守備指標における失策の取り扱い
FP (Fielding Percentage): (刺殺+補殺)/(刺殺+補殺+失策)
RF (Range Factor): (刺殺+補殺)/9イニング
ZR(Zone Rating):処理した打球/責任打球(内野手はゴロに責任、外野手はフライとライナーに責任)
DER(Defensive Efficiency Ratio): チームが処理した打球/チームBIP
守備率を除く多くの守備指標は、公式を見るとわかるように失策(失策出塁)をただ安打と同じように扱っています。
OAA、DRS、UZRとFP、DERの相関関係(相関係数基準)
OAA | DRS | UZR | |
DER | 0.492 | 0.618 | 0.417 |
FP | 0.364 | 0.285 | 0.463 |
UZR(Ultimate Zone Rating):守備区域を数十個に細かく分け、状況別(ランナー状況、左打/右打など)で打球(ゴロ/フライ/ライナー)でタイプ区分、弱/中/強で打球強度区分)処理率を 計算する方法です。
DRS(Defensive Runs Saved):UZRに似ていますが、守備ゾーンをどれだけ細かく分けるかと、何年値のデータを使用するか、シフト処理、パークファクタなどに違いがあります。
OAA (Outs Above Average): 追跡システムで打球の速度と発射角度、守備手と落球位置の距離、ランナーの速度などを測定して守備力を評価します。
2016~2022年MLB 210チームを対象としており、OAAはRAA, DRSはrPM、UZRはRngR+ErrR基準です。 FP、DERは比率指標なので、リーグ平均に対する貢献度に換算しました。
守備率は、OAAとの相関が意味のあるレベル(中程度の相関)であることがわかります。 UZRとの相関は、むしろFPがDERより高い。 (FP 0.463> DER 0.417)
失策出塁と安打の違い
つまり失策は審判が見たときは簡単な打球で、安打は難しい打球ということです。 そうすれば、すべての打球は守備手がアウトに失敗したときに安打として記録されるべき打球(安打性の打球)と失策出塁で記録される可能性のある打球(失策性の打球)に分けられる。 そして、失策性の打球は安打性の打球よりアウトさせやすいという仮定を立ててみることができます。
安打性の打球と失策性の打球の守備難易度
DERをOAAと回帰分析を行い、安打性の打球と失策性の打球の守備難易度を推定してみることができます。
打球 | アウト率 | 非アウト率 |
全体 | 69.5% | 30.5% |
安打性 | 66.7% | 33.3% |
失策性 | 90.1% | 9.9% |
安打性の打球のアウト率は67%、失策性の打球のアウト率は90%程度でした。
UZRとDRSはどのような違いがあるのか、他の種類別に推定アウト率をOAAと比較してみましょう。
安打性 | 失策性 | |
OAA | 66.7% | 90.1% |
DRS | 68.6% | 81.7% |
UZR | 63.7% | 93.9% |
違いはありますが、どのような守備指標と推定しても、失策性の打球が安打性の打球よりはるかに握りやすいものとして現れています。
失策性の打球のアウト率による補正DERとOAA、DRS、UZRの相関関係
70% | 75% | 80% | 85% | 90% | 95% | |
OAA | 0.493 | 0.500 | 0.510 | 0.523 | 0.534 | 0.490 |
DRS | 0.619 | 0.621 | 0.623 | 0.622 | 0.604 | 0.487 |
UZR | 0.418 | 0.431 | 0.449 | 0.476 | 0.514 | 0.534 |
失策性の打球のアウト率が70%であれば、安打性の打球のアウト率とほぼ同じであり、失策性の打球のアウト率が高くなるほど安打性の打球のアウト率は低くなります。 失策性の打球のアウト率が高くなると、OAA、DRS、UZRとも相関関係が上昇しますが、上昇幅には大きな違いがあります。 そして、相関関係の高点を過ぎて下落が始まる時点もそれぞれ異なります。 DRSは、失策性の打球のアウト率が高くなっても相関関係の上昇がほとんどなく、90%を超えると、むしろ相関関係が大幅に下落しています。 それに対し、UZRは失策性の打球のアウト率が高くなるほど相関関係も非常に大きく上がり、95%の時も非常に高い相関関係を見せています。
OAAと最も相関が高い点は、失策性の打球のアウト率90%です。 これを基準にすると、DRSはわずかに低下しますが、UZRは大幅に上昇します。
OAA | DRS | UZR | |
DER (補正) | 0.534 | 0.604 | 0.514 |
DER | 0.492 | 0.618 | 0.417 |
FP | 0.364 | 0.285 | 0.463 |
安打性の打球と失策性の打球の補正例
2021年ドジャースとブレイブスのDER
チーム | 打球 | アウト | DER | DER PP |
ドジャース | 3639 | 2639 | 0.7252 | 91.5 |
ブレイブス | 3762 | 2682 | 0.7129 | 48.4 |
MLB | 115822 | 81083 | 0.7001 | 0 |
DERと評価すると、ドジャースはリーグ平均に比べて91個の打球をさらにアウトさせ、ブレイブスは48個の打球をさらにアウトさせました。
それでは今回は安打と失策を区別してみましょう。
チーム | 安打 | 失策 | 安打性の打球 | 失策性の打球 | 安打性の処理率 | 失策性の処理率 | 安打性PP | 失策性PP | PP |
ドジャース | 946 | 54 | 3057.3 | 581.7 | 0.6906 | 0.9072 | 44.8 | 2.6 | 47.4 |
ブレイブス | 1054 | 26 | 3476.2 | 285.8 | 0.6968 | 0.909 | 72.6 | 1.8 | 74.4 |
MLB | 33540 | 1199 | 103490 | 12332 | 0.6759 | 0.9028 | 0 | 0 | 0 |
安打城打球と失策星打球を区別すると、ブレイブスがドジャースより守備力に優れているようです。
他の守備指標はどうか見てみましょう。
チーム | OAA RAA | DRS rPM | UZR RngR+ErrR |
ドジャース | -10 | 7 | -8.2 |
ブレイブス | 3 | 6 | -10.3 |
DRSとUZRは両チームが似ていますが、OAAはブレイブスが高いです。
NPBの打球別守備難易度
NPBの場合はどうか見てみましょう。 NPBはまだOAAのような守備指標を持っておらず、UZRはデータスタジアムとデルタの2社によって発表されています。デルタの2014~2022年UZRで回帰分析を行いました。
打球 | アウト率 | 非アウト率 |
全体 | 70.0% | 30.0% |
安打性 | 68.5% | 31.5% |
失策性 | 86.4% | 13.6% |
失策性の打球のアウト率による補正DERとUZRの相関関係
70% | 75% | 80% | 85% | 90% | 95% | |
UZR | 0.802 | 0.807 | 0.813 | 0.818 | 0.813 | 0.745 |
デルタのUZRは、MLBのUZRよりもむしろMLBのDRSと同様の側面を示しています。 相関関係の上昇幅が小さく、失策性の打球のアウト率が90%を超えると、むしろ相関関係が大幅に下落します。
清宮と野村のデーター見たけど
WARとかの数値ぜんぜんデタラメじゃん
↑WARには決まった計算式が定められていると勘違いしてる人
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