way to do it since leverage makes a difference. Also, there is always this value. And it is possible that can be converted to $$. But again, a hit by pitch when down by 20 is much different than a hit by pitch when down by 1, so I don’t know how that would change $$ values.

At this point I am rambling so I will let someone smarter than myself make more sense.

...and now I'm here

by Librocrat on May 18, 2009 1:30 AM PDT reply actions 0 recs

What you have to keep in mind though is the assumption that all events are roughly equal regardless of situation

because over a large enough sample size, you should see a normal distribution of leverages – the value of an HBP is the average value of that event across all leverages.

I’m not sure how leverage can be factored in, but that just reeks of going down the path to results-based analysis to me, and thus isn’t something I’d be interested in. Essentially, the dollar value of a run of 1/10 the dollar value of a win. Like WAR, it doesn’t really matter how you get there.

by seattlebruin on May 18, 2009 10:27 AM PDT up reply actions 0 recs

Yeah, I don't care much about leverage for the purposes of this idea

I was thinking more about using the average run value of a HBP. Tangotiger has that at .385 which I think in this example could be weighted a little lower since an intentional HBP almost always occurs with nobody on base.

So you’re saying that if a HBP is worth .35 runs, and a win is worth around 4.5 million, the HBP costs the team, on average, .35/10 * 4.5 million = $157,500?

If this is true, why aren’t players immediately released when they intentionally hit a batter?

by Schaefer on May 18, 2009 10:54 AM PDT up reply actions 0 recs

Mainly because analytical tools aren't really designed to account for things like intentional HBPs

also, intentional HBPs almost always occur in low-leverage situations – even though it’s an overall negative for the team, they often occur in situations where it doesn’t really matter.

Essentially what I’m getting at is that game theory plays a very important role in all of this, not just pure run value calculations.

by seattlebruin on May 18, 2009 11:01 AM PDT up reply actions 0 recs

Events cancel each other out.

Look at last year’s leaderboard for WPA on Fangraphs. See how everyone has a -WPA value? That is where they fucked up and hurt their team’s chances of winning. Roy Halladay had a -WPA of -15.13. No sane person would argue that the Blue Jays should release Halladay because he did some things over the course of a season that amounted to -15.13 wins. If you subtracted the extra .035 wins of an intentional HBP, it would still be inexcusably stupid to argue that Roy Halladay should be released.

by Vatinius on May 18, 2009 1:36 PM PDT up reply actions 0 recs