A Batter Game Score for the Regression-Minded

Since attempting (somewhat haphazardly) to identify the top performances of the Futures Game by way of game scores, I’ve been experimenting both with a pitcher and also batter version of same that might weight the relevant inputs in a manner that reflects the rate at which those various inputs become reliable.

Because it’s likely flawed — and also because the prospect of doing so is tedious — I won’t provide a particularly detailed explanation of my own methodology here. But what I’ve got seems to produce reasonable enough results, which is really my only concern.

What I did was to start with the FIP-based pitcher game score proposed by Tango Tiger in these same pages a few years ago — the formula for which starts at 40 (as opposed to 50) so as to reflect the idea of replacement level. What I did then was to weight strikeouts three time more heavily than in the normal FIP formula (because it becomes strikeout rate becomes reliable three times more quickly than home-run rate) and walks about a third more heavily. Hits of any sort are excluded from consideration, as BABIP requires far too large a sample to integrate meaningfully with the other three variables. Multiplying plate appearances by 3 centers the equation.

Below is the resulting equation:

Game Score: 3 * PA + (13 * HR + 4 * BB – 6 * K) + 40

Applying the formula to an “average” game — that is, league-average rates prorated to 4.5 plate appearances — results in a game score of 51. A player going 4-for-4 with four home runs produces a score of 104. To produce a 0, a player would need to strike out in about 13 of 13 plate appearances — which, that’s an unlikely result. Away from the margins, however, the scores are reasonable.

Here, for example, are yesterday’s 10-best players:

# Name Team PA BB SO HR Score
1 Mark Teixeira Yankees 5 3 0 1 80
2 Matt Kemp Dodgers 4 0 0 2 78
3 J.P. Arencibia Rangers 5 0 1 2 75
4 Jose Abreu White Sox 5 1 0 1 72
5 Jimmy Rollins Phillies 5 1 0 1 72
6 Josh Hamilton Angels 6 0 0 1 71
7 Yangervis Solarte Padres 4 1 0 1 69
8 Josh Harrison Pirates 4 1 0 1 69
9 Brett Gardner Yankees 5 0 0 1 68
10 Anthony Rizzo Cubs 8 1 0 0 68

And 10 worst:

# Name Team PA BB SO HR Score
1 Carlos Gomez Brewers 4 0 4 0 28
2 Logan Schafer Brewers 3 0 3 0 31
3 Mark Trumbo D-backs 4 0 3 0 34
4 Marc Krauss Astros 4 0 3 0 34
5 James Jones Mariners 4 0 3 0 34
6 Dillon Gee Mets 2 0 2 0 34
7 Tyson Ross Padres 2 0 2 0 34
8 Chris Iannetta Angels 2 0 2 0 34
9 Justin Ruggiano Cubs 7 0 4 0 37
10 Tyler Flowers White Sox 5 0 3 0 37

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Carson Cistulli occasionally publishes spirited ejaculations at The New Enthusiast.

14 Responses to “A Batter Game Score for the Regression-Minded”

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  1. AK7007 says:

    Can we have these in some sort of daily “look what happened yesterday” post.

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    • DUMBrowski says:

      I would love something like this. Not necessarily with the information included in this post, but more of a “Here’s some interesting stuff that happened in baseball last night” type of post. This could include historical feats, great/bad moves by managers, potential pitcher adjustments, or even a variety of humorous whimsy to help us through our NotGraphs withdrawal.

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      • AK7007 says:

        Well, if occasionally there is a 100 game score batting performance, I’d like to see some carson related whimsy there too.

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    • frivoflava29 says:

      As somebody who checks every individual game’s box score every single day, I agree wholeheartedly.

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  2. John Elway says:

    My latest #Instagraph, in honor of tonight’s Sharknado 2 sequel.


    Just neighing.


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  3. Stathead says:

    If you want to weight things differently then you should use a weighted linear regression, which I’m pretty sure isn’t what this is, but I haven’t looked at that in a while.

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  4. Larry Bernandez says:

    So a guy who goes 4-4 with 3 doubles and a triple receives the same score as the guy who goes 0-4 with 2 groundouts and 2 flyouts? That seems a bit flawed.

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    • Game-changer says:

      Not sure if this is true, I think the tables just don’t show other hits, but I wonder if using total bases in some way is better than HRs.

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    • ElJosharino says:

      I think maybe that’s the point, a little bit. In theory, a lot of the difference between the two could be chalked up to batted ball luck.

      That said, maybe there’s room for some sort of BABIP component somewhere, perhaps weighting the specific batted ball types within the game to formulate some sort of weird xBABIP for the game and then incorporating that into the formula somewhere. Or I dunno, I’m just spitballin’ here.

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    • Z S says:

      Yeah, I agree. Focusing on the true out comes – strikeouts, HRs and walks – makes some sense when applied to pitchers, because it focuses on the things that they directly influence. But flipping it around and using those outcomes for batters, exclusively, is odd. Larry’s is just one of many counter-examples you could provide where an outstanding performance isn’t reflected in the proposed batter game score. Sure, there’s an element of BABIP/luck/defense involved in getting hits on balls in play, but it seems weird to create a system that discounts singles/doubles/triples/stolen bases entirely.

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  5. jcxy says:

    One of the criticisms of wine ratings, in particular the 0-100 wine scale popularized by Robert Parker, is that a vast majority of wines score in a 15 point range–from 80 to 95. In effect, and despite it’s best intentions, the 100 point scale has become a 15 point scale.

    With that in mind, it seems too gracious that Carlos Gomez be awarded any number of points with a day like that. Woody Allen may be right that 90% of life is about showing up…but Carlos Gomez should have stayed home. Instead of adding 40 to each score (for showing up), perhaps that could be reduced? This way, game score could better represent the negative effect of Mr Gomez’s performance at the plate.

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  6. Josh B says:

    Off topic, but I think the front page should contain more than just the last 3 InstaGraphs posts.

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  7. Tangotiger says:

    The PA has to have a value of under 2. The reason is because if you have 0 HR, 0 BB, 0 SO, all you have left is BABIP, which would given you a wOBA of around .300, below average. Hence, 4.5 balls in play must give you a below average result (under 50).

    Taking a quick guess, and I think 1 point per PA works.

    I’ll have to think about the other terms, though I don’t know why they wouldn’t be what FIP suggests.

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